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1. Which of the following is the same unit as the farad? A s B s –1 C –1 s D –1 s –1 (Total 1 mark) 2. An emf will only be induced across the wing tips of an aircraft if it is flying horizontally in A a north-south direction B an east-west direction C a region where there is a horizontal component of the earth’s magnetic field D a region where there is a vertical component of the earth’s magnetic field. (Total 1 mark) 3. A top quark has a mass of 171 2 c GeV . Its mass in kilograms is about A 3 × 10 –31 B 3 × 10 –28 C 3 × 10 –25 D 3 × 10 –19 (Total 1 mark) 1
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Page 1: Phys 4 Qs

1. Which of the following is the same unit as the farad?

A s

B s–1

C –1 s

D –1 s–1

(Total 1 mark)

2. An emf will only be induced across the wing tips of an aircraft if it is flying horizontally in

A a north-south direction

B an east-west direction

C a region where there is a horizontal component of the earth’s magnetic field

D a region where there is a vertical component of the earth’s magnetic field.(Total 1 mark)

3. A top quark has a mass of 171 2cGeV

. Its mass in kilograms is about

A 3 × 10–31

B 3 × 10–28

C 3 × 10–25

D 3 × 10–19

(Total 1 mark)

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Page 2: Phys 4 Qs

4. The following are four possible graphs of a quantity Y plotted against another quantity X.

A B C D

Y

X

Y

X

Y

X

Y

X

Which graph best represents Y when it is the kinetic energy of an electron and X is its momentum?

(Total 1 mark)

5. The following are four possible graphs of a quantity Y plotted against another quantity X.

A B C D

Y

X

Y

X

Y

X

Y

X

Which graph best represents Y when it is the electric field strength between two parallel plates with a constant potential difference across them and X is the distance apart of the plates?

(Total 1 mark)

6. The following are four possible graphs of a quantity Y plotted against another quantity X.

A B C D

Y

X

Y

X

Y

X

Y

X

Which graph best represents Y when it is the radius of the circle described by an electron in a constant magnetic field at right angles to the path of the electron and X is the momentum of the electron?

(Total 1 mark)

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Page 3: Phys 4 Qs

7. Each of the diagrams below is a free-body force diagram representing the forces acting on a body.

A B C D

Which diagram best illustrates the forces acting on a charged sphere, supported on a nylon thread, in equilibrium alongside a second similarly charged sphere?

(Total 1 mark)

8. A + pion is composed of which combination of quarks?

A ud

B du

C du

D du(Total 1 mark)

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Page 4: Phys 4 Qs

9. The diagram shows two charged spheres X and Y, of masses 2m and m respectively, which are just prevented from falling under gravity by the uniform electric field between the two parallel plates.

X Y

Which of the following is a property of a uniform electric field?

A The field strength is the same at all points.

B The field acts equally in all directions.

C The field produces no force on a stationary charged particle.

D The field produces a force on a moving charged particle which is always perpendicular to its direction of travel.

(Total 1 mark)

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Page 5: Phys 4 Qs

10. The diagram shows two charged spheres X and Y, of masses 2m and m respectively, which are just prevented from falling under gravity by the uniform electric field between the two parallel plates.

X Y

If the plates are moved closer together

A X and Y will both remain stationary.

B X and Y will both move upwards with the same acceleration.

C X will have a greater upward acceleration than Y.

D Y will have a greater upward acceleration than X.(Total 1 mark)

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Page 6: Phys 4 Qs

11. Figure 1 shows the London Eye, a tourist attraction in the form of a very large wheel.Passengers ride in capsules, describing a vertical circle at constant speed. Figure 2 is a free-body force diagram showing the forces acting on a passenger in one of the capsules at point X of the circle.

R

F 2

F 1

Figure 1 Figure 2

A teacher asks the class why the forces F1 and F2 are equal and opposite. A student suggests that this is because of Newton’s third law.

(a) State two reasons why the forces F1 and F2 cannot be a Newton’s third law pair.

Reason 1 .....................................................................................................................

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Reason 2 .....................................................................................................................

.....................................................................................................................................(2)

(b) Explain why the forces F1 and F2 must be equal and opposite.

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(c) State what causes the force R.

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(Total 5 marks)

12. (a) State what is meant by the term baryon.

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(b) In β– decay a neutron decays into a proton.

Explain how the quark structure of the baryon changes in this process.

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.....................................................................................................................................(2)

(Total 3 marks)

13. Quarks were discovered using the Stanford Linear Accelerator (SLAC). The diagram below shows the principle of a linear accelerator (LINAC).

E lec tro n

b eam

T 1

T 2

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Page 8: Phys 4 Qs

(a) State what is connected between terminals T1 and T2.

.....................................................................................................................................

.....................................................................................................................................(2)

(b) Explain why the electrons travel with constant velocity whilst in the cylinders.

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.....................................................................................................................................(2)

(c) Explain why the cylinders gradually increase in length along the accelerator.

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(Total 6 marks)

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Page 9: Phys 4 Qs

14. At the start of the 20th century it was thought that the atom contained an even distribution of positive charge with electrons embedded in it. Rutherford directed a series of experiments using α-particles to investigate the structure of the atom.

In 1913 Rutherford wrote that “the observations on the scattering of α-particles by matter afford strong experimental evidence for the theory that the atom consists of a positively charged nucleus of minute dimensions surrounded by a compensating distribution of negative electrons”.

Outline the experimental observations to which Rutherford is referring and explain how they led him to this deduction.

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15. (a) A 2200 µF capacitor is charged to a potential difference of 12 V and then discharged through an electric motor. The motor lifts a 50 g mass through a height of 24 cm.

(i) Show that the energy stored in the capacitor is approximately 0.16 J.

Energy = ..........................................(2)

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Page 10: Phys 4 Qs

(ii) What is the efficiency of the electric motor in this situation?

Efficiency = .....................................(2)

(b) The capacitor is charged to 12 V again and then discharged through a 16 resistor.

(i) Show that the time constant for this discharge is approximately 35 ms.

...........................................................................................................................

...........................................................................................................................(1)

(ii) Sketch a graph of current against time for this discharge on the grid below. You should indicate the current at t = 0 and t = 35 ms.

1 2 0

1 0 0

8 0

6 0

4 0

2 0

0

mA

0 2 0 4 0 6 0 8 0 1 0 0m s

(3)

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(c) Capacitors are used in audio systems when connecting the amplifier to the loudspeaker.In one such circuit the capacitor has a value of 2200 F and the loudspeaker has a resistance of 16 .

2 2 0 0 F

1 6

(i) The loudspeaker produces longitudinal waves. What is meant by longitudinal in this context?

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Ideally, the time constant for such a circuit should be much greater than the time period of the lowest frequency note. Discuss the extent to which this circuit would be effective if the lowest frequency note is 20 Hz.

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...........................................................................................................................(2)

(Total 12 marks)

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Page 12: Phys 4 Qs

16. (a) In their famous experiment conducted in 1932, Cockcroft and Walton accelerated protons through a potential difference of 300 kV and used them to bombard a lithium ( Li7

3 ) target. They found that two alpha particles were produced. The energy of the alpha particles was subsequently calculated from the tracks they made in a cloud chamber.

Complete the nuclear equation for this event.

Li73 +

(2)

(b) Cockcroft and Walton reported to the Royal Society that “if momentum is conserved in the process, then each of the -particles must take up equal amounts of energy, and from the observed range of the -particles we conclude that an energy of 17.2 million electron-volts [MeV] would be liberated in this disintegration process”.

(i) State two other properties, in addition to momentum, that are conserved in such a process.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Use the data below to show that the energy released in this process is approximately 2.8 × 10–12 J.

Mass of lithium nucleus = 7.0143 uMass of proton = 1.0073 uMass of -particle = 4.0015 u

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(iii) Hence discuss the extent to which Cockcroft and Walton’s results confirm Einstein’s prediction that E is equal to mc2.

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(Total 13 marks)

17. (a) State the principle of conservation of linear momentum.

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.....................................................................................................................................(2)

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Page 14: Phys 4 Qs

(b) The diagram shows two gliders on an air track. The magnets on the top of the gliders repel each other. The mass of glider A is 300 g and that of glider B is 100 g.

A

B

S

SN

N

Glider A is given a push to start it moving towards glider B which is initially at rest.

Describe how you could determine the velocity of A before the gliders interact and the velocities of both A and B after the interaction. You may add to the diagram to show any additional apparatus required.

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(c) A student obtains the following velocities:

velocity of A before interaction = 5.2 cm s–1

velocity of A after interaction = 2.7 cm s–1

velocity of B after interaction = 7.5 cm s–1

Show if these results confirm that momentum is conserved in the interaction.

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.....................................................................................................................................(2)

(Total 10 marks)

18. A do-it-yourself company is advertising a wind turbine that they state can deliver a power of 1 kW.

Their specification provides the following data:

• area swept out by the blades in one revolution = 2.4 m2

• power output = 1 kW at a wind speed of 12.5 m s–1

• typical operating speed of blades = 600 revolutions per minute

(a) (i) Show that the length of each blade is approximately 0.9 m.

...........................................................................................................................

...........................................................................................................................(1)

(ii) Show that the angular velocity of the blades at the typical operating speed is approximately 63 rad s–1.

...........................................................................................................................

...........................................................................................................................(1)

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Page 16: Phys 4 Qs

(iii) Calculate the speed at which the tips of the blades will then be travelling.

Speed = ............................................(1)

(b) The theoretical power available from a wind turbine is given by

p = ½ ρAv3

where ρ = density of air = 1.3 kg m–3

A = area swept out by blades per revolutionv = wind speed

(i) Show that when the wind speed is 12.5 m s–1, the theoretical power from the advertised turbine is about 3 kW.

Power = ...........................................(2)

(ii) Suggest two reasons why the actual power is less than the theoretical power.

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...........................................................................................................................(2)

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Page 17: Phys 4 Qs

(c) The manufacturer has to ensure that when the turbine is attached to a chimney stack, the force exerted on the chimney does not cause it to collapse. The turbine is designed to cut out at a wind speed of 14 m s–1.

(i) Calculate the mass of air hitting the blades each second when the wind speed is 14 m s–1.

Mass of air = ...................................(2)

(ii) Hence calculate the maximum force that the wind could exert on the blades.

Maximum force ............................(2)

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Page 18: Phys 4 Qs

(d) The average wind speed in the UK is 5.8 m s–1, which results in an actual average power output of 100W. Discuss whether it would be better for the environment to replace some filament light bulbs with low energy bulbs than to use this turbine.Assume each filament light bulb is rated at 100W and each low energy bulb is rated at 11 W.

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(Total 16 marks)

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Page 19: Phys 4 Qs

19. (a) The lines A and B show part of the paths of two alpha particles as they travel through an atom.

A to m

N u c le u s

A

B

Add to the diagram the subsequent paths of each alpha particle as they travel through and out of the atom.

(2)

(b) Rutherford investigated the scattering of alpha particles by gold foil in an evacuated container. The evidence from his investigations led to the nuclear model of the atom.

Why was it important for this investigation that

(i) the alpha source was inside the container,

...........................................................................................................................

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...........................................................................................................................(1)

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Page 20: Phys 4 Qs

(ii) the alpha particles had the same initial kinetic energy,

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...........................................................................................................................(1)

(iii) the container was evacuated?

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...........................................................................................................................(1)

(Total 5 marks)

20. Classify each of the following particles by ticking all the appropriate boxes in the table.

Particle Lepton Baryon Hadron Meson

Neutron, n

Neutrino, υ

Muon, μ(Total 3 marks)

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Page 21: Phys 4 Qs

21. (i) Two particle reactions are shown. Use appropriate conservation laws to show whether these reactions are possible.

Δ0 + K0 → K+ + Σ+ Ω– → Ξ– + 0K

(udd) )sd( )su( (uus) (sss) (ssd) )ds(

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(ii) Using only the information given above deduce the charges on each of the strange, up and down quarks. Justify your answers.

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(Total 5 marks)

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Page 22: Phys 4 Qs

22. (a) A satellite is moving at a constant speed v in a circular orbit around the Earth. The only force acting on the satellite is its weight W.

S a te llitev

W

E arth

(i) Although an unbalanced force is acting on the satellite, its speed does not change.

Explain why.

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(ii) According to Newton’s second law, the unbalanced force causes an acceleration.

Explain how the satellite can accelerate while its speed remains constant.

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Page 23: Phys 4 Qs

(b) A satellite used in the global positioning system travels in an orbit of radius2.7 × 104 km. At this distance from the Earth, the acceleration of the satellite i0.56 m s–2.

Calculate its speed.

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Speed = .............................................(2)

(Total 6 marks)

23. A capacitor C1 is connected to a supply. When a potential difference of 4.0 V is applied across the capacitor, it stores a charge of 0.80 nC.

C 4 . 0 V1

(a) (i) Calculate the electrical work done by the supply as it transfers this charge.

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Work done = ....................................(2)

(ii) Mark on the diagram above the magnitudes and polarities of the charges stored on the plates of the capacitor.

(1)

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Page 24: Phys 4 Qs

(b) A graph of charge stored against potential difference across the capacitor is shown.

C h arg e s to red o n C /n C

0 .8

0 .6

0 .4

0 .2

0 . 00 1 .0 2 .0 3 .0 4 .0 P o ten tia l d iffe ren ce / V

1

Explain how this graph supports the fact that the charged capacitor is storing 1.6 nJ of energy.

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.....................................................................................................................................(2)

(c) With capacitor C1 charged to 4.0 V, the supply is removed and a second, uncharged capacitor C2 is connected in its place as shown.

C C1 2

Capacitor C1 transfers some of its charge to the plates of capacitor C2. As a result the potential difference across C1 falls to 3.0 V.

(i) By referring to the graph for capacitor C1, deduce how much charge transfers to capacitor C2.

...........................................................................................................................

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Charge transferred to C2 = .................................(1)

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Page 25: Phys 4 Qs

(ii) On the grid below, show how the charge stored on capacitor C2 varies with potential difference during this charge transfer process.

C h arg e s to red o n C /n C

0 .8

0 .6

0 .4

0 .2

0 . 00 1 .0 2 .0 3 .0 4 .0 P o ten tia l d iffe ren ce / V

2

(2)

(iii) Use the values you have plotted to find the capacitance of capacitor C2.

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Capacitance of C2 = ..............................(2)

(Total 10 marks)

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Page 26: Phys 4 Qs

24. A simplified diagram of a cathode ray oscilloscope is shown.

E lec tro n g u n sy s tem

C ath o d e A n o d e

E le c tro n b e am

Va cu u m

L ig h t

P h o sp h o r c o a tin g

S c re en

(a) Electrons liberated from the cathode are accelerated to the anode through a large potential difference, giving each electron in the beam an energy of 1.2 keV.

(i) Calculate the velocity of electrons in the beam.

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Velocity = .......................................(3)

(ii) The phosphor coating produces green light, each photon of which has an energy of 2.4 eV. The efficiency of the conversion of electron kinetic energy to light in the phosphor is 8.0%. Calculate the number of photons that will be liberated from the phosphor coating by the arrival of one electron in the beam.

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Number of photons = ....................(2)

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Page 27: Phys 4 Qs

(b) In a badly-designed cathode ray tube, electrons arriving at the screen are not conducted away but build up in the area where the beam hits it. Explain how this will have an adverse effect on the amount of light emitted by the phosphor. You may be awarded a mark for the clarity of your answer.

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(Total 9 marks)

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Page 28: Phys 4 Qs

25. A small ‘search coil’, connected to a data-logger, is used to investigate a steady magnetic field. The coil is placed so that the field is perpendicular to the plane of the coil. The coil is then turned through 90° in 40 ms, finishing with its plane parallel to the field. This induces an e.m.f. across the ends of the coil.

The data-logger indicates that the mean value of the e.m.f. during the process is 0.12 V.

It also displays the following trace.

00 1 0 2 0 3 0 4 0

Tim e / m s

E .m .f. / V

(a) Add an appropriate scale to the vertical axis on the graph above.(1)

(b) The search coil has 5000 turns.

(i) The mean e.m.f. induced during the rotation is 0.12 V. Show that the magnetic flux through the coil before rotation was approximately 1 µWb.

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(ii) The coil has a diameter of 1.0 cm. Calculate the magnetic flux density of the magnetic field in which the coil is rotated.

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Magnetic flux density = .....................................(2)

(Total 5 marks)

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Page 30: Phys 4 Qs

26. (a) The dashed line on the graph below shows how the kinetic energy of a proton would vary with the square of its speed if the relationship

k.e. = ½mυ2

were to hold for all values of υ, no matter how high.

9

8

7

6

5

4

3

2

1

00 1 0 2 0 3 0 4 0 5 0

k .e . / 1 0 J– 11

v / 1 0 m s – 221 62

Use data from the graph to show that the rest mass of the proton is about 1.7 × 10−27 kg.

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(b) The curved line on the graph shows how the kinetic energy of a high-energy proton actually varies with the square of its speed. This is greater than that predicted by the ½mυ2 expression because of relativistic effects.

(i) Complete the table below to show the extra energy ΔE, caused by relativistic effects, for protons accelerated to the three speeds υ shown in the left column.

υ/108 m s−1 υ2/1016 m2 s−2 ΔE/10−11 J

2.00 4.0

2.24 5.0

2.45 6.0

(ii) For any one of your values for ΔE, calculate the equivalent mass increase Δm of a proton moving at that speed and express this mass increase as a percentage of the rest mass of a proton.

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(Total 8 marks)

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Page 32: Phys 4 Qs

27. In 2002 the Jefferson Laboratory released the results of an experiment involving collisions of high speed electrons with protons. The results suggested that protons are not spherical, but have a bulging shape. In a subsequent paper some of these results were explained by modelling a nucleon as ‘a relativistic system of three bound quarks surrounded by a cloud of pions.’

Protons and neutrons are the two types of nucleon and both consist of up and down quarks.

Nucleon Quark composition

proton uud

neutron udd

Quark Charge

up quark +2/3 e

down quark –1/3 e

(a) Use the information in the tables to show how the charge of the proton and the charge of the neutron are arrived at.

proton ..........................................................................................................................

neutron ........................................................................................................................(2)

(b) Protons, neutrons and pions are all hadrons. There are two types of hadron, with different quark combinations.

(i) Complete the table below to name the two types of hadron.

Particles Hadron type

proton, neutron

pion

(ii) State the differences in quark composition between these two types of hadron.

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(c) Explain why high speed particles are used to examine the internal structure of other particles.

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(d) The model mentions a ‘relativistic system’. State the condition needed for relativistic effects to be significant.

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(Total 11 marks)

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28. A student is researching information about CERN, the particle research centre near Geneva.He finds the following statement on a web site:

“The circular tunnel is eight kilometres in diameter … fully accelerated particles circle the tube twenty thousand times in one second …”

Calculate the speed of the particles, and comment on the likely accuracy of the statement.

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29. The photograph shows a flexible copper wire attached to the terminals of a dry cell.A strong circular magnet, 12 mm in diameter, is attached to the side of the cell. The interaction between the current in the wire and the magnetic field of the magnet causes the wire to levitate.

The diagram shows the arrangement viewed from above.

S N

+

N O T TO S C A L E

(a) Draw on the diagram the magnetic field produced by the magnet.(2)

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(b) The following measurements were made:

upward force on wire = 8.0 × 10–3 N

current in wire = 5.8 A

length of wire in magnetic field = 12mm

(i) Show that the magnetic flux density is about 0.1 T.

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(ii) State one assumption you made in your calculation.

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(c) The manufacturer’s data sheet supplied with the magnets gives a value of 0.3 T for the magnetic flux density. Suggest a reason why this is different from the value given in (b)(i).

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(d) Explain what would happen to the wire in the following arrangement.

N S

+N O T TO S C A L E

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(Total 8 marks)

30. Devices which contain electrically charged grids are sometimes used to control the numbers of flying insects. The grids are connected to capacitors that store charge at a high voltage.

(a) Explain why a capacitor cannot be charged directly from the mains supply.

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(b) A user reports on his device in a magazine: “The grids in my device didn’t work very well, so I opened it up to have a look. I found that it only produced a voltage of 600 V, which was too low. I replaced it with a circuit that charged a 100 nF capacitor to 1800 V. This worked better.”

The graph shows how the voltage across the 100 nF capacitor varies with time as it discharges through an insect.

1 8 0 0

1 6 0 0

1 4 0 0

1 2 0 0

1 0 0 0

8 0 0

6 0 0

4 0 0

2 0 0

00 0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .25 0 .3 0

Tim e / s

Volta

ge /

V

(i) Use the graph to estimate the time constant for the circuit containing the capacitor and the insect.

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Time constant = ........................................................(2)

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(ii) Calculate a value for the resistance of the insect.

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...........................................................................................................................

Resistance = .............................................................(2)

(c) The user continues: “The manufacturers have recently introduced a new device incorporating a capacitor of 100 µF charged to 300 V.”

(i) Calculate the charge stored on this capacitor when fully charged.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Charge = ...................................................................(2)

(ii) Calculate the energy stored in this capacitor when fully charged.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Energy stored = ........................................................(2)

(Total 10 marks)

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31.

Two students are watching an action film in which a car drives down a ramp onto the back of a moving lorry. Both are moving at high speed, the car slightly faster than the lorry.

One student complains that this is impossible because the car would not be able to stop before hitting the cab of the lorry.

The car has mass 1250 kg and is moving at a speed of 28.0 m s–1. The lorry has mass 3500 kg and a speed of 25.5 m s–1. The length of the flat back of the lorry allows a braking distance of 5.0 m.

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By considering both momentum and energy show that the stunt is possible, provided a minimum force of about 600 N slows the car down. You should support your explanations with calculations.

Treat the situation as one in which two objects join together.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................(Total 8 marks)

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32. PET (positron emission tomography) scanning is often used to see how cancers are responding to therapy. It requires a radioactive isotope which emits positrons. A positron soon meets an electron and annihilates. The resulting photons can be detected and an image produced. An isotope of fluorine F18

9 can be used as it can be added to a glucose molecule. The patient is given a glucose drink containing this fluorine isotope which will then be absorbed by the cancer.

(a) The fluorine isotope is produced by bombarding an isotope of oxygen O188 with a high

energy proton. Write a nuclear equation for this process.

............................................................ ..............................................................(3)

(b) The protons are typically given an energy of 19 MeV. Briefly suggest how this might be achieved.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(c) Fluorine 18F emits positrons and has a half-life of 110 minutes. Explain the meaning of half-life and suggest why 110 minutes is suitable for this application.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

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(d) Two identical photons are produced when an electron meets a positron. Calculate the wavelength of each photon.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(4)

(e) Detectors placed on opposite sides of the patient detect these photons and can then accurately predict the precise location of the positron annihilation within the patient.

Explain why the two photons must be emitted in opposite directions.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(Total 14 marks)

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33. (a) The ratio nucleus of radius

atom of radius for a given atom is about 105.

Use this value to calculate the ratio nucleus ofdensity atom ofdensity

.

State the assumption you have made.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Assumption .................................................................................................................

.....................................................................................................................................(4)

(b) What observation is made in the alpha particle scattering experiment that supports your assumption?

.....................................................................................................................................

.....................................................................................................................................(1)

(Total 5 marks)

34. (a) The Earth rotates about its axis. Show that its angular speed is approximately7 × 10−5 rad s−1.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

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(b) A stone is resting on the ground at a point on the equator.

S to n e

E q u a to r

N o rthP o le

Figure 1

(i) The radius of the Earth is 6400 km. Calculate the acceleration of the stone as it follows its circular path.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Acceleration = ................................................(2)

(ii) Draw an arrow on Figure 1 to show the direction of the stone’s acceleration.(1)

(iii) In the space below, draw a labelled free-body force diagram for the stone when it is at the point shown in Figure 1.

(2)

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(iv) With reference to your free-body force diagram, explain how the stone’s acceleration is produced.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(Total 9 marks)

35. The diagram shows a capacitor and a resistor connected to a 6.0 V battery. Both the ammeter and the battery have negligible internal resistance.

5 6 0 Fμ

A

6 .0 V

2 0 0 k

The switch is closed. Some time later the ammeter reads 20 µA.

(a) Show that the potential difference across the capacitor at this instant is 2.0 V.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

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(b) Calculate the charge stored in the capacitor when the potential difference across it is 2.0 V.

.....................................................................................................................................

.....................................................................................................................................

Charge = ..................................(2)

(c) Calculate the electrical energy now stored in the capacitor.

.....................................................................................................................................

.....................................................................................................................................

Electrical energy stored = ........................................(1)

(d) Calculate the electrical energy transferred in the battery up to this instant.

.....................................................................................................................................

.....................................................................................................................................

Electrical energy transferred = .................................................(1)

(e) What is the main reason for the difference between the energy values you have calculated in (c) and (d)?

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(1)

(Total 7 marks)

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36. (a) A proton has a mass of 1.67 × 10–27 kg. Calculate the magnitude of the potential difference needed to accelerate it from rest to a speed of 2.77 × 105 ms–1 in a vacuum.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Potential difference = ...............................................(3)

(b) The proton now passes the point A between two parallel conducting plates across which a steady potential difference is maintained. The path of the proton is shown in the diagram.

B

A

D irec tio n o f p ro to n

Add to the diagram the path the same proton would have taken had it entered at the point B.

(1)

(c) (i) An alpha particle enters at point A with the same velocity as the proton. Add its path to the diagram.

(2)

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(ii) Explain your answer to (c)(i).

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(Total 8 marks)

37. A square rigid metal frame PQRS, of side 12 cm, forms a closed circuit with an ammeter.

The area enclosed by the dotted line is a region of uniform magnetic field of flux density2.0 × 10–2 T. The field is confined to this area and directed into the page.

A QP

RS

P O S IT IO N 1

M o v em en t

A QP

RS

P O S IT IO N 2

M o v em en t

A QP

RS

P O S IT IO N 3

M o v em en t

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(a) The frame is moved at a constant speed of 5.0 cm s–1 through the uniform magnetic field region as shown in the diagram.

(i) For each position of the frame shown in the diagram either give the direction of the current through the ammeter, or if there is no current, state ‘no current’.

Position 1 = .......................................................................................................

Position 2 = .......................................................................................................

Position 3 = .......................................................................................................(2)

(ii) The total electrical resistance of the frame and ammeter is 2.0 Ω. Calculate the maximum current recorded by the ammeter.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Maximum current = .................................................(4)

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(b) The frame is now moved with uniform acceleration through the magnetic field.Explain how the magnitude of the current changes as the frame moves from position 1, through position 2 to position 3. You may be awarded a mark for the clarity of your answer.

......................................................................................................................................

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......................................................................................................................................(4)

(Total 10 marks)

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38. The photograph shows an arrangement known as Newton’s cradle. Five steel balls are freely suspended from a frame. One or more balls on one side may be pulled back and then released so that they collide with the remaining balls.

The diagram shows what happens when two balls are released.

B e fo re A fte r

A student makes these measurements:

mass of each ball = 0.024 kgspeed of the two incoming balls at impact = 0.88 m s–1

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(a) Calculate the total momentum of the two moving balls before the collision.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Total momentum = ...................................................(2)

(b) Show that the kinetic energy of the two moving balls before the collision is about 0.019 J.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(c) The student notices that the number of balls moving away after the collision is always the same as the number of balls released. To understand why two balls move away after this particular collision, the student uses a spreadsheet to model the situation.He applies the principle of conservation of momentum to find the theoretical speeds at which different numbers of balls would move away together. He also finds the kinetic energy that these balls would have.

A B C D1 number mass speed after KE after2 of balls moving of balls moving collision collision

3 away after collision after collision (m s–1) (J)4 (kg)56 1 0.024 1.76 0.03727 2 0.048 0.88 0.01868 3 0.072 0.59 0.01249 4 0.096 0.44 0.0093

10 5 0.12 0.35 0.0074

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(i) State the condition required for the total momentum of all the balls to be conserved.

...........................................................................................................................

...........................................................................................................................(1)

(ii) Show that the value in cell C8 has been correctly calculated.

...........................................................................................................................

...........................................................................................................................(1)

(iii) What would be a suitable formula for the calculation of cell D9?

...........................................................................................................................

...........................................................................................................................(1)

(iv) Explain how the spreadsheet calculations show that two balls moving away is the only likely outcome of the collision.

...........................................................................................................................

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...........................................................................................................................(3)

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(d) The two balls that moved away then swing back and collide, and the pattern is repeated. After a number of collisions, depending on the quality of the cradle, the pattern breaks down. Eventually more than two balls will be in motion, and they will not all have the same speed.

Suggest why this occurs, making reference to the spreadsheet.

......................................................................................................................................

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......................................................................................................................................(2)

(Total 12 marks)

39. Research suggests that big capacitors may soon be able to act alongside batteries as a way of storing significant amounts of energy. Researchers used a capacitor of capacitance 2500 F.

One part of the research concerns the leakage of charge through the insulating material between the two capacitor plates.

In one experiment, researchers charged the 2500 F capacitor to a potential difference (p.d.) of 8.00 V.

(a) Calculate how much energy this capacitor stores when charged to a p.d. of 2.0 V.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Energy = ...................................................................(2)

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They then measured the p.d. across the plates every ten days.

The first two columns in the table are the results they obtained.

Time / days p.d. across plates/ V ln(p.d. / V)

0 8.00 2.08

10 6.32 1.84

20 5.04

30 4.00

40 3.20

They suspect that the p.d. is falling exponentially with time. To check this idea, they first find the natural logarithms of all the p.d. values, and enter them in the third column of the table.

(b) Complete the table by filling in the three remaining natural logarithm values.(2)

(c) Plot an appropriate graph on the grid below to show that the p.d. is falling exponentially.(4)

(d) Use your graph to find a value for the resistance of the insulating material between the plates of the capacitor.

.....................................................................................................................................

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Resistance = .............................................................(4)

(Total 12 marks)

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40. In 2007 the Large Hadron Collider (LHC) was opened at CERN. The circular accelerator is 27 km in circumference and has five thousand superconducting magnets. The LHC can give a proton an energy of up to 7 TeV.

1 TeV = 1 × 1012eV

(a) One of the experiments on the LHC will attempt to create the Higgs particle, which has not been created by any of the existing, lower energy accelerators. The theoretical upper limit for the rest mass of the Higgs particle is 251 GeV/c2.

Explain why the LHC should be able to create the Higgs particle.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(b) Provided the energy of an accelerated particle is much greater than its rest-mass energy, its momentum may be calculated using

momentum = cenergy particle

(i) Show that a 7 TeV proton has energy much greater than its rest-mass energy.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Show that the momentum of a 7 TeV proton is about 4 × 10–15 kg m s–1.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

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(iii) Calculate the magnetic flux density provided by the superconducting magnets.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Magnetic flux density = ...........................................(4)

(iv) A student says “The magnetic field needs to be in the vertical direction to cause the protons to travel in a horizontal circle”. Comment on this statement.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(Total 12 marks)

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41. On one type of theme park ride, a boat swings freely along a circular path from successively higher starting positions. As the boat moves through the lowest point on its swing, the riders are travelling at high speeds, and feel quite big forces on them.

With some rides, such as Rush at Thorpe Park, the highest starting point is with the supporting arm horizontal as shown.

1 8 m

B o a t

R u sh b o a t a t s ta rtin g p o in t

The length of the supporting arm of Rush is 18 m. The mass of a typical rider is 70 kg.

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(a) Calculate the maximum “g-force” felt by a typical rider on Rush.

“g-force” = rider ofweight seat from force

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(b) Two students in the queue are having a discussion.

A says: “If they made a new ride twice as big the g-force at the bottom would be amazing!”

B says: “I think the g-force wouldn’t be any different.”

With reference to your calculation, explain which student is correct.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(1)

(Total 6 marks)

42. The diagram shows a car travelling at constant velocity.

M o tio n

P

(a) P is a point on the rim of one of the rear wheels. Tick the two boxes in the table below which describe the motion of P at the instant shown.

To the left Upwards Downwards Zero

Velocity of P

Acceleration of P(2)

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(b) When the tyres are correctly inflated, the effective radius of each wheel is 28 cm.Calculate the period of rotation of the wheels when the car is travelling at 21 m s–1.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Period = .............................................................(2)

(c) (i) Low tyre pressures would reduce the effective radius of the wheels. Explain how this would change the angular speed of the wheels at a given road speed.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(1)

(ii) The reading on the car’s speedometer is determined by the frequency of rotation of the wheels, so it is accurate only if the tyres are correctly inflated. Explain whether the speedometer would read too high or too low if the tyre pressures were too low.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(1)

(Total 6 marks)

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43. Communication satellites are often placed in geostationary orbit. The speed v of a geostationary satellite is given by the expression

v = ωr

where r is the radius of the orbit.

(a) A student calculates that ω has the numerical value of 7.27 × 10–5. Show how he arrives at this figure.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

State the unit of ω.

.....................................................................................................................................

.....................................................................................................................................(3)

(b) Hence, or otherwise, calculate the height of such satellites above the Earth’s surface, given that the Earth has a mass of 5.98 × 1024 kg and a radius of 6.38 × 106 m.

.....................................................................................................................................

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.....................................................................................................................................

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.....................................................................................................................................

Height above Earth’s surface = ................................................(4)

(Total 7 marks)

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44. The diagram shows the path of an alpha particle, He42 , as it closely approaches and then moves

away from a gold nucleus, Au19779 .

p a th o f a lp h a p a rtic le

g o ld n u c leu s

A

B

(i) Add to the diagram the direction of the electric force acting on the alpha particle at each of the points A and B.

(1)

(ii) At point A the distance of the alpha particle from the nucleus is 1.5 × 10–13 m.Calculate the magnitude of the force acting on the alpha particle at this point.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Magnitude of force = ................................................................(3)

(iii) How does the speed of the alpha particle vary as it moves from A to B?

.....................................................................................................................................

.....................................................................................................................................(1)

(Total 5 marks)

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45. A student is experimenting with a bicycle wheel. He turns the bicycle upside down and spins the wheel in a vertical plane at a constant rate. The diagram shows the wheel. At the place where the experiment is performed, the Earth’s magnetic field is in a horizontal direction. It acts into and perpendicular to the paper.

D ire c tio n o f m o tio n

H u b

R im

S p o k e

D irec tio n o f m o tio n

6 0 cm

(a) A constant e.m.f. is induced across the length of each spoke.

(i) Label the hub and rim either plus or minus to show the polarity of the e.m.f.(1)

(ii) Explain why a constant e.m.f. is induced.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

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(iii) The magnitude of the e.m.f. is 25 μV. Calculate the time it takes for the wheel to complete one revolution. Assume the area of the hub is negligible.

Assume that the Earth’s magnetic flux density has a value of 2.8 × 10–5 T.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Time = .....................................(3)

(b) State and explain what effect, if any, there would be on the magnitude of this e.m.f. in each of the following cases.

(i) The student turns the bicycle so that the wheel is still spinning in a vertical plane, but the plane is now at 45° to the Earth’s field.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(ii) The student causes the wheel to accelerate.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

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(iii) The student turns the bicycle so that the wheel spins in a horizontal plane.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(Total 9 marks)

46. Below are some extracts from the novel “Angels and Demons” by Dan Brown. A discussion about antimatter is taking place between two characters.

(a) Extract 1

A: “So antimatter is real?”

B: “A fact of nature. Everything has its opposite. Protons have electrons. Up quarks have down quarks. There is a cosmic symmetry at the subatomic level.”

In the context of antimatter, comment on the scientific accuracy of the two statements in bold type.

Protons have electrons. .............................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Up quarks have down quarks. .................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(5)

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(b) Extract 2

A: “There would be no way to separate the particles from their antiparticles.”

B: “He applied a magnetic field. Matter arced right, and antimatter arced left.”

Comment on the physics of this method for separating particles from their antiparticles.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(c) Extract 3

A: “You collected visible amounts of antimatter?”

B: “Five thousand nanograms ... a plasma containing millions of positrons.”

Calculate how many positrons there would be in a sample of five thousand nanograms.

.....................................................................................................................................

.....................................................................................................................................

Number of positrons = ...........................................(1)

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(d) Extract 4

B: “Antimatter releases pure energy. A one hundred per cent conversion of mass to photons. So don’t look directly at the sample. Shield your eyes.”

(i) A positron annihilates with an electron to produce two identical photons.Calculate the wavelength of each photon.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Wavelength = .........................................................(3)

(ii) Comment on the two sentences in bold type in relation to the wavelength you have calculated.

...........................................................................................................................

...........................................................................................................................(1)

(Total 12 marks)

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47. One of the hazards of long flights in space for humans will be exposure to radiation, particularly high energy protons from the Sun travelling as part of the ‘solar wind’.Magnetic shielding could reduce the radiation reaching the crew. A strong magnetic field would be established around the outside of the spaceship. This field would then deflect the protons. The path of a proton which just misses the spaceship is shown.

U n ifo rmm ag n e tic f ie ld in to p a g e

p ro to n

sp ac esh ip

ex ten t o ffie ld d

P

(a) (i) Draw an arrow on the diagram to show the direction of the force on the proton at point P.

(1)

(ii) Calculate the force on a proton entering the field as shown in the diagram with a speed of 800 km s–1. Magnetic flux density = 0.50 T.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Force = ......................................................(2)

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(iii) Calculate the minimum value of d, the extent of this field, needed to prevent protons of this speed from striking the spaceship.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

d = ......................................................(2)

(iv) Calculate the time this proton spends in the field.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Time = .......................................................(2)

(v) Calculate the average resultant force exerted on the proton during this process of reversing its direction of travel.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Force = ......................................................(3)

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(b) An alternative proposal is to maintain a positive charge on a spaceship to repel protons. To repel protons travelling at 800 km s–1 would require a spherical ship of 5 m radius to carry a charge of 1.9 µC.

Calculate the force exerted by this positive charge on a proton close to the surface of this spaceship. Assume that this charge acts as though it is concentrated at the centre of the ship.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Force = ......................................................(2)

(Total 12 marks)

48. The diagram shows the bottom part of a hand-held metal detector.

H a nd le

O u te r rin g

In n e r r in g

The outer ring contains the transmitter coil. Alternating current is passed through this coil.This creates a magnetic field which penetrates into the ground.

If the magnetic field encounters a metal object, a current is induced in the object. This current generates a magnetic field of its own. The direction of the object’s magnetic field is opposite to the direction of the transmitter coil’s magnetic field.

The inner ring is able to detect varying magnetic fields coming from objects in the ground.

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(i) Explain why a current is induced in the object.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(ii) Explain why the direction of the object’s magnetic field is opposite to the direction of the transmitter coil’s magnetic field.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(1)

(Total 4 marks)

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49. The photograph shows an ‘everlasting torch’ – so called because it operates without batteries.

When the torch is shaken, the strong permanent magnet moves through the coil of copper wire, generating an electric current.

Energy is stored by a capacitor. This then acts as the energy source for an LED.

(a) The following graph shows how the voltage of the capacitor varies with the charge on the capacitor.

V /V

1

2

3

4

5

0Q /C

1 2 3 4

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(i) Calculate a value for the capacitance of the capacitor.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Capacitance = .......................................................................(2)

(ii) Use the graph to derive the expression W = QV21

for the energy stored by a

capacitor.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(iii) Calculate the energy stored by the capacitor when the voltage across it is 4.0 V.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Energy = ........................................................................(2)

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(b) The graph shows how the charge on the capacitor varies with time when the torch is in use.

C h arg e /C

Tim e /s

3 .0

2 .0

1 .0

0 1 0 0 2 0 0 3 0 0 4 0 0

(i) Explain why the output power from the LED decreases with time.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Use the graph to determine the time constant for the capacitor-LED circuit.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Time constant = .......................................................................(1)

(Total 10 marks)

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50. Explain the role of magnetic fields in particle accelerators and detectors.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(Total 5 marks)

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51. A small fluffy toy hangs on a string in the rear window of a car. As the car travels round a bend at 30 m s–1 the string hangs sideways at an angle of 20° to the vertical.

(i) Mark on the diagram the forces acting on the toy.

To y

2 0 °

(ii) Calculate the radius of the curve in the road.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Radius = .......................................................................(Total 5 marks)

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52. Meteosat is a weather satellite which is in a geostationary orbit around the Earth, i.e. it stays above the same point on the Earth’s surface all the time.

(a) Write down an expression for the gravitational force on this satellite, mass m, in an orbit of radius r around the Earth, mass M.

.....................................................................................................................................

.....................................................................................................................................(1)

(b) Hence derive an expression for the gravitational field strength at a distance r from the centre of the Earth.

.....................................................................................................................................

.....................................................................................................................................(1)

(c) Use this, together with an expression for the centripetal acceleration, to show that the radius r of the geostationary orbit is given by

r3 = 2

2

π4GMT

where T is the time for one orbit of the satellite.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

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(d) Calculate this radius.

Mass M of the Earth = 6.0 × 1024 kg.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Radius = ......................................................(2)

(e) The mass and speed of the satellite do not appear in the above equation. Explain whether a satellite could remain in geostationary orbit with

(i) a greater mass.

...........................................................................................................................

...........................................................................................................................

(ii) a greater speed.

...........................................................................................................................

...........................................................................................................................(2)

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(f) Explain why a satellite has to be over the equator to remain in a geostationary orbit.You may use the diagram to help your explanation.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(Total 11 marks)

53. During a game of football the ball, mass 0.42 kg, is kicked towards the goal. It hits one of the posts and rebounds directly back into play. The diagram shows the ball as it is just colliding with the post. At impact its speed is 27 m s–1.

F o o tb a llP o st

D ire c tio n o f m o tio n

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(a) Calculate the ball’s momentum at impact.

.....................................................................................................................................

.....................................................................................................................................

Momentum = ...........................................(2)

(b) The ball’s speed at the moment it loses contact with the post is 20 m s–1 in the opposite direction. Calculate its momentum at this instant.

.....................................................................................................................................

.....................................................................................................................................

Momentum = ...........................................(2)

(c) (i) The ball remains in contact with the post for 0.22 s. Determine the average force exerted on the ball due to the collision.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Average force = ......................................(3)

(ii) Show the direction of this force on the diagram.(1)

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(d) State one difference and one similarity between this force and the force that acts on the post due to the impact of the ball.

Difference: ..................................................................................................................

.....................................................................................................................................

Similarity: ...................................................................................................................

.....................................................................................................................................(2)

(Total 10 marks)

54. An elastic collision is one in which kinetic energy is conserved.

A proton, mass 1.67 × 10–27 kg, travelling with a speed of 2.40 × 106 m s–1, has a head-on elastic collision with a stationary helium nucleus. After the collision the helium nucleus, mass 6.65 × 10–27 kg, moves off with a speed of 9.65 × 105 m s–1.

(a) Show that the kinetic energy of the helium nucleus is approximately 3 × 10–15 J.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(b) (i) How much kinetic energy is lost by the proton?

...........................................................................................................................(1)

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(ii) Hence determine the speed of the proton after the collision.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Speed of proton = ...............................................(3)

(c) Name a quantity, other than kinetic energy, that is conserved in this collision.

.....................................................................................................................................(1)

(Total 7 marks)

55. The scattering of alpha particles by thin films of metal, such as gold, reveals details about the structure of an atom.

(a) For each of the two observations below give one clear deduction that can be made concerning atomic structure.

(i) Most alpha particles pass through the metal film without being deflected.

...........................................................................................................................

...........................................................................................................................

(ii) Some alpha particles are deflected by angles greater than 90° from their original direction.

...........................................................................................................................

...........................................................................................................................(2)

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(b) Of the alpha particles that are deflected most are deflected through angles much less than 90° from their original direction.

Explain why, from this observation alone, it is impossible to deduce the sign of the charge on the nucleus. You may use a diagram to illustrate your explanation.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(c) The ratio of atomic diameter to nuclear diameter can be expressed in the form 10n.Suggest an appropriate value for n.

Value for n = ............................................(1)

(Total 5 marks)

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56. A student researching capacitance finds the following statements in different sources:

“A human body charged to 30 000 V has only about 0.045 J of stored electrical energy.’’

“The human body can be modelled as a capacitor of about 10 pF in parallel with a resistor.’’

(a) (i) Determine whether the data given in the first statement are consistent with the capacitance quoted in the second statement.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(3)

(ii) Calculate the static charge on the body referred to in the first statement.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Charge = ..............................(2)

(b) (i) A spark is seen when a person charged to 30 000 V brings his hand towards an earthed metal plate. Such sparks occur when the electric field strength is sufficient to ionise the air. The minimum electric field strength for this is 3.0 × 106 Vm–1. Assume that the hand and the metal plate can be treated as a pair of parallel plates, and that the voltage between the hand and the earth remains 30 000 V. Calculate the greatest separation of hand and plate for which the spark could occur.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Greatest separation = ...............................(2)

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(ii) Ions and electrons produced in the electric field between the hand and the plate(3.0 × 106 V m–1) are accelerated and may collide with other particles, causing further ionisation.

Calculate the force on an electron in this field.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Force = .................................(2)

(c) The ionization energy of a typical particle in the air is 35 eV. Calculate the maximum number of such particles an electron could ionise while it is moving a total distance of 1 mm in this field.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Number = .............................(3)

(Total 12 marks)

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57. Black holes are formed when stars collapse into a state of extremely high density. The gravitational field strength is so great that nothing can escape from within the black hole – not even light.

Even so, Professor Stephen Hawking suggested a way in which black holes might ‘evaporate’ over time.

Spontaneous production of particle-antiparticle pairs close to the black hole can enable it to lose mass. If one particle falls into the black hole and the other escapes, the mass and energy of the escaping particle are lost by the black hole.

P a rtic leA n tip a r tic le

(a) Explain why you would expect the initial motion of the particle and antiparticle to be in opposite directions at the instant at which they are produced.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(b) In a particular event, a particle (+) and its antiparticle (–) are produced. Complete the table of their properties.

Particle name π+ π–

mass 0.140 GeV/c2

charge +1.6 × 10–19 C

quark composition du(3)

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(c) Circle the word below which correctly describes a π+ particle.

meson baryon lepton(1)

In the event described, the π+ escapes.

(d) State the minimum energy in eV lost by the black hole.

.....................................................................................................................................

.....................................................................................................................................

Minimum energy = ............................ eV(2)

(e) Explain why this energy is a minimum.

.....................................................................................................................................

.....................................................................................................................................(1)

(f) Calculate the minimum mass in kg lost by the black hole in this event.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Mass loss = ............................ kg(2)

(Total 11 marks)

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58. Alex Coomber won a bronze medal in the women’s bobsled at the 2002 Winter Olympics.This involved hurtling down an icy track on her sled at speeds of up to 35 m s–1.

During one section of the run, her speed remained constant at 35 m s–1 as she slid in a straight line down a slope of 10°. Figure 1 shows the three forces acting upon her during this time. Figure 2 is the first part of a scale drawing combining these forces.

D

R

We ig h t8 5 0 N

1 0 °

F igu re 1

F ig u re 2

S ca le1 c m ∫ 1 0 0 N

Weight = 850

N

(a) Complete the scale drawing to find the size of the drag force D.

Drag force D = ............................(3)

Figure 3 shows Alex turning a corner. The banking angle is 40°. Figure 3 shows the two forces which affect her as she takes the corner at a speed of 35 m s–1.

F ig u re 3

P u sh P

40 °

Weig h t

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(b) Show that the size of P, the push on the sled from the ice, is about 1000 N.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(c) (i) Explain why there needs to be a resultant force on Alex to take her round the corner.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) State what provides this force.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(d) Calculate the radius of the corner. The combined mass of Alex and the sled is 87 kg.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Radius = ..................................(3)

(Total 12 marks)

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59. Faraday’s and Lenz’s laws are given at the back of this paper as E = –d(NΦ)/dt.

(a) Explain the symbol E.

.....................................................................................................................................

.....................................................................................................................................(2)

(b) Explain the significance of the minus sign.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

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(c) When a car has its headlights on with the engine running, the headlights receive their power from a dynamo which is turned by the engine. A driver sits in his car with the lights off, his foot off the accelerator, and the engine running slowly. He notices that when he switches the lights on, the engine slows slightly. Explain the physics causing this effect.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(4)

(Total 8 marks)

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60. Most desktop computers store data on discs coated with a magnetic medium which records the data in a digital form. As a disc spins at very high speeds the magnetic field at each place on the disc can be detected in order to ‘read’ the data.

The diagram shows a school laboratory model set up to demonstrate how the system works.

To d a ta lo g g e r

S o le n o id

M a g n e t

Wo o d entu rn tab le

M o to r

The ten flat magnets on this model disc can be arranged with either the north pole or south pole facing upwards. These are interpreted as 1 or 0 respectively and are detected by the coil linked to the datalogger as the disc spins.

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(a) The diagram below shows one of the magnets on this model. Sketch its magnetic field.

North

South

(2)

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(b) Figure 1 shows how the magnetic flux varies as an upward-facing north pole moves beneath the coil. Figure 2 shows the corresponding output from the coil.

F lu x

O u tp u t

F ig u re 1

Tim e

F ig u re 2

Tim e0

Explain how the output is generated and why it has this shape.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(5)

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(c) Show that the maximum number of sequences possible with ten magnets (as on this model) is about 1000.

.....................................................................................................................................

.....................................................................................................................................(1)

(d) The diagram shows an output generated during part of one trial.

Write the number sequence represented by this output. Remember: a north pole facing upwards is interpreted as 1 and a south pole upwards as 0.

.....................................................................................................................................(1)

(e) A real hard disc spins at very high speeds, making 7200 complete revolutions in one minute. The reading head is following a ring of magnetized regions with diameter 8.9 cm, and the length occupied by each separate magnetized region is 0.83 m.Assume that there are no gaps between adjacent magnetized regions. Calculate the rate at which the head is reading bits of data.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Rate = .............................................................(3)

(Total 12 marks)

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61. (a) State Newton’s second law of motion in terms of momentum.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(b) A wind blows steadily against a tree. The area of the tree perpendicular to the direction of the wind is 10 m2 and the velocity of the wind is 20 m s–1.

(i) Show that the mass of air hitting the tree each second is about 250 kg. (Density of air is 1.23 kg m–3.)

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(2)

(ii) Calculate the momentum of this mass of air when it is moving at 20 m s–1.

...........................................................................................................................

...........................................................................................................................

Momentum = …………………………………….

(iii) Assuming that all the air is stopped by the tree, state the magnitude of the force exerted on the tree by the wind.

...........................................................................................................................

Force = …………………………………….(2)

(Total 6 marks)

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62. The equation for – decay can be written as:

n p + – + v

(i) For each particle, either give its quark composition or state that fundamental particle.

n ..................................................................................................................................

p ..................................................................................................................................

β ..................................................................................................................................

v .................................................................................................................................(2)

(ii) Write a similar equation for β+ decay.

(2)(Total 4 marks)

63. In 1995 scientists at CERN created atoms of antihydrogen.

(i) Name the particles that make up antihydrogen.

.....................................................................................................................................

.....................................................................................................................................(1)

(ii) Describe these particles in terms of charge and quark structure where relevant.

.....................................................................................................................................

.....................................................................................................................................(2)

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(iii) State the charge of an atom of antihydrogen.

.....................................................................................................................................(1)

(iv) Explain why it is not possible to store atoms of antihydrogen.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(Total 6 marks)

64. A ball attached to the end of a long string is made to rotate in a horizontal circular path at a constant speed. The forces acting on the ball are its weight, W, and the tension, T, in the string.

°

L o n gs trin g

B a ll

H o rizo n ta lc ircu la r p a th

T

B all

WF ree -b o d y fo rce

d iag ram

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With reference to the free-body force diagram, explain how it is possible for the ball to move with constant speed and yet still be accelerating.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(Total 4 marks)

65. (a) State in words the formula which gives the electric force between two charged particles.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

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(b) What are the base units of the constant in this formula?

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

(Total 5 marks)

66. Electrons are accelerated from rest from the cathode to the anode of a vacuum tube through a potential difference of 5000 V.

Figure 1

C ath o d e A n o d e

5 0 0 0 V

E m e rg in g e lec tro n b ea m

(a) Show that the speed v of an electron as it leaves the anode is approximately 4 × 107 m s–1.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

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(b) The emerging beam of electrons follows a parabolic path as it passes between a pair of horizontal parallel plates 5.0 cm apart with a potential difference of 1400 V between them.

Figure 2

v

E m erg in g e lec tro nb ea m

H o riz o n ta l p la te

1 2 cm

+ 1 40 0 V

5 .0 cmh

0 V

(i) Calculate the strength E of the uniform electric field between the horizontal plates.

...........................................................................................................................

E = ..........................................(1)

(ii) Hence determine the force F exerted by this field on each electron.

...........................................................................................................................

...........................................................................................................................

F = ..........................................(1)

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(c) An electron experiences an upward acceleration a as it travels between the plates. Its vertical displacement h after a time t is given by

h = 2

21 at

Calculate the value of h as the electron leaves the plates.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

h = ..........................................(4)

(d) (i) Add to Figure 2 the path that the electron beam would follow if the potential difference between the horizontal plates were decreased. Label this path A.

(1)

(ii) Add to Figure 2 the path that the electron beam would follow if the potential difference between the cathode and the anode were decreased. Label this path B.

(1)(Total 11 marks)

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67. A U-shaped permanent magnet of mass 85.0 g rests on an electronic balance as shown in the diagram. An aluminium rod connected in a circuit is supported between the opposite poles of the magnet so that it is unable to move.

C lam p

M ag n e t

E lec tro n ic b a lan ce

A lu m in iu mro d

The switch is closed. The reading on the balance increases to 85.4 g.

(a) (i) Calculate the additional force on the magnet when there is current in the circuit.

...........................................................................................................................

Force = ..........................................(1)

(ii) Explain how this additional force originates. You may be awarded a mark for the clarity of your answer.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(4)

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(b) The diagram below shows a plan view of the rod and the poles of the magnet.

(i) On the diagram label the poles of the magnet to indicate the direction of field needed to produce a downward force on the magnet.

VIEW AS SEEN FROM ABOVE

C u rre n tin ro d

M a g n e t

5 .0 cm

2 0 .0 cm

C lam p

A lu m in iu m ro dI

(1)

(ii) The rod is 20.0 cm long and the magnet is 5.0 cm wide. The magnetic flux density of the magnet is 30.0 mT. Calculate the current in the rod.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Current = ..........................................(3)

(iii) The direction of the current is reversed. What would be the new reading on the balance?

...........................................................................................................................

Balance reading = ..........................................(2)

(Total 11 marks)

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68. The diagram shows part of a linear accelerator - a linac. Alternate metal tubes are connected together and to opposite terminals of a high-frequency alternating potential difference of fixed frequency.

A

B

C

De tc

H ig h fre q u en cya lte rn a tin gp o te n tia ld iffe ren ce

P ro to nb e am

In je c te dp ro to n s

(a) Describe how the protons are accelerated as they move along the linac and explain why the tubes get longer towards the right. You may be awarded a mark for the clarity of your answer.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(5)

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(b) A particular linac has 420 metal tubes and the peak voltage of the alternating supply is800 kV.

(i) Show that the emerging protons have gained a kinetic energy of about 5 × 10–11 J and express the mass equivalent of this energy as a fraction of the mass of a stationary proton. Take the mass of a proton mp as 1.01 u.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................(6)

(ii) The frequency of the alternating supply is 390 MHz. Calculate how long it takes a proton to travel along the linac.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

Time = ..........................................(2)

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(c) The emerging protons can be made to collide with

(i) a target of fixed protons, e.g. liquid hydrogen, or

(ii) a similar beam of protons travelling in the opposite direction.

State some advantages of either or both experimental arrangement(s).

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(2)

(Total 15 marks)

69. This is an extract from an article on thunderstorms.

“The electric field required to cause damp air to ionise, as happens in a lightning strike, is 3 × 105 V m–1. When this happens, 40 C of charge passes between the cloud (at a height of 5 km) and the ground. The strike lasts 20 ms, and completely discharges the cloud.”

The cloud and the ground below it may be modelled as a capacitor, as in the diagram.

– – – – – – – – – – – –

+ + + + + + + + + + + +

5 k m

C lo u d

G ro u n d

Calculate the voltage between the cloud and the ground when the strike occurs.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Voltage = ...........................................(2)

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Calculate the capacitance between the cloud and the ground.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Capacitance = ...........................................(2)

Find an approximate value for the resistance of the air between the cloud and the ground during the strike.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Resistance = ...........................................(2)

A different way of modelling a thunder cloud is to treat the charge of –40 C as a point charge at a height of 5 km, as shown in the diagram below.

Assume in this simple model that the ground has no effect on the field strength or shape.

5 k m

G ro u n dX

Using this model,

(i) draw on the shaded area of the diagram the electric field in that region,(2)

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(ii) calculate the value of the electric field this point charge of –40 C would cause at the point X on the ground immediately below it,

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Electric field = ...........................................(2)

(iii) explain why one might expect the lightning strike to begin from the cloud and not from the ground.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(1)

(Total 11 marks)

70. The picture shows a toy with two plastic spheres, each suspended by plastic rods. Each sphere is able to swing freely in a vertical circle.

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A student decides to carry out an experiment with the toy to investigate momentum. He allows one sphere to strike the other, and measures their speeds just before and just after the collision.

The table shows his data for one collision.

mass of sphere 1 54.0 g

mass of sphere 2 29.0 g

speed of sphere 1before collision

2.57 m s–1

speed of sphere 2before collision

0

speed of sphere 2after collision

2.12 m s–1

1

2

P iv o t

P la s tic ro d s

S p h e re

Show that the speed of sphere 1 just after the collision is about 1.4 m s–l. Assume that the mass of each rod is negligible.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

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Determine whether this is an elastic collision or an inelastic collision.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

In another experiment the student uses the toy to investigate motion in a vertical circle. He times sphere 2 (mass 29 g) as it swings around a complete vertical circle of radius 17 cm. This takes 0.37 s.

Calculate the average speed of the sphere.

...............................................................................................................................................

...............................................................................................................................................

Speed = .....................................................(2)

Assuming that the sphere travels at this speed throughout its circular path,

(i) calculate the centripetal force acting on it while it is in motion

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.....................................................................................................................................

.....................................................................................................................................

Centripetal force = .....................................................(2)

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(ii) calculate the net force exerted by the rods on the sphere when it is at the top of the circle.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

Tension = .....................................................(2)

(Total 12 marks)

71. The table below summarises some properties of some particles in the standard quark-lepton model.

Quarks Leptons

Name Symbol Charge Name Symbol Charge

up u +2/3 electron e– –1

down d –1/3 electron-neutrino νe 0

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Write bullet points to explain the composition of everyday matter using the information in the table.

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72. The following extract is taken from an article about the Continuous Electron Beam Accelerator Facility (CEBAF), which produces high-energy electrons for particle experiments.

The sheer size of the magnets reflects a bizarre phenomenon at work within CEBAF. At speeds close to the speed of light, Einstein’s special theory of relativity predicts that objects appear to gain mass. The electrons in CEBAF move so fast that they act as if they have gained 8000 times their normal mass, making them far more reluctant to change course – hence the need for powerful magnets.

The gain in mass of an electron is another way of saying that it has gained energy equivalent to 8000 electron masses. Calculate the voltage through which an electron has to be accelerated from rest to gain this energy.

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...............................................................................................................................................

...............................................................................................................................................

Voltage = .....................................................(3)

The electrons are guided along a path which has two straight sections with two semicircular sections at each end, as shown.

A B

CD

r = 11 0 m

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Explain the role of the magnets in this particle accelerator, including an approximate calculation of field strength. You may wish to refer to the various sections AB, BC, CD and DA along the path.

Assume that the electrons are travelling close to the speed of light so that they have a mass of 8000 times their normal mass.

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(Total 10 marks)

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73. Most smoke detectors contain an isotope of Americium (241Am), the nuclei of which decay by emitting an alpha particle. When a nucleus of Americium emits an alpha particle the principle of conservation of momentum and the principle of conservation of energy are obeyed.

Show that the ratio nucleus resulting ofenergy kineticparticle alpha ofenergy kinetic

is about 60 and briefly discuss the origin

of this energy.

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74. (a) A toy truck of mass 80 g is released from a height h and rolls down a slope as shown below.

h

What would the height h have to be for the truck to reach a speed of 4.0 m s–1 at the bottom of the slope? You may assume that any friction at its axles is negligible.

.....................................................................................................................................

.....................................................................................................................................

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.....................................................................................................................................

Height = ..................................................................(3)

(b) On reaching the bottom, it joins magnetically to two stationary trucks, identical to the first, and the trucks all move off together.

(i) State the law of conservation of linear momentum.

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...........................................................................................................................(2)

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(ii) Use this law to calculate the speed of the trucks immediately after the collision.

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...........................................................................................................................

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Speed = ……………………………………….(2)

(c) One of the stationary trucks has a total frictional force of 0.12 N at its axles. How much time does it take for the three trucks to stop moving if this is the only frictional force acting?

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Time = ………………………………………(3)

(Total 10 marks)

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75. In 1964 the following reaction was observed for the first time. The K particles are kaons (a type of meson) and X was a new particle.

K– + p K0 + K+ + X

Use conservation laws to deduce the nature of particle X in order to underline the correct words in the sentence below. Show all your working.

Particle X is a meson/baryon/lepton with a charge of –1 / 0 / +1

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...............................................................................................................................................

...............................................................................................................................................(4)

Add the quark content of the proton and the K+ to the table.

Particle Quark content

K– us

P

K0 sd

K+

(2)(Total 6 marks)

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76. The London Eye is a tourist attraction designed to give passengers a panoramic view over London. The giant wheel completes two revolutions in one hour. Each capsule moves with a constant speed of 0.26 m s–1 as it follows a circular path.

Figure 1

A

B

0 .2 6 m s – 1

H u b

G ro u n d

N o t to sc a le

P assen g e rcap su le

(a) Calculate the radius of this circular path.

......................................................................................................................................

......................................................................................................................................

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Radius = .............................................(2)

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(b) A man of mass 85 kg follows a circular path of this radius as he rides in a capsule.What is the magnitude and direction of the resultant force acting on the man?

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......................................................................................................................................(3)

(c) Figure 2 shows the free-body force diagram for the man when the capsule is at position A as shown in Figure 1.

Figure 2

F o rce P

M an

F o rce Q

(i) Name forces P and Q

Force P: .............................................................................................................

Force Q: ............................................................................................................(2)

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(ii) When the man is at position A there is no resultant vertical force acting on him. In this position force P = force Q in magnitude. Explain why the man continues his motion in a circle.

............................................................................................................................

............................................................................................................................

............................................................................................................................(2)

(iii) Explain why force Q must be larger than force P when the capsule is at position B.

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............................................................................................................................

............................................................................................................................(1)

(Total 10 marks)

77. In July 2003 scientists at the SPring-8 synchrotron in Japan announced the discovery of a pentaquark – a particle made up of 5 quarks.

The pentaquark was produced by firing gamma photons at a target. It decayed very rapidly into other products.

The diagram shows some of the particles involved in the production and decay of the pentaquark, including the quark composition for several of them.

P h o to n

N eu tro n

ud

d

O th erp a rtic les

udd

P en ta q u a rk N eu tro n

X

K –

us

s uud

d

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Name three quantities conserved during the decay of the pentaquark.

...............................................................................................................................................

...............................................................................................................................................(2)

The table shows the charges of the six types of quarks as a fraction of the charge on a proton.

Quark type Charge

up charm top 2/3 e

down strange bottom –1/3 e

Find the charge of the pentaquark. Express your answer as a fraction of the charge on a proton.

...............................................................................................................................................

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Charge = ...............................................(1)

Explain whether particle X must be positive, negative or neutral.

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...............................................................................................................................................(1)

Suggest a possible quark composition for particle X. Explain your choice of quarks.

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...............................................................................................................................................(2)

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The pentaquark had a mass of 1.54 GeV/c2. Find its mass in kg.

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Mass = ...............................................kg(2)

(Total 8 marks)

78. The diagram below illustrates an experiment with electrons. A beam of electrons is created using an electron gun, and deflected using an electric field.

E lec tro n

+ v e p la te

– v e p la te

Explain how the electron gun creates a beam of electrons. Add to the diagram if that will help your explanation.

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The electrons are accelerated from rest through a potential difference of 340 V. Calculate their speed as they leave the gun.

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Speed = ...............................................(3)

Explain what is meant by the term electric field.

...............................................................................................................................................

...............................................................................................................................................(1)

The electric field which deflects the beam is created by applying a potential difference of 2500 V across plates 9.0 cm apart. Show that the vertical acceleration of the electrons due to this field is about 5 × 1015 m s–2.

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(Total 12 marks)

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79. A class is visiting a go-karting track to study the physics involved.

To keep a go-kart moving forward at constant speed, the engine must exert a forward force. When a go-kart at constant speed goes round a bend in the track, an additional force is required.

State the direction in which this additional force acts.

...............................................................................................................................................(1)

Explain why this additional force is required.

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...............................................................................................................................................(2)

State what provides this additional force.

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...............................................................................................................................................(1)

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As an initial experiment, student A sits in the go-kart and his classmates attach a forcemeter to its side and drag it sideways. They find that the force needed to make it begin to slide sideways over the ground is 470 N.

At one point on the circuit the track bends through a right-angle as shown.

B A

Student A drives his kart round this bend taking the path marked A. The radius of this circular path is 14 m. Calculate the maximum speed at which he can drive round this bend. The total mass of student A and his kart is 160 kg.

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Maximum speed = ......................................(3)

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Student B and his kart have the same total mass as student A and his kart. Student B approaches the same corner at the same speed as student A did (the maximum speed that you calculated for student A). He intends to take the dotted path shown. However, he slides off the track.

Explain why he is not able to follow the dotted path.

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...............................................................................................................................................(3)

The teacher and his kart have a mass much greater than 160 kg. He approaches the bend along the same path that student A took, at the same speed. Explain whether he would be likely to get round the corner at this same speed without sliding off the track.

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(Total 12 marks)

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80. A particle experiment shows the track of an alpha particle (a helium nucleus He42 ) travelling at

right angles to a magnetic field of magnetic flux density 3.7 T. Make an appropriate measurement and hence find the approximate energy of the alpha particle.

D iag ra m d ra w nac tu a l s ize

Trac k o f p a rtic le ( H e) 42

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Energy = ...................................................(Total 7 marks)

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81. The diagram shows an electric toothbrush. An electric toothbrush recharges its batteries despite there being no metal contacts between the toothbrush and the base.

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(a) State a reason for avoiding metal contacts between the toothbrush and the base.

.....................................................................................................................................

.....................................................................................................................................(1)

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(b) The base, which is connected to an a.c. supply, contains a coil around a metal bar(coil X). The toothbrush contains a second coil (coil Y). When you put the toothbrush on to the base, coil Y goes around the bar and coil X without the two coils making contact.

Explain how this arrangement is able to charge the battery in the toothbrush.

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(Total 7 marks)

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82. (i) Particle energies are often quoted in units of mega-electronvolts (MeV). Show that the base units of the electronvolt can be expressed as kg m2 s–2.

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......................................................................................................................................(3)

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(ii) Calculate the theoretical energy released when a 23892 U nucleus is formed from individual

protons and neutrons. Give your answer in MeV.

Data (masses):

23892 U = 238.0003 u

proton = 1.0073 uneutron = 1.0087 u

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(Total 7 marks)

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83. (a) Explain why a body moving at constant speed in a circular path needs a resultant force acting on it.

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.......................................................................................................................................(2)

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(b) (i) A girl standing at the equator is in circular motion about the Earth’s axis. Calculate the angular speed of the girl.

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Angular speed = ................................(2)

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(ii) The radius of the Earth is 6400 km. The girl has a mass of 60 kg. Calculate the resultant force on the girl necessary for this circular motion.

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Force = ..............................................(2)

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(iii) If the girl were to stand on weighing scales calibrated in newtons, what reading would they give?

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Scale reading = .................................(3)

(Total 9 marks)

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84. The diagram shows the path of an electron in a uniform electric field between two parallel conducting plates AB and CD. The electron enters the field at a point midway between A and D. It leaves the field at B.

C u rv e d p a tho f e le c tro n

E lec tricfie ld lin e

A B

CD

5 .0 c m

(a) Mark on the diagram the direction of the electric field lines.(1)

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(b) (i) The conducting plates are 5.0 cm apart and have a potential difference of 250 V between them. Calculate the force on the electron due to the electric field.

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Force = ...............................................(3)

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(ii) State the direction of this force on the electron and explain why it does not affect the horizontal velocity of the electron.

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............................................................................................................................(2)

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(c) To leave the electric field at B the electron must enter the field with a speed of 1.30 × 107 m s–1. Calculate the potential difference required to accelerate an electron from rest to this speed.

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Potential difference = .........................(3)

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(d) A very thin beam of electrons enters a uniform electric field at right angles to the field. The electrons have a range of speeds.

(i) Draw a diagram to show the shape of the beam as it moves through the field.

(ii) On your diagram label which electrons have the fastest speed.(2)

(Total 11 marks)

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85. The photograph shows the path of an electron spiralling inwards anticlockwise in a bubble chamber. The photograph is full size.

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(a) (i) Explain how the electron produces the white track. You may be awarded a mark for the clarity of your answer.

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(ii) Explain the origin of the centripetal force that is making the electron spiral in this manner.

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Why does the radius of the circle in which it is moving gradually decrease?

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(b) Theory shows that the momentum p of the electron at any point on its path is given by p = Ber, where B is the magnetic flux density perpendicular to its motion, r is the radius of its path at that point and e has its usual meaning.

(i) The magnetic flux density in the bubble chamber is 1.2 T. By making suitable measurements on the photograph, determine approximate values for the momentum of the electron at P, Q and R. If you are using a transparent ruler, it may help to place a piece of white paper underneath it. (Take the centre of the spiral to be at S.)

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(ii) The speed v of the electron at all three places P, Q and R on its spiral is 3.0 × 108 m s–1 to two significant figures. Deduce the effective mass of the electron at each point and comment on your results.

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(Total 15 marks)

86. The diagram is taken from the notes of an accident investigator after a collision in the countryside.

N

S

EW

P ath o f ca r 1

45 °3 0°

2 3 .9 m

2 1 .7 m

C ar 1

C ar 2

P a th o f ca r 2

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The driver of car 1 said he was driving within the speed limit and car 2 suddenly drove across the junction in front of him.

The driver of car 2 said that he obeyed the traffic sign and stopped at the junction. He looked carefully before moving slowly straight across the junction. He was suddenly struck by car 1. He thought he hadn’t seen it because of the bend in the road 50 m away, and that it must have been speeding.

The investigator found the masses of both cars with their drivers and used a test car to find that the surface produced a deceleration of 3.43 m s–2. The table shows some of the investigator’s notes.

Car 1 Car 2

Mass of car and driver/kg 1950 1430

Distance travelled after collision/m 21.7 23.9

Angle between path followed and main road/degrees 45.0 30.0

Speed immediately after collision/m s–1 12.2

Magnitude of momentum immediately after collision/kg m s–1 23 800

Show that the speed of car 2 immediately after the collision was about 13 m s–1.

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.................................................................................................................................................(2)

Calculate the magnitude of the momentum of car 2 immediately after the collision.

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Momentum = ..............................................(2)

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Next the investigator calculated the component of the momentum to the East immediately after the collision for each car.

Calculate this component of the momentum for each car.

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East momentum component for car 1 = ..........................................................

East momentum component for car 2 = ..........................................................(3)

Hence determine whether car 1 was speeding before the accident. The speed limit was17.8 m s–1.

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.................................................................................................................................................(3)

Explain, without calculation, how the investigator could use a conservation law to deduce that car 2 was travelling across the junction at speed.

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(Total 12 marks)

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87. In 1989 the Large Electron Positron collider (LEP) at CERN was opened. It was used until 2000, when it was shut down to allow the construction of a new accelerator. At LEP, beams of electrons and positrons were accelerated to energies of 100 GeV in a huge ring with a circumference of 27 km before being made to collide with each other.

Just before LEP closed, scientists using it found some evidence for the proposed Higgs boson at a mass of 115 GeV/c2.

Explain why 1 eV is equal to 1.6 × 10–19 J.

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.................................................................................................................................................(2)

Show how GeV/c2 can be used as a unit of mass.

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.................................................................................................................................................(2)

If the Higgs boson has a mass of 115 GeV/c2, find its mass in kg.

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Mass = ................................................... kg(2)

The positron is the antiparticle to the electron. What is an antiparticle?

.................................................................................................................................................

.................................................................................................................................................(1)

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A description of LEP refers to ‘....the relatively small magnetic field required for LEP’s gentle curvature....’.

Explain the need for a magnetic field and why it can be ‘relatively small’ in this case.

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(Total 11 marks)

88. A student wants to test Coulomb’s law, which is about the force between two charged objects.

She plans to hang two balloons on insulated threads, charge them both with equal positive charges, and measure the angles at which they hang away from each other. The dimensions she plans to use in her experiment are shown on the diagram.

0 .5 m

0 .5 m

1 .8 m

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She thinks she can make accurate measurements if the balloons hang at an angle of 1.5° or more from the vertical. Add to the diagram to show all the forces acting on one of the balloons. Hence show that the minimum charge Q she needs on each balloon must be about 0.1 C.[Assume that each balloon behaves as though the charge were concentrated at its centre.]

The mass of each balloon = 0.0018 kg.

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89. A neutron of mass 1.7 × 10–27 kg travelling at 2.96 ×107 m s–1 collides with a stationary nucleus of nitrogen of mass 23.3 × 10–27 kg. Calculate the magnitude of the momentum of the neutron before it collides with the nucleus of nitrogen.

...............................................................................................................................................

...............................................................................................................................................

Momentum of neutron = .........................................(2)

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Given that the neutron ‘sticks’ to the original nucleus after the collision, calculate the speed of the new heavier nucleus of nitrogen.

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Speed = ....................................................................(3)

An elastic collision is one where kinetic energy is conserved. Make suitable calculations to determine whether this collision is elastic.

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...............................................................................................................................................(3)

(Total 8 marks)

90. The following strong interaction has been observed.

– + p X + K– + n(dds) (ūs)

Is particle X positive, negative or neutral?

...............................................................................................................................................(1)

Is particle X a baryon, a meson or a lepton?

...............................................................................................................................................(1)

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State the quark composition of the proton and the neutron.

...............................................................................................................................................

proton .......................................................... neutron ...........................................................(1)

Explain why particle X cannot contain a strange quark, and deduce the identity of particle X. You may be awarded a mark for the clarity of your answer.

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(Total 7 marks)

91. To make an object of mass m move at speed around a circular path of radius r, a resultant force must act on it. The magnitude of the resultant force is given by m2/r.

Explain why a resultant force is required, and state its direction.

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When vehicles corner on a level road, the resultant force is provided by friction. For a given vehicle and road surface, the friction cannot exceed a certain maximum value. Use these facts, together with the expression for the resultant force, to explain why roads designed for high-speed travel have no sharp bends.

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...............................................................................................................................................(2)

On a bobsleigh run, the bobsleigh travels along an ice channel with little friction. When cornering, it slides up the side of the channel until the required resultant force is provided.

The diagram shows a head-on view of a bobsleigh travelling at speed round a bend which is part of a horizontal circle centred at the point O. The bobsleigh is tilted through an angle .

O(C e n tre o f

c irc le )

r

Ice

B o b s le ig h

Below is a free-body force diagram for the bobsleigh. Friction is assumed to be negligible.

N

m g

B o b sle ig h

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The normal contact force exerted by the ice on the bobsleigh is N, and its weight is mg.

Write down an equation expressing the condition for no vertical acceleration.

.............................................................................................................................................

Write down an equation applying Newton’s second law horizontally.

.............................................................................................................................................

Hence show that

tan = rg

2

(tan = sin / cos )

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................(4)

Calculate the value of angle for a bobsleigh travelling at 30.0 m s–1 around a bend of radius 20.0 m.

.............................................................................................................................................

.............................................................................................................................................

=…...................................................(1)

(Total 10 marks)

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92. Experiments supervised by Rutherford about 100 years ago involved firing alpha particles at thin gold foils. Outline the results of these experiments, and the conclusions scientists drew from them.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

The relationship between the rate of alpha detection (N) and the angle of scatter () is predicted to be of the form

N (sin /2)x

Explain how you would determine x graphically from a set of experimental results for N and .

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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The symbols for an alpha particle and a gold nucleus are given below.

He42 Au197

79

alpha particle gold nucleus

Explain the meaning of the numbers in the symbol for the gold nucleus.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Show that the mass of an alpha particle is about 7 × 10–27 kg.

...............................................................................................................................................

...............................................................................................................................................(1)

In these experiments, an alpha particle may approach a gold nucleus to within a distance of 5 × 10–14 m. Calculate the electric force between them at this separation.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

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Force = ....................................(3)

(Total 12 marks)

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93. The formulae list states:

In a magnetic field F = Bq sin

Describe the situation to which this equation refers, stating the meaning of each symbol.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

The formulae list also gives an equation r = p/BQ.

Describe the situation modelled by this equation, stating the meaning of the symbol p.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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Particles arriving from the Sun can enter the Earth’s magnetic field in such a way that they spiral along towards the North pole as shown in the diagram below. As they near the North pole they give rise to the beautiful Aurora Borealis, or Northern Lights.

E arth ’sm ag n e ticfie ld

S p ira lin gp a th o f th ep a rtic les

Explain why the path of a particle is curved.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Explain why the spiralling circular path of a particle decreases in radius as it nears the North Pole.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 10 marks)

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94. A possible explanation for the extinction of the dinosaurs is that the Earth was struck by an asteroid. Studies are currently under way to find a way of avoiding such a collision in the future. One possibility is to change the orbit of an asteroid which is on a collision course with the Earth. This could be done by hitting it with a large mass in order to change its velocity.

Simulations of the impact of a 5.8 × 106 kg mass on the asteroid Castalia, mass 1.2 × 1012 kg, have been carried out to predict the effect. In all the simulations the two bodies join together on impact. The speed of the colliding mass was taken as 35 000 m s–1, and that of Castalia as 25 000 m s–1.

Discuss whether this would be an elastic or an inelastic collision.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

If the mass strikes Castalia at 90°, sketch a momentum vector diagram labelled with the appropriate quantities. The diagram does not need to be drawn to scale.

(2)

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Hence calculate the resulting change in Castalia’s direction.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Change in direction = .............................(2)

Such an impact may fracture the asteroid and leave some fragments still on a collision course with the Earth. An alternative approach would be to apply a smaller steady force over a longer period, for example by using rocket engines.

State a formula for net force in terms of momentum.

...............................................................................................................................................(1)

The momentum change of Castalia at the impact is 2.0 × 1011 N s. The average thrust of a typical rocket is 7 × 106 N, and it can burn for 130 s. Calculate the number of rockets required to produce the same change in Castalia’s momentum as in the collision above.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Number of rockets = ...............................(2)

(Total 9 marks)

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95. In 1995 scientists at CERN created, for the first time, anti-atoms of hydrogen. Each of these consisted of an anti-electron (a positron) in orbit around an antiproton. Each anti-atom produced survived for only about forty nanoseconds.

How do the properties of particles and antiparticles compare?

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

Show that the energy required to produce an antiproton is about 1 GeV.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

Why did each anti-atom produced survive for only about forty nanoseconds?

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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Tick appropriate boxes in the table below to show the nature of each of the named particles.

Meson Baryon Lepton

proton

antiproton

electron

positron

(2)

A proton consists of two up quarks and a down quark. Describe the quark structure of an antiproton and show how this structure provides the correct charge.

(Charge of up quark = + 32 e)

(Charge of down quark = – 31 e)

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 10 marks)

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96. The diagram shows a device called a Residual Current Circuit Breaker (RCCB). It is designed to protect users of appliances connected to the mains a.c. power supply, e.g. an electric lawnmower.

L iv e

L aw n m o w e r

C o il 2

C o il 1

T h irdco il

Ir o n core

R e la y co n tac t 1

Relay coil

and core

N e u tra l

Explain why, in normal operation, the resultant flux in the iron core due to coils 1 and 2 is zero.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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If there is a difference in the currents flowing in the live and neutral wires, for example caused by a person coming into contact with a bare wire, the RCCB breaks the circuit. Explain how.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(5)

(Total 7 marks)

97. The diagram shows a simple timing circuit.

S

s

E lec tro n ic p ro cesso r

B u zze r

(2 .2 M )C

( 4 7 F )

0 V

+ V

RVc

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The electronic processor operates so that the buzzer sounds when Vc is greater than 43 Vs. The

switch S is normally open. Explain in detail what happens in the circuit after the switch S is closed for a moment then opened again. Your answer should include an appropriate calculation and a sketch graph.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................(Total 7 marks)

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98. In the Rutherford scattering experiment, fast-moving alpha particles were fired at a thin gold foil. What observations from this experiment suggested that the atom has a small, massive nucleus?

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

The diagram shows the path followed by one alpha particle which passes close to a gold nucleus N.

AX

P

Y

B

N

Add arrows to the diagram at points X and Y to show the direction of the force on the alpha particle when it is at each of these points.

(1)

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The speed of the alpha particle was the same at points A and B. On the axes below, sketch a graph showing how the speed would vary with distance along the path from A to B.

0AA P B

S p eed

D istan ce

(2)

With reference to the forces you added to the previous diagram, explain the shape of the graph.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

The diagram below shows the path of the alpha particle again.

N

Add a line to this diagram to show the path which would be followed by an alpha particle which was travelling initially along the same line as before, but more slowly.

(1)

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The evidence for a small, massive nucleus from Rutherford scattering might have been less convincing if the alpha particles used had been of lower energy. Suggest how the observations would have changed if lower energy alpha particles had been used.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

(Total 9 marks)

99. Neutrons, like electrons, are often used to study crystal structure. A suitable de Broglie wavelength for the neutrons would be about 1 nm.

Explain why the neutrons must have a de Broglie wavelength of this order of magnitude.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Given the mass of a neutron as 1.67 × 10–27 kg, calculate the kinetic energy of a neutron which has a de Broglie wavelength of 1.20 nm.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Kinetic energy = ............................................(3)

(Total 5 marks)

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100. In a washing machine clothes are placed inside a metal drum with small holes in it. When the wet clothes are spun, the drum rotates at high speed and water escapes through the holes. The drum has a radius of 0.220 m and rotates at 800 revolutions per minute.

Show that the speed of the rim of the drum is approximately 18 m s–1.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

The diagram shows a piece of clothing in the drum which is spinning anticlockwise.

C e n tre o f d ru m

C lo th in g

P

0 .2 2 0 mD ru m

Estimate the magnitude of the acceleration of this piece of clothing.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Acceleration = ............................................(2)

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Add an arrow to the diagram to show the direction of this acceleration. Label the arrow A.

Explain what force produces this acceleration.

...............................................................................................................................................

...............................................................................................................................................(2)

A drop of water becomes detached from the clothing at point P, which is next to one of the holes in the drum. Draw an arrow on the diagram to show the path which the drop of water now follows. Label this arrow B.

(1)(Total 8 marks)

101. The diagram shows the top view of a square of wire of side 1.5 cm. It is in a uniform magnetic field of flux density 8.0 mT formed between magnetic north and south poles. The current in the wire is 2.0 A

1 .5 c m

N

M

OL

S

N

2 .0 A

What is the meaning of uniform in the phrase uniform magnetic field?

...............................................................................................................................................

...............................................................................................................................................(1)

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Determine the sizes and directions of the electromagnetic forces that act on the sides LM and NO of the square of wire.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Force on LM: ......................................... Force on NO: ...................................................

Direction: ............................................... Direction: ........................................................(3)

Why do no electromagnetic forces act on the sides MN and OL of the square?

...............................................................................................................................................

...............................................................................................................................................(1)

What effect will the forces acting on LM and NO have on the square of wire?

...............................................................................................................................................

...............................................................................................................................................(1)

The magnetic poles are now moved further apart. Describe and explain what effect, if any, this will have on the magnitudes of the forces produced on LM and NO assuming the current of 2.0 A is unchanged.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 8 marks)

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102. The potential difference between the plates of a 220 µF capacitor is 5.0 V.

Calculate the charge stored on the capacitor.

...............................................................................................................................................

...............................................................................................................................................

Charge = ...............................................................(2)

Calculate the energy stored by the capacitor.

...............................................................................................................................................

...............................................................................................................................................

Energy = ...............................................................(2)

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Describe how you would show experimentally that the charge stored on a 220 µF capacitor is proportional to the potential difference across the capacitor for a range of potential differences between 0 and 15 V. Your answer should include a circuit diagram.

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...............................................................................................................................................(5)

(Total 9 marks)

103. State Lenz’s law of electromagnetic induction.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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A bar magnet is dropped from rest through the centre of a coil of wire which is connected to a resistor and datalogger.

N

S

To d a ta lo g g e r C o il

State the induced magnetic polarity on the top side of the coil as the magnet falls towards it.

...............................................................................................................................................

Add an arrow to the wire to show the direction of the induced current as the magnet falls towards the coil.

(2)

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The graph shows the variation of induced current in the resistor with time as the magnet falls.

In d u c edcu rren t

0 Tim e

I1

I2

Explain why the magnitude of I2 is greater than I1.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 6 marks)

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104. A student is learning about how capacitors work. He uses the circuit shown in Figure 1 to investigate the capacitor C. Letter X labels a connection which he can make to either of the points L or M. Each cell has an e.m.f. of 1.5 V.

1 0 0 k L M

C

AA

1

2

X

I / A

1 0

00 5 1 0 t/s

C o n n e c tio n X toL m ad e a t = 3 st

F ig u re 1 F ig u re 2

He connects X to L. He sketches how the reading on ammeter 1 varies with time (Figure 2).

Explain in terms of charge what has happened in the circuit.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(3)

Explain what he would have seen if he had watched ammeter 2.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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Use his sketch graph (Figure 2) to estimate the charge which has passed through ammeter 1 between the times t = 3 s and t = 10 s.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Charge = ..................................................(2)

Use the graph and your answer above to estimate the capacitance of the capacitor.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Capacitance = ..........................................(3)

State and explain what he would observe on each ammeter if he then continued the experiment by moving the connection X from L to M.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 12 marks)

105. Faraday’s and Lenz’s laws are given at the back of this paper as E = –d(NΦ)/dt. Explain the meaning of E.

...............................................................................................................................................

...............................................................................................................................................(2)

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Define and explain the meaning of Φ.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

A student does an experiment on electromagnetic braking. She arranges an aluminium disc to spin horizontally as shown in Figure 1. Above the disc she fixes an iron core with a coil around it. She can vary the braking current Ib to this coil.

R o ta tin ga lu m in iu m d isc

R o ta tin ga lu m in iu m d isc

V ie w fro m ab o v e

R e g io n o f d iscb e lo w iro n co re

Iro n co re a n d c o il

A

I b

F ig u re 1 F ig u re 2

The braking current in the coil causes currents to flow in the rotating aluminium disc. Figure 2 shows the paths of two of these currents in the region of the disc below the iron core.

Add to the diagram to show the complete paths of these two currents.(1)

Explain

(i) why these currents flow,

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

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(ii) why these currents cause a force tending to slow the disc.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................(3)

The student reasons that the braking effect might be proportional to the square of the braking current Ib. Use appropriate equations to explain her reasoning.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

(Total 11 marks)

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106. The diagram shows the apparatus used in an experiment to discover if matter can carry ‘fractional charge’, that is, charge which is a fraction of the charge on an electron.

A magnetic force is used to keep a niobium sphere stationary between two metal plates.

To p p la te

B o tto m p la teN io b iu m sp h e re

The sphere carries some electric charge. Once the sphere is stationary, an electric field is applied between the plates. This causes an electric force on the sphere, which causes it to accelerate in a vertical direction. This acceleration is measured. The charge on the sphere can then be calculated.

The electric field is created by applying a potential difference of 2000 V across the plates, with the top plate being positive. The plates are 0.80 cm apart.

Sketch on the diagram the pattern of the electric field between the plates.(2)

Calculate the electric field strength between the plates.

...............................................................................................................................................

...............................................................................................................................................

Electric field strength = ......................................(2)

The niobium sphere has mass 1.8 × 10–7 kg. During one experiment its acceleration is3.0 × 10–7 m s–2 upwards. Calculate the magnitude of the charge on the sphere, and state its sign.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Charge = ..............................................................(4)

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Explain why it is important for the experiment to be carried out in a vacuum.

...............................................................................................................................................

...............................................................................................................................................(1)

(Total 9 marks)

107. High energy X-rays can be used for radiation therapy for cancers.

An X-ray photon interacts with an atom to produce an electron-positron pair. The positron soon meets an electron and the energy is released, helping to destroy the cancer cells.

How do the properties of a positron compare with those of an electron?

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Calculate the minimum energy of the X-ray photon in MeV.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Energy = ........................................................ MeV(3)

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Name the process that occurs when a positron meets an electron, and describe how this energy is released.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

(Total 8 marks)

108. The oscillations of a child on a swing are approximately simple harmonic. State the conditions which are needed for simple harmonic motion.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Why is the child’s motion only approximately simple harmonic?

...............................................................................................................................................

...............................................................................................................................................(1)

The child completes six oscillations of amplitude 1.2 m in 20 s.

(i) Calculate the period and the frequency of the oscillations.

.....................................................................................................................................

.....................................................................................................................................

Period = ...........................................................

Frequency = .....................................................

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(ii) The quantity ω in the equations for simple harmonic motion is defined as 2πf, where f is the frequency of the oscillations.

Calculate ω for these oscillations.

.....................................................................................................................................

.....................................................................................................................................

ω = ....................................................................

(iii) Calculate the child’s acceleration when the displacement is maximum.

.....................................................................................................................................

.....................................................................................................................................

Acceleration = ..................................................(5)

Explain how pushing a child on a swing can be an example of resonance.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(2)

(Total 10 marks)

109. The following is an extract describing the origins of a spectacular show of light detected by the spacecraft Galileo as it passed close to one of Jupiter’s moons, Io, in 1995.

“As Io sweeps through Jupiter’s enormous magnetic field, a large e.m.f. builds up across the opposite sides of its surface. Io now acts like a large battery, driving a massive current of about a million amperes through the gases that surround it. As electrons flow through Io’s atmosphere, they collide with molecules of gas and various different elements emit specific colours of light.”

[From The New Scientist, Vol 165 No. 2220]

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Use this extract to explain all the processes involved in the production of this light show, stating relevant physics principles, laws and equations.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................(Total 7 marks)

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110. The nuclear atom may be represented as in the diagram.

N u c leu s

‘C lo u d ’o f e lec tro n s

Explain how the results of the alpha particle scattering experiment verify the nuclear modelof the atom. You may be awarded a mark for the clarify of your answer.

................................................................................................................................................

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................................................................................................................................................(Total 5 marks)

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111. A wooden mallet is being used to hammer a tent peg into hard ground.

The head of the mallet is a cylinder of diameter 0.100 m and length 0.196 m. The density of the wood is 750 kg m–3. Show that the mass of the head is approximately 1.2 kg.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(3)

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The head strikes the tent peg as shown at a speed of 4.20 m s–1 and rebounds at 0.58 m s–1.Calculate the magnitude of its momentum change in the collision.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

Momentum change = ...............................(3)

The head is in contact with the peg for 0.012 s. Estimate the average force exerted on the peg by the head during this period.

...............................................................................................................................................

...............................................................................................................................................

Average force = .......................................(2)

Give a reason why your value for the force will only be approximate.

...............................................................................................................................................

...............................................................................................................................................(1)

With reference to your calculations above, discuss whether a mallet with a rubber head of the same mass would be more or less effective for hammering in tent pegs.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 11 marks)

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112. The momentum p of a photon of energy E is given by the expression p = E /c where c is the speed of light. Show that this expression is homogeneous with respect to units.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(Total 4 marks)

113. A xi minus particle Ξ decays to a lambda particle Λ and a pi meson π as shown below.

Ξ → Λ + π

(dss) (uds) (ud)

Classify each particle as either a baryon, a meson or a lepton.

Ξ ...........................................................................................................................................

Λ ............................................................................................................................................

π ............................................................................................................................................(3)

By considering the quark composition of the Ξ show that the strange quark has charge of 31 .

................................................................................................................................................

................................................................................................................................................(1)

Is the Λ particle positive, negative or neutral? Justify your answer.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(2)

(Total 6 marks)

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114. A body of mass m travelling at constant speed v around a circular path of radius r must have a resultant force F acting upon it. Write down a formula for the magnitude of F and state the direction in which it acts.

Formula: ..........................................................................................................................

Direction: .........................................................................................................................(2)

The diagram shows a car at the highest point A of a hump-backed bridge.

2 5 .0 m

O

A

When the car is driven over the bridge it follows part of a vertical circle of radius 25.0 m centred at the point O below the bridge.

Below is a free-body force diagram for the car at point A.

N o rm al reac tio n R

W eig h t

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The mass of the car is 925 kg. Calculate the normal reaction force R

(i) when the car is parked at rest at A,

.....................................................................................................................................

R = ..................................................................

(ii) when the car is passing point A at a speed of 10.0 m s–1.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

R = ..................................................................(4)

If the car is driven across the bridge repeatedly, at gradually increasing speeds, it is found that, above a certain critical speed, the car loses contact with the road at A, and “takes off ”.Explain why this happens.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(1)

Calculate the critical speed for this particular bridge.

................................................................................................................................................

................................................................................................................................................

Critical speed = ..............................................(2)

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An object which is in free fall is said to be “apparently weightless”. Explain what this means, illustrating your answer with reference to the situation described in this question.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(2)

(Total 11 marks)

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115. A current-carrying conductor is situated in a magnetic field. Describe how you could demonstrate that the magnitude of the force on the conductor is directly proportional to the magnitude of the current in it. You may wish to include a diagram in your answer.You may be awarded a mark for the clarity of your answer.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(4)

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An aluminium rod of mass 50 g is placed across two parallel horizontal copper tubes which are connected to a low voltage supply. The aluminium rod lies across the centre of and perpendicular to the uniform magnetic field of a permanent magnet as shown in the diagram.

The magnetic field acts over a region measuring 6.0 cm × 5.0 cm.

× ×× ×× ×× ×× ×× × C o p p e r tub es

A lu m in iu m ro d

6 .0 cm

5 .0 cm

M ag n e tic fie ld o f th ep erm an en t m ag n et P L A N V IE W

(N O T T O S C A L E )

The magnetic flux density of the field between the poles is 0.20 T. Calculate the initial acceleration of the rod, assuming that it slides without rolling, when the current in the rodis 4.5 A.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

Initial acceleration = ............................................(4)

(Total 8 marks)

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116. A bar magnet is suspended above a vertical coil of wire. It is then displaced to one side and released such that it oscillates above the coil as shown in the diagram. The coil of wire has its ends connected to an oscilloscope.

S

N

O scillo sco p e

P a th o f m ag n e t

C o il

Explain why an e.m.f. is induced across the ends of the coil.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(2)

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By considering Lenz’s law, label with an X on the diagram each position of the magnet at which the induced e.m.f. changes polarity.

(2)

The maximum induced e.m.f. is 3.0 mV. Calculate the rate of change of flux needed to induce this e.m.f. in a coil of 500 turns.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

Rate of change of flux = ......................................(2)

State three changes that could be made to the apparatus in order to increase the maximum induced e.m.f.

1 .......................................................................................................................................

2 .......................................................................................................................................

3 .......................................................................................................................................(3)

(Total 9 marks)

117. The diagram shows two parallel plates with a potential difference of 3000 V applied across them. The plates are in a vacuum.

+ 3 0 0 0 V

0 V

2 5 m m

On the diagram sketch the electric field pattern in the region between the plates.(2)

On the same diagram sketch and label two equipotential lines.(1)

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The plates are 25 mm apart. Show that the force experienced by an electron just above the bottom plate is about 2 × 10–14 N.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................(3)

Complete the graph to show how the force on the electron varies with the distance of the electron from the bottom plate.

F o rc e

00

D istan ce / m m2 5

(2)

This force causes the electron to accelerate.

The electron is initially at rest in contact with the bottom plate when the potential difference is applied. Calculate its speed as it reaches the upper plate.

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

................................................................................................................................................

Speed = ................................................................(3)

(Total 11 marks)

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118. Particle physics often involves passing beams of particles through electric and/or magnetic fields. The diagram illustrates a beam of positive ions, each with charge q and travelling at speed v, entering a region containing both an electric field of strength E and a magnetic field of flux density B. The electric field acts between the parallel plates. The magnetic field acts into the page.

M a g n e tic f ie ldin to p a g e

+ p la te

– p la te

P o s itiv e io n

v, q

The electric field causes a force on an ion when it is between the plates. State a formula for the magnitude of this force.

...............................................................................................................................................(1)

In which direction does this force act?

...............................................................................................................................................(1)

The magnetic field causes a force on the ion in the opposite direction to the force from the electric field.

With a suitable combination of values of , E and B, the electric and magnetic forces balance and each ion will travel straight through the region without changing direction. Calculate the value of for an ion to travel straight through the region if E = 1.2 × 104 N C–1 and B = 0.40 T.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

= ........................................................................(3)

Explain why ignoring the effect of gravity on the ion is justified.

...............................................................................................................................................(2)

(Total 7 marks)

119. A student hastily writes out some notes about particle physics. Some of the notes (shown below)

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contain errors.

Identify three of these errors. Draw a ring carefully round only the word or phrase that contains the error, and write below it a correct word, phrase or statement which could take the place of the wrong word or phrase you have ringed. An example has been given to show you what to do.

An electron, which is a lepton, has no antipartic le

an antiparticle

To every quark there is a corresponding antiquark.

Leptons are made from a quark and an antiquark.

A meson is nor made up from any smaller particles.

A proton is made from three quarks.

A neutron is made from a quark and an antiquark.

For the event: electron + positron photons

a process called annihilation occurs

momentum is conserved

the equation = c2m can be used to calculate the total momentum of the photons(Total 6 marks)

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120. Riders on a theme park ride lie back in capsules round the rim of a large wheel. Initially the wheel is horizontal but it then moves into a vertical plane in which it rotates. The diagram shows the wheel when it is rotating in a vertical plane.

W

P

R o ta tio n

A

B

State the direction of the centripetal acceleration of the rider at A.

...............................................................................................................................................

...............................................................................................................................................(1)

Explain why the resultant force on the rider at A has to be in this same direction.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

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The radius of the wheel is 8.0 m and the time for 1 revolution at maximum speed is 4.5 s. Show that at this speed the resultant force acting on a rider of mass 60 kg is about 900 N.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

Calculate the weight W of the rider.

...............................................................................................................................................

...............................................................................................................................................

Weight = ..............................................................(1)

Calculate P, the magnitude of the push from the capsule on the rider, when he is at point A.

...............................................................................................................................................

...............................................................................................................................................

Push = ..................................................................(1)

Draw labelled arrows on the diagram to show the two principal forces acting on the rider when he is at point B.

(2)(Total 10 marks)

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121. As it moves through space, the Earth collides with small amounts of stationary material such as comet debris. After the collisions the pieces of material move with the Earth through space. As the Earth gives momentum to the material it collides with, it experiences a very small retarding force, and hence deceleration. Calculate this deceleration and comment on your answer.

Mass of extra material collected by the Earth each second = 7.0 kgSpeed of the Earth through space = 3.0 × 104 m s–1

Mass of Earth = 6.0 × 1024 kg

(Allow one lined page)(Total 5 marks)

122. Define momentum and state its unit.

Definition: ........................................................................................................................

Unit: ........................................................(2)

A stationary nucleus of thorium-226 decays by alpha particle emission into radium.The equation for the decay is:

Th22690 Ra222

88 + He42

State the value of the momentum of the thorium nucleus before the decay ..........................(1)

After the decay, both the alpha particle and the radium nucleus are moving.

Which has the greater speed? Justify your answer.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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What can be said about the directions of travel of the two particles?

...............................................................................................................................................

...............................................................................................................................................(3)

(Total 6 marks)

123. Add the quark content of the proton to column (ii) of the table below.

(i)

particle

(ii)

quark content

(iii)

antiparticle

(iv)

quark content

proton

– d u

K0 d s

Complete column (iii) to give the antiparticles of the particles in column (i).

Complete column (iv) to show the quark content of the antiparticles.(Total 5 marks)

124. A satellite S orbits the Earth once every 87 minutes.

Show that its angular speed is approximately 1 × 10–3 radians per second.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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In the space on the right draw a free-body force diagram for the satellite in the position shown.

E a rth

S

(1)

With reference to your free-body force diagram, explain why the satellite is accelerating.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

The radius of the satellite’s orbit is 6500 km. Calculate the magnitude of its acceleration.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Acceleration = ................................................(2)

(Total 6 marks)

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125. The diagram shows a high-speed alpha particle entering the space between two charged plates in a vacuum.

+ 2 0 00 V

0 V

p artic le

Add to the diagram the subsequent path of the alpha particle as it passes between the plates and well beyond them.

(3)

The gap between the plates is 10 mm. Calculate the magnitude of the electric force on the alpha particle as it passes between the plates.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Electric force = ....................................................(3)

(Total 6 marks)

126. In London the Earth’s magnetic field has a magnetic flux density of 4.8 × 10–5 T at 66  to the horizontal as shown in the diagram.

6 6 º

E a rth 's m ag n etic f ie ld

E ar th 's surfac e

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Calculate the magnitude of the horizontal component of the Earth’s magnetic field in London.

...............................................................................................................................................

...............................................................................................................................................

Horizontal component = ......................................(2)

For a conductor of length I moving at a speed i) perpendicular to a field of flux density B, the induced voltage V between the ends of the conductor is given by

V = Bl

A metal scaffolding pole falls from rest off a high building. The pole is aligned horizontally in an east-west direction. The Earth’s magnetic field lines at this point lie in a north-south direction.

D irec tio no f fa l l

2 .5 m

Calculate the induced voltage across the pole 2.0 s after it started to fall.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Induced voltage = ................................................(3)

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What would be the induced voltage after 2.0 s if the pole were aligned in a north-south direction? explain your answer.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 7 marks)

127. The simplified diagram shows the ‘dees’ of a cyclotron connected to a high frequency alternating supply. The dashed line shows the path of an accelerated proton. In the shaded region a uniform magnetic field B of flux density 0.80 T acts upwards out of the paper.

P ro to nb eam

P ro to n so u rce

H ig h freq u e n cy su p p ly

(i) Explain why the magnetic field must be upwards out of the paper when accelerating protons.

(ii) By considering a proton of mass m and charge e (1.6 × 10–19 C) moving in a circle of radius r in the cyclotron, show that the time t taken to complete one semicircle is given by

Bemt

(5)

(iii) Describe how the energy of the proton is increased in a cyclotron. Give one reason why the energy cannot be increased indefinitely. You may be awarded a mark for the clarity of your answer.

(4)

(iv) Show that the gain in energy of a proton accelerated through a potential difference of 12

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kV is about 2 × 10–15 J.

(v) The kinetic energy of a proton circling at a radius r can be expressed as

mreB

2k.e.

222

Calculate the radius of the circle in which a proton will be moving after being accelerated 850 times across a potential difference of 12 kV.

(4)(Total 13 marks)

128. Bubble chambers can be used to observe the tracks of charmed particles through magnetic fields. As charged particles pass through the liquid they cause ionisation which triggers the formation of bubbles, recording the tracks of the particles. The photograph below shows the spiral track of an electron in a bubble chamber.

State whether the electron is travelling clockwise or anticlockwise.

...............................................................................................................................................(1)

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Explain why the track is curved, and why it has a spiral shape.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

Take measurements from the photograph to estimate the maximum momentum of the electron in kg in kg m s–1. (Magnetic flux density = 4.0.T)

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Momentum =................................ kg m s–1

(3)

The diagram below shows a second set of tracks, produced by an event which occursat point X.

X

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It is thought that the event which occurs at X is:

photon electron + positron

Give two ways in which the tracks are consistent with this interpretation.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Explain how this event obeys two conservation laws.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 11 marks)

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129. A person at the equator of the Earth is moving, in a circle and therefore must have a centripetal acceleration.

R o ta tio n

E q u ato r

Explain why a person moving in a circle must have an acceleration.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

Show that the centripetal acceleration of a person at the equator is about 0.03 m s–2.(Radius of the Earth = 6.4 × 106 m.)

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

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For a person standing at the equator, the force R from the ground is slightly different from their weight mg as shown below. State and explain which of these forces is the larger.

R

m g

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

The size of the force R provides a measure of the apparent strength of the gravitational field. Show that the apparent field strength g at the equator differs from that at the poles by about 0.3%.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

(Total 7 marks)

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130. To restore a regular heart rhythm to a patient in an emergency, paramedics can use a machine called a defibrillator. The defibrillator uses a capacitor to store energy at a voltage of several thousand volts. Conducting ‘paddles’ are placed on either side of the patient’s chest, and a short pulse of current flows between them when the capacitor is discharged.

The graph below shows voltage against charge for the capacitor used in a defibrillator.

6 0 0 0

5 0 0 0

4 0 0 0

3 0 0 0

2 0 0 0

1 0 0 0

00 0 .5 0 .1 0 0 .1 5 0 .2 0 0 .2 5 0 .30 0 .3 5 0 .4 0

Vo ltag e /V

C h arg e /C

With reference to the graph, show that the energy stored in a capacitor is given by the

formula W = 21

QV.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Calculate the energy stored by the capacitor when charged to 5000 V.

...............................................................................................................................................

...............................................................................................................................................

Energy = .....................................................(1)

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The graph below shows how voltage varies with time as the capacitor’s discharged across a test circuit that has a resistance equivalent to that of the patient’s chest.

6 0 0 0

5 0 0 0

4 0 0 0

3 0 0 0

2 0 0 0

1 0 0 0

0

Vo ltag e /V

0 .0 1 .0 2 .0 3 .0 4 .0 5 .0 6 .0Tim e /m s

Use the graph to find the time constant for the circuit.

...............................................................................................................................................

...............................................................................................................................................

Time constant = ..........................................(2)

The total resistance of the circuit, including the paddles and chest, is 47 . Calculate the capacitance of the capacitor.

...............................................................................................................................................

...............................................................................................................................................

Capacitance = .............................................(2)

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The energy delivered to the patient’s chest is selected by the operator from these settings: 50 J, 180 J, 380 J. This is achieved inside the machine electronically, by allowing the discharge to proceed for an appropriate length of time.

On one particular setting, the discharge lasts for 2.0 ms. Calculate the energy left in the capacitor at this time.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Some energy loss occurs and roughly 60% of the energy leaving the capacitor during the discharge actually goes into the patient. Find which setting the operator has selected.

...............................................................................................................................................

...............................................................................................................................................

Energy setting = .................................(2)

(Total 11 marks)

131. One type of particle detector at CERN consists of a thin wafer of silicon. On both sides of the wafer are aluminium electrodes, with a voltage of 100 V across them. The electrodes are 300 m apart. When a particle enters the wafer, it creates an electron/hole pair as shown (a hole acts like a positive electron).

3 0 0 m H o leE le c tro n

P ar tic le

E lec tro de

E lec tro de+ 1 0 0 V

0 V

Electric field = ....................................(2)

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Calculate the force due to this field on an electron in the wafer.

...............................................................................................................................................

...............................................................................................................................................

Force = ..................................(2)

Indicate on the diagram the direction of this force on the free electron shown. Explain why the force has this direction.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

The hole can move in the direction of the electric field, provided that it can gain enough energy from the field to move it from one atom to the next. The distance between atoms is2.8 × 10–10 m. Calculate how much energy the hole gains in moving this distance in the direction of the field.

...............................................................................................................................................

...............................................................................................................................................

Energy = ...................................(2)

(Total 8 marks)

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132. The dynamo torch, Figure 1, is operated by successive squeezes of the handle. These cause a permanent magnet to rotate within a fixed coil of wires, see Figure 2. Harder squeezes rotate the magnet faster.

NN

S

S

C o n n ec tin gw ires

H a n d le

B u lb

F ix e d co ilo f w ires

F ig u re 1 F ig u re 2

C ro ss-sec tio no fw ire sin c o il

M ag n etro ta t ing

(L in k ag e b e tw een h an d lean d m ag n e t n o t sh o w n )

On Figure 2 sketch the field of the permanent magnet.

Discuss the physics of how the torch works and the factors which affect the brightness of the bulb.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(Total 6 marks)

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133. A hydroelectric power station in North Wales uses a Pelton wheel to convert water power to electricity. A Pelton wheel has a series of bucket-shaped paddles around the rim. The water is directed onto the paddles at high speed from a series of nozzles as shown in the diagram.

B u c ke t-sh ap ed pa d d le

W a te r je tD am

2 5 0 mP elton w h ee l

B u ck e ts

N o zz le

W ate ro u t

The Pelton wheel uses bucket-shaped paddles which are curved in order to deflect a water jet through 180°. By considering momentum, explain why this will provide more force than a jet of water hittinc, a flat paddle and simply falling off.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

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The power station provides 500 kW of power. The water falls from a height of 250 m at a rate of 270 kg s–1. Calculate the percentage efficiency of the percentage efficiency of the station.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Efficiency = ........................................(3)

The manufacturers of the Pelton wheel cast it from a mixture of iron, chromium and nickel. By adjusting the quantities used they were able to produce a corrosion-resistant wheel. State and explain two other desirable properties for the material from which the wheel is made.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

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The power company invested one million pounds in this power station. There is an international agreement to encourage power generation using non-fossil fuels. Under this agreement the company will receive 4.74 p per kW h of electrical energy generated by the station.

Calculate the time, in years, to repay the initial investment, stating, one assumption made.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Time = .....................................

Assumption: .........................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

(Total 14 marks)

134. Two possible structures of the atom were proposed in the early 1900s.They were the Rutherford and “plum pudding” models, as shown.

= elec tro n

S m a ll d en se n uc leu s

R u the rfo rd m o de l: a sm all d e n sen u c le u s su rro u n d ed b y e lec tro n s

U n ifo rm p o s itiv e ch arg e

P lu m p u d d in g m o d el: e lec tro n sem b ed d ed in a reg io n o f u n ifo rm

p o sitiv e ch a rg e

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Geiger and Marsden scattered alpha particles off gold atoms. Outline the evidence from this experiment that supported Rutherford’s model.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

Suggest what Geiger and Marsden would have observed if the “plum pudding” model had been correct.

...............................................................................................................................................

...............................................................................................................................................

Explain your answer.

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 5 marks)

135. State what is meant by a fundamental particle.

...............................................................................................................................................

...............................................................................................................................................

Circle any fundamental particles in the following list.

positron; neutron; muon; K0 meson.(3)

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Explain why it is not possible to have a meson with a charge of +2. You may be awarded a mark for the clarity of your answer.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

(Total 6 marks)

136. A space station orbits the Earth once every 91 minutes. Calculate the angular speed of the space station.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Angular speed = .......................................................(3)

The space station orbit is 210 km above the surface of the Earth, which has a radius of6370 km. Find the acceleration of the space station.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Acceleration = ...............................................(3)

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A box of mass 4.1 kg is located inside the space station. What is the size and direction of the resultant force acting on the box in the space station?

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Resultant force = ...........................................(3)

(Total 9 marks)

137. The diagram is of a simplified cathode ray tube.

E le c tro n g u n

F ilam en t

1 0 k V

A n o d e

E v a cu a tedtu b e

S c ree n

P6 .3 V

An electron beam is produced by the electron gun in the tube. A beam of electrons emerges from the hole in the anode and strikes the screen at point P.

Explain why electrons are emitted from the surface of the filament.

...............................................................................................................................................

...............................................................................................................................................(2)

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Explain why the electrons move from the filament towards the anode.

...............................................................................................................................................

...............................................................................................................................................(1)

The potential difference between the filament and the anode is 10 kV. Calculate the energy in joules of an electron emerging from the hole in the anode.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Energy = ....................................................... H(2)

The electron beam forms a current of 1.5 mA. Show that the number of electrons passing through the hole in the anode is about 9 × 1015 per second.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Hence calculate the rate at which energy is being delivered to the screen by the beam of electrons.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Rate = .................................................(2)

(Total 9 marks)

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138. In 1932 Cockroft and Walton accelerated protons through a few hundred kilovolts and directed them at a lithium-7 target placed in a cloud chamber. The diagram illustrates the outcome of the experiment.

-p artic le

-p art ic le

P ro to n

L ith iu m fo ilE n d o f tra ck

E n d o f trac k

(a) (i) What evidence is there in the diagram that the two -particles have the same initial energy?

(ii) Write a nuclear equation for this event.(4)

(iii) Calculate the kinetic energy of the pair of -particles in joules, given

mass of proton = 1.007 28 umass of lithium nucleus = 7.014 37 u

mass of -particle = 4.001 50 u

State any assumption you make.(4)

(Total 8 marks)

139. A lambda particle enters a detection chamber, and decays, at point C, into a pion (which has charge –1) and a proton. The lambda particle itself leaves no visible track. A magnetic field acts at right angles to the plane of the diagram.

P ro to n

P io n

4 9 °C

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Explain how the diagram confirms that the pion is negatively charged.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(2)

State the charge carried by the lambda particle, explaining your reasoning.

...............................................................................................................................................

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...............................................................................................................................................(2)

Explain how you can deduce from the diagram that the proton has more momentum than the pion.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

The angle between the proton and the pion tracks at point C is 49°. The momentum of the proton is 6.0 × 10–18 kg m s–1, and the momentum of the pion is 5.0 × 10–18 kg m s–1.Use a scale drawing to find the magnitude of the momentum of the lambda particle.

(3)

231

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The quark composition of two of the three particles is as follows:

pion du lambda uds

Particles composed of quarks are classified as either baryons or mesons. Tick the correct classification for each of these two particles.

baryon meson

pion .............. ...........

lambda ............. ...........(2)

The charge of an up quark (u) is + e32

.

Deduce the charge of a down quark (d).

...............................................................................................................................................(1)

(Total 12 marks)

232

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140. A large current such as that in a power station or power line (e.g. 2000 A) is hard to measure using a conventional meter simply connected in series. The usual technique makes use of the fact that this current is alternating. A ring of iron is clamped round the wire whose current (I1 in the diagram) is to be measured. A coil with 1000 turns is wound round the iron. An induced current flows in this coil; by measuring this current (I2) with a conventional meter, it is possible to calculate the value of I1.

I

I

A

Iro n r in g

P ow er lin e

2

1

Suggest a reason why it is difficult to measure a large current with a conventional meter in series in the circuit.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

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Explain how the alternating current I1 causes the current I2.

...............................................................................................................................................

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...............................................................................................................................................

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...............................................................................................................................................(4)

(Total 5 marks)

141. In 1998 NASA launched the probe called Deep Space 1. Once in orbit, this probe was the first to use a solar powered ion drive to propel it on its mission.

The diagram shows the main features of the ion drive.

+

+

+

++

+

+

+

++

+

+

+

+

+

+

P ositiv ee lec tro d e+ 1 0 6 0 V

N eg a tiv ee lec trod e– 2 2 5 V

Io nso u rce A cce le ra to r

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Atoms of xenon are ionised and then accelerated until they are ejected out of the rear of the probe, providing the means of propulsion.

Explain how the ions are accelerated.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

A xenon atom is ionised by the loss of a single electron. Show that its speed after being accelerated is about 4 × 104 m s–1.

Mass of xenon ion = 2.20 × 10–25 kg.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

The mass of xenon ejected in one second is 2.10 × 10–6 kg. Calculate the thrust on the space probe.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Thrust = ....................................................................(3)

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Simply firing xenon ions into space would leave the probe negatively charged. Suggest a reason why this would lead to reduced thrust.

...............................................................................................................................................

...............................................................................................................................................(1)

Chemical rockets eject their propellant at about a tenth of the velocity achieved by ion drives, but produce much greater thrust by ejecting more than a thousand kilograms per second.

Suggest why ion drives may be preferable for missions extending over long distances and periods of time.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 12 marks)

142. The following passage describing the inhabited part of the spaceship Discovery is adapted from 2001: A Space Odyssey by Arthur C. Clarke.

The space ship travelling through deep space contained a slowly rotating drum, ten metres in diameter. As it made one revolution every ten seconds, this produced an artificial gravity equal to that of the moon.

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Diagram 1 below represents an astronaut standing on the surface of the moon.Diagram 2 represents the astronaut standing inside the rotating drum as described in the passage.

D ia g r am 1 D ia g ra m 2

M o o n 's su rfac e

W eig h t

R o ta tio n

D ru m

Complete the diagrams by adding arrows to show any other forces acting on the astronaut.(2)

Discuss the extent to which the astronaut in the rotating drum would experience an artificial gravity equivalent to the gravity of the moon.

Gravitational field strength on the moon = 1.6 N kg–1.

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...............................................................................................................................................(5)

(Total 7 marks)

237

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143. A student has four identical lamps. She connects up circuit 1. Using 5 V the lamp flashes briefly when the switch is moved from left to right. She then connects up circuit 2. Using10 V with this arrangement, each of the four lamps gives a similar flash to the lamp in circuit 1.

C C

C irc u it 1 C ircu it 2

5 V 1 0 V

1 0 V 1 0 V

Discuss the physics of what the student has observed.

...............................................................................................................................................

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...............................................................................................................................................

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...............................................................................................................................................(6)

(Total 6 marks)

238

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144. The diagram shows an experiment with two trolleys.

0 .9 5 k g A B 1 .4 0 k g

A B

1.2 0 m s – 1

Initially the trolleys are at rest, in contact, on a horizontal bench. A spring-loaded piston is then released in one trolley, pushing the trolleys apart.

Describe an experimental technique by which you could determine accurately the speeds of the trolleys after they separate.

...............................................................................................................................................

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...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(3)

State the total momentum of the trolleys as they move apart, and explain your answer.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

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The masses of A and B are 0.95 kg and 1.40 kg respectively. B moves off at 1.20 m s–1. Calculate the speed of A.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Speed .............................................................(3)

(Total 8 marks)

145. State one similarity and one difference between a proton and an antiproton.

Similarity ..............................................................................................................................

Difference .............................................................................................................................

...............................................................................................................................................(2)

Write down two particle-antiparticle pairs of leptons.

...............................................................................................................................................

...............................................................................................................................................(2)

What happens when a particle and its antiparticle collide?

...............................................................................................................................................

...............................................................................................................................................(1)

(Total 5 marks)

240

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146. The electron in a hydrogen atom can be described by a stationary wave which is confined within the atom. This means that its de Broglie wavelength must be similar to the size of the atom, of the order of 10–10 m.

Calculate the speed of an electron whose de Broglie wavelength is 1.0 × 10–10 m.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Speed = .........................................................

Calculate the kinetic energy of this electron, in electron volts.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Kinetic energy = ...................................... eV(5)

When radiation was first discovered, it was suggested that the atomic nucleus must contain electrons. However, it was soon realised that this was impossible because such electrons would possess far too much energy to be bound within the nucleus. Using the ideas of the earlier parts of this question, suggest why an electron confined within the nucleus would have a very high energy.

...............................................................................................................................................

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...............................................................................................................................................(2)

(Total 7 marks)

241

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147. State Faraday’s law of electromagnetic induction.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Microphones convert longitudinal sound waves into electrical signals, which can be amplified. One type of microphone consists of a flexible diaphragm connected to a coil of wire, which is near a cylindrical magnet.

R ig idfra m e F lex ib le

d iap h ra g m

C o il

To am p lifie r

C y lin d r ic a lm ag n et S

N

N

242

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Describe how sound waves are converted into electrical signals. You may be awarded a mark for the clarity of your answer.

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...............................................................................................................................................(4)

(Total 6 marks)

148. A defibrillator is a machine that is used to correct irregular heartbeats by passing a large current through the heart for a short time. The machine uses a 6000 V supply to charge a capacitor of capacitance 20 F. The capacitor is then discharged through the metal electrodes (defibrillator paddles) which have been placed on the chest of the patient.

Calculate the charge on the capacitor plates when charged to 6000 V.

...............................................................................................................................................

Charge = ..........................................................(2)

Calculate the energy stored in the capacitor.

...............................................................................................................................................

...............................................................................................................................................

Energy = .......................................................(2)

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When the capacitor is discharged, there is an initial current of 40 A through the patient.

Calculate the electrical resistance of the body tissue between the metal electrodes of the paddles.

...............................................................................................................................................

...............................................................................................................................................

Resistance = ...............................................(1)

Assuming a constant discharge rate of 40 A, calculate how long it would take to discharge the capacitor.

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...............................................................................................................................................

...............................................................................................................................................

Time = ..........................................................(2)

In practice the time for discharge is longer than this calculated time. Suggest a reason for this

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(1)

(Total 8 marks)

244

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149. One practical arrangement for verifying Coulomb’s law is to use a lightweight, negatively-charged, freely-suspended ball. It is repelled by the negative charge on a larger sphere that is held near it, on an insulated support. The small angle of deflection is then measured.

r

C h arg edsph e re

C h arg edsu sp en d e d b a ll

T h rea d

Draw a free-body force diagram for the suspended ball.

(3)

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The weight of the ball is W. Show that the force of repulsion F on the suspended ball is given by

F = W tan

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

A student takes several sets of readings by moving the larger sphere towards the suspended ball in order to increase the mutual force of repulsion between them. He measures the angle of deflection and the separation distance r in each case. He then calculates the magnitude of the force F.

Here are some of his results.

Force F/10–3 N 142 568

Distance r/10–3 m 36.0 27.0 18.0 9.0

Calculate the values that you would expect the student to have obtained for the missing forces, assuming that Coulomb’s law was obeyed.

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Write your answers in the table.(4)

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Suggest why, in practice, it was necessary for the student to take measurements quickly using this arrangement.

...............................................................................................................................................

...............................................................................................................................................(1)

(Total 10 marks)

150. (i) A 4700 F capacitor is charged to 25 V and discharged through a tightly wound bundle of fine insulated wire.

V2 5 V

4 7 0 0 F

++

B u nd le o ffin e w ire

Calculate the energy dissipated in the wire.

Explain why it would be difficult to use this arrangement to demonstrate that Wc V2 for a range of potential differences up to about 50 V. You may be awarded a mark for the clarity of your answer.

(6)

247

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(ii) The graph shows how the charge on the capacitor varies with time as it discharges.

1 2 0

1 0 0

8 0

6 0

4 0

2 0

00 20 4 0 6 0 8 0

t/m s

Q /m C

State what name is given to this shape of graph and name another physical phenomenon which gives rise to graphs of this shape.

Showing your working, determine a value for the resistance of the bundle of wire.(6)

(Total 12 marks)

248

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151. The family of quarks is shown below, together with the charge and mass of each.

quark charge mass (GeV/c2)

up32 0.005

down31– 0.01

strange32 0.2

charm32 1.3

bottom31– 4.3

top32 180

What is meant by “charge = 32 ”?

...............................................................................................................................................

...............................................................................................................................................(2)

Calculate the mass of the strange quark in kilograms.

...............................................................................................................................................

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...............................................................................................................................................

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Mass = ................................................. kg(2)

What would be the charge and mass of the anti-particle to the charm quark? (Use the same units as in the table above.)

...............................................................................................................................................

...............................................................................................................................................(2)

249

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The top quark was predicted by theoretical physicists several years before it was actually found experimentally in 1994. What made them confident that the top quark existed?

...............................................................................................................................................

...............................................................................................................................................(1)

Give one reason why it took such a long time to find experimental evidence for the top quark.

...............................................................................................................................................

...............................................................................................................................................(1)

In their search for the top quark, physicists thought that another particle called the W might decay while stationary into one top and one bottom quark.

They predicted “The resulting top quark moves off relatively sluggishly on one side while the lighter bottom quark travels more rapidly in the opposite direction”.

Using an appropriate conservation law, explain why the top quark moves off more sluggishly than the bottom quark.

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...............................................................................................................................................(3)

(Total 11 marks)

152. In order to monitor the performance of a motor, it is necessary to measure its rate of rotation. A simple sensor consists of a small bar magnet attached to the output shaft of the motor. A coil of wire is placed so that the magnet rotates close to it as shown below.

NS

C o il

M a gn e t

R o ta tin gsh af t

To c .r.o .

250

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The voltage induced across the coil is displayed on a c.r.o. (cathode ray oscilloscope). The c.r.o. screen is shown below.

1 2 3 4

NS

2 0 m V

5 m s

F ig u re i

Explain how the movement of the magnet produces the voltage shown. As part of your explanation, fill in the three empty boxes (2, 3 and 4) below figure (i) to show the corresponding positions of the magnet.

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The rotation rate of the shaft is now doubled. The c.r.o. settings are not changed. This produces the c.r.o screen shown below.

2 0 m V

5 m s

F ig u re i i

Explain the differences between figure (i) and figure (ii).

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(3)

The shaded area in figure (i) is equal to

2 × (number of turns on coil) × (flux at one end of magnet)

The coil has 240 turns. Show that the flux at each end of the magnet is about 3 × 10–7 Wb.

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...............................................................................................................................................(3)

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The dimensions of the end of the bar magnet are 1.0 cm × 0.5 cm. Calculate an approximate value for the magnetic flux density at the end of the bar magnet.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Magnetic flux density = ................................................(2)

(Total 12 marks)

253

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153. It has been suggested that the centripetal force causing the Moon to orbit the Earth might be the result of electrical attraction and not gravitational attraction at all. Assuming the necessary force could arise as a result of the Earth and the Moon carrying equal charges (of opposite sign), show that the magnitude of these charges would have to be about 6 × 1013C.

Data: Mass of Moon = 7.4 × 1022 kgRadius of Moon’s orbit = 3.8 × 108 mTime of Moon’s orbit = 27 days

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...............................................................................................................................................(Total 6 marks)

254

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¼ 154. An atom of antihydrogen (a positron orbiting around an antiproton) has been produced.

Is an atom of antihydrogen positive, negative or neutral?

...............................................................................................................................................(1)

State the quark composition of an antiproton.

...............................................................................................................................................(1)

Show that an antiproton has a charge of –1.

...............................................................................................................................................

...............................................................................................................................................(1)

Explain why it is extremely difficult to store antimatter.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Complete the following quark table.

Q u ark s C h arg e

u p

d o w n

ch arm

str an g e

+ 2/3

– 1 /3(1)

Selecting from the shaded boxes only, use the table to deduce the quark composition of the following particles.

(i) A neutral strange meson

....................................................................................................................................

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(ii) A positive charmed meson

....................................................................................................................................

(iii) A neutral strange baryon

....................................................................................................................................(3)

(Total 9 marks)

155. Use the laws of conservation of charge and baryon number to decide whether the following reactions are possible or not possible. In each case show how you applied the laws. Pions( +, – and 0) are mesons.

(i) – + p n + – + + + 0

....................................................................................................................................

....................................................................................................................................

....................................................................................................................................

(ii) p + p p + p + p + p

....................................................................................................................................

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....................................................................................................................................(Total 4 marks)

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156. A tennis ball connected to a long piece of string is swung around in a horizontal circle above the head of a pupil.

The pupil feels that there is a tension in the string and argues that for equilibrium there must be an outward “centrifugal” force acting on the ball. Criticise his argument and explain why there is a tension in the string.

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...............................................................................................................................................(5)

The pupil lets go of the string. Draw a free-body force diagram for the ball at the instant after release.

(1)(Total 6 marks)

257

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157. In February 2000 scientists at CERN announced that they had made some “quark-gluon plasma” (QGP) - the extremely dense energetic matter that was present throughout the universe about 1 s after the Big Bang. They did this by colliding lead ions in the accelerator.

A particular isotope of lead (symbol Pb) has 82 protons and 124 neutrons in its nucleus.

Complete the symbol for this particular nucleus.

Pb................

What other particles are present in a neutral atom of this lead isotopes

...............................................................................................................................................(1)

When QGP existed in the early universe, all the particles listed in the table below were present.

Quarks Leptons

Name Symbol Charge Name Symbol Charge

up u +2/3 electron e– –1down d –1/3 electron-neutrino ve 0

charm c +2/3 muon –1strange s –1/3 muon-neutrino v 0

top t +2/3 tau – –1bottom b –1/3 tau-neutrino v 0

Protons and neutrons are made entirely of up and down quarks. Show how an appropriate number of quarks can combine to give the correct charge for a proton.

...............................................................................................................................................

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...............................................................................................................................................(2)

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Explain briefly what circumstances are required for the remaining quarks in the table to be created.

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...............................................................................................................................................(2)

The early universe also contained positrons. Describe how the positron relates to one of the particles in the table.

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...............................................................................................................................................(2)

(Total 8 marks)

259

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158. The diagram shows a solar sail, a possible method of propelling spacecraft.

The solar sail uses “radiation pressure” caused by the momentum of photons of sunlight as they strike the sail. A sail with an area of 1.5 × 106 m2 could be used to propel a spacecraft of mass 1.2 × 103 kg.

The energy E and momentum p of a photon are related by the expression E = pc, where c is the speed of light.

Calculate the total momentum of the photons striking 1 m2 of sail in one second. Assume the solar radiation flux (intensity) is 1400 W m–2.

...............................................................................................................................................

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...............................................................................................................................................

Momentum = ............................................................(2)

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Hence find the force exerted on the whole sail if it is completely non-reflective so that all of the incident light is absorbed.

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Force = ...................................................................................(2)

Explain why this force is doubled if a totally reflective material is used.

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...............................................................................................................................................(2)

An advantage of this form of propulsion is that it can be used for long periods of time allowing high speeds to be attained. Calculate the maximum increase in speed during one week, using a non-reflective sail. Assume the solar radiation flux remains constant during this time. 1 week = 604 800 s.

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Maximum speed increase = ...............................................................(3)

(Total 9 marks)

261

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159. The timer on an electric toaster uses a resistor-capacitor circuit. When the bread is lowered, switch S1 is closed and the capacitor C starts to charge up. When the voltage across it reaches 4.0 V, another circuit is activated which makes the toast pop up, and at the same time switch S1 is opened and switch S1 is closed for a few seconds (to discharge the capacitor). The resistor R can be varied. The capacitance C = 100 F.

6 .0 V

S

S

R

CTo p o p -u pc ircu it

1

2

Calculate the energy stored in the capacitor when the voltage across it reaches 4.0 V.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Energy stored = ........................................................(2)

Which parts of this circuit will transfer this energy to the surroundings at the end of the toasting cycle?

...............................................................................................................................................

...............................................................................................................................................(1)

Discuss whether this energy transfer process may damage the toaster.

...............................................................................................................................................

...............................................................................................................................................(1)

262

Page 263: Phys 4 Qs

The toaster is set so that switch S1 opens after 200 s. Complete the graph below to show how the voltage across the capacitor will vary with time from the moment (at t = 0 s) when S1 is closed.

6 .0

4 .0

2 .0

00 1 0 0 2 0 0 3 0 0 t/s

p .d ./V

(3)

By estimating the time constant for the circuit, calculate an approximate value for Rwhen C = 100 F.

...............................................................................................................................................

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...............................................................................................................................................

R = ............................................................................(2)

Discuss the effect of increasing the resistance, R.

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...............................................................................................................................................(2)

(Total 11 marks)

263

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160. There have been several space missions experimenting with tethered satellites. In a 1992 mission, the tethered satellite was connected to the shuttle Atlantis by a long, conducting cable, the satellite being in the higher orbit. As the shuttle orbited through the Earth’s magnetic field, an e.m.f. was induced in the conducting cable.

The shuttle, cable and satellite were all moving through the ionosphere, which contains many charmed particles. The charged particles were able to complete a circuit, allowing a current to flow through the cable. One result of this current was that the orbit height of the shuttle, cable and satellite gradually became less.

Explain

(a) the origin of the induced e.m.f.,

(b) the reduction in the orbit height due to the flow of current.

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....................................................................................................................................(Total 5 marks)

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161. A model of a fairground ride consists of a track with a circular loop in it of radius 0.05 m. A model vehicle is rolling freely on a track which has negligible resistance to motion. The vehicle is raised to a certain height above the level of the top of the loop and then released.

0 .5 0 m

N O T T O S C A L E

x

The vehicle will not fall off the track at the top of the loop if its centripetal acceleration at that point is greater than g. Calculate the minimum height x above the top of the loop (marked x on the diagram) from which the vehicle can be released and still complete the loop while staying in contact with the track.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

x = .............................................................................(Total 5 marks)

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162. State the principle of conservation of linear momentum.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(2)

This principle is a consequence of two of Newton’s laws of motion. Which two?

..............................................................................................................................................(1)

In one experiment to test the principle of conservation of momentum, a moving trolley collides with and sticks to an identical trolley which is initially at rest on a horizontal bench. Describe how you would check whether momentum was conserved.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(4)

A student performing this experiment found that the final momentum was always slightly smaller than the initial momentum. Assuming that the measuring technique was accurate, suggest a reason for this.

..............................................................................................................................................

..............................................................................................................................................(1)

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In a test laboratory, a car is crashed into a concrete wall and comes to rest. There is no damage to the wall. Explain how the principle of conservation of momentum applies to this situation.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(2)

(Total 10 marks)

163. State the relationship between current and charge

..............................................................................................................................................

..............................................................................................................................................(1)

Two students are studying the charging of a capacitor using the circuit shown. The voltmeter has a very high resistance.

V

m AS

9 .0 V

R

R h eo sta t w h ich is co n tin u a llya d ju s ted to ke ep cu rre n tc o ns tan t

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The capacitor is initially uncharged. At time zero, one student closes switch S. She watches the milliammeter and continually adjusts the rheostat R so that there is a constant current in the circuit. Her partner records the voltage across the capacitor at regular intervals of time. The graph below shows how this voltage changes with time.

10

8

6

4

2

00 1 0 2 0 3 0 4 0

V /V

t /s

Explain why the graph is a straight line.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(2)

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The capacitance used was 4700 F. Use the graph to determine the charging current.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

Current =......................................................(3)

In order to keep the current constant, did the student have to increase or decrease the resistance of the rheostat as time passed? Explain your answer.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(3)

The students repeat the experiment, with the capacitor initially uncharged. The initial current is the same as before, but this time the first student forgets to adjust the rheostat and leaves it at a fixed value. Draw a second graph on the same axes to show qualitatively how the voltage across the capacitor will now change with time.

(2)(Total 11 marks)

164. A beam of electrons is directed at a target. They are accelerated from rest through 12 cm in a uniform electric field of strength 7.5 × 105 N C–1.

Calculate the potential difference through which the electrons are accelerated.

..............................................................................................................................................

..............................................................................................................................................

Potential difference = .................................

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Calculate the maximum kinetic energy in joules of one of these electrons.

..............................................................................................................................................

..............................................................................................................................................

Maximum kinetic energy = ................................................(4)

Calculate the maximum speed of one of these electrons.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

Maximum speed = .......................................(2)

Draw a diagram to represent the electric field close to an isolated electron.

(2)(Total 8 marks)

165. A metal framed window is 1.3 m high and 0.7 m wide. It pivots about a vertical edge and faces due south.

Calculate the magnetic flux through the closed window. (Horizontal component of the Earth’s magnetic field = 20 T. Vertical component of the Earth’s magnetic field = 50 T.)

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

Flux =.......................................(2)

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The window is opened through an angle of 90° in a time of 0.80 s. Calculate the average e.m.f. induced.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

e.m.f. =...............................................(2)

State and explain the effect on the induced e.m.f. of converting the window to a sliding mechanism for opening.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(2)

(Total 6 marks)

166. A car travelling at 30 m s–1 collides with a wall. The driver, wearing a seatbelt, is brought to rest in 0.070 s.

The driver has a mass of 50kg. Calculate the momentum of the driver before the crash.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

Momentum = .........................................................(2)

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Calculate the average resultant force exerted on the driver during impact.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

Average resultant force = .......................................(3)

Explain why the resultant force is not the same as the force exerted on the driver by the seatbelt.

..............................................................................................................................................

..............................................................................................................................................(1)

(Total 6 marks)

167. The following strong interaction has been observed.

K– + p n + X

The K– is a strange meson of quark composition su .

The u quark has a charge of +2/3.

The d quark has a charge of –1/3.

Deduce the charge of the strange quark.

..............................................................................................................................................(1)

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Use the appropriate conservation law to decide whether particle X is positive, negative or neutral.

..............................................................................................................................................

..............................................................................................................................................(2)

Is particle X a baryon or a meson? Show how you obtained your answer.

..............................................................................................................................................

..............................................................................................................................................(2)

State the quark composition of X. Justify your answer.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(3)

(Total 8 marks)

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168. The graph below shows how the momentum of this lorry varies over the first Minute.

8 0

6 0

4 0

2 0

01 0 2 0 3 0 40 5 0 6 0 t/s

M o m en tu m /1 0 N s4

Define momentum.

...............................................................................................................................................

...............................................................................................................................................(1)

State the physical quantity represented by the slope of this graph.

...............................................................................................................................................

...............................................................................................................................................(1)

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Determine the magnitude of this quantity at t = 20 s.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Explain the shape of this graph.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 7 marks)

169. Some radioisotopes for use in hospital treatments have short half-lives. These radioisotopes are manufactured in the hospital where they will be used. Some hospitals use a relatively cheap machine such as a cyclotron to produce a beam of high energy protons. This beam is allowed to collide with the target material to produce the radioisotope.

N o rth P o le

D ee

D e eB ea m

M a g n etic f ie ld

S o u th P o le

H ig h fre q ue n cya lte rn a tin g v o lta g e

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In a cyclotron. the protons are accelerated by a high frequency alternating voltage. A uniform magnetic field. of strength 200 mT. causes the protons to follow a circular path which increases in radius as the protons gain kinetic energy.

Immediately before the protons leave the cyclotron they are moving in a circular arc of radius 1.5 m.

Show that the speed of these protons is about 10% of the speed of light.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(3)

Calculate the approximate time taken for the proton to complete the last semi-circle of its orbit.

...............................................................................................................................................

Time =..........................................................(2)

Hence calculate the frequency of the accelerating p.d.

...............................................................................................................................................

Frequency =.................................................(1)

(Total 6 marks)

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170. Most types of microphone detect sound because the sound waves cause a diaphragm to vibrate. In one type of microphone this diaphragm forms one plate of a parallel plate capacitor. As the diaphragm plate moves. the capacitance chances. Moving the plates closer together increases the capacitance. Moving the plates further apart reduces the capacitance.

This effect is used to produce the electrical signal. The circuit shown below consists of a 3 V supply, an uncharged capacitor microphone C. a resistor R. and a switch S.

The switch S is closed. Sketch a graph of the voltage across the capacitor microphone against time. Assume that the capacitor microphone is not detecting any sound.

V /V

3

2

1

R C t(3)

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Explain why movement of the diaphragm causes a potential difference (the signal) across R.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

(Total 7 marks)

171. The results of particle collisions are observed using particle detectors. Sometimes the products of these collisions are themselves unstable and decay to give further particles; the products of decay can be photons.

In one collision, a stationary º meson is produced which then decays to give two gamma ray photons. The rest mass of the meson is 135 MeV/c2.

º +

Calculate the wavelength of each photon.

...............................................................................................................................................

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Wavelength =............................................(5)

(Total 5 marks)

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172. A mass spectrometer is used to determine the relative amounts of ions of different masses in a sample of material.

A diagram of a new type of mass spectrometer is shown below. In this mass spectrometer, a very short pulse of laser light is directed at the sample of material, which becomes ionised. Each ion has a charge of +1.6 × 10–19 C. This happens mid-way between a pair of parallel charged plates.

The time the ion takes to reach the detector depends on its mass. Thus the material in the original sample can be analysed.

L aser p u lse

P a th o f io n s

H o le in p la te

+ 4 k V

S am p le

0 V 0 V

P a ra lle lch arg ed p la te s

D etec to r

E v acu a te d c ha m b e r

Describe the movement of an ion from the sample to the detector. Hence explain why the time an ion takes to reach the detector depends on its mass. You should include relevant equations.

(Allow one lined page)(Total 7 marks)

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173. According to Newton’s second law of motion, the rate of change of momentum of an object is proportional to the resultant force F acting on it. Show how this statement leads to the equation

F = ma

where m is the mass and a the acceleration of the object.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

When jumping from a height on to a hard surface, it is advisable to bend one’s knees on landing.

How does bending the knees affect the time one takes to come to rest?

...............................................................................................................................................

............................................................................................................................................... (1)

With reference to Newton’s second law, explain why it is a good idea to bend one’s knees.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 7 marks)

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174. Explain why a body moving at constant speed in a circular path needs a resultant force acting on it.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

The diagram shows a student at the equator standing on a set of weighing scales, and a free-body force diagram for the student.

W eig h in g sca le s

S tu d en t

A B

N

Identify the bodies applying forces A and B.

...............................................................................................................................................

...............................................................................................................................................(2)

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Because of the Earth’s daily rotation the student is performing circular motion about the Earth’s axis. Calculate the angular speed of the student.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Angular speed =.................................(2)

The radius of the Earth is 6400 km. The student’s mass is 55 kg. Calculate the resultant force on the student.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Resultant force =......................................(3)

Force A is 539 N. Calculate the value of force B.

...............................................................................................................................................

...............................................................................................................................................

Force B =...................................

State, with a reason, the force indicated by the weighing scales.

...............................................................................................................................................

...............................................................................................................................................(3)

(Total 12 marks)

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175. A student assembles the circuit shown in which the switch is initially open and the capacitor uncharged.

9 .0 V

2 2 0 k

He closes the switch and reads the microammeter at regular intervals of time. The battery maintains a steady p.d. of 9.0 V throughout. The graph shows how the current I varies with the time t since the switch was closed.

5 0

4 0

3 0

2 0

1 0

00 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0

I

t/s

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Use the graph to estimate the total charge delivered to the capacitor.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Charge =.............................................(3)

Estimate its capacitance.

...............................................................................................................................................

...............................................................................................................................................

Capacitance =.........................................(2)

(Total 5 marks)

176. A circuit is set up as shown in the diagram

m A

R

V

C

s9 .0 V

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At t = 0 switch S is closed. Readings of the potential difference across the resistor are taken at regular intervals and the graph shown is obtained.

1 0

8

6

4

2

00 1 0 2 0 3 0 4 0

V /VR

t/s

Use the graph to estimate the time constant for this circuit.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

Time constant =..........................................(2)

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The initial current I0 = 0. 19 mA.

Calculate the resistance of resistor R and hence the capacitance of the capacitor C.

...............................................................................................................................................

...............................................................................................................................................

Resistance =....................................................

...............................................................................................................................................

...............................................................................................................................................

Capacitance =.....................................................(3)

Add to the graph a line showing how the potential difference across the capacitor varies with time over the same period.

(2)(Total 7 marks)

177. A horizontal metal rod, 1.5 m long, is aligned in an E W direction and dropped from rest from the top of a high building.

1 .5 m

D irec tio n o f fa ll

Calculate the e.m.f. induced across the falling rod 2.5 s after release. The horizontal component of the Earth’s magnetic field = 2.0 × 10–5 T.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

e.m.f. =......................................(3)

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Explain briefly why the magnitude of the vertical component of the Earth’s magnetic field is not required in this calculation.

...............................................................................................................................................

...............................................................................................................................................

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...............................................................................................................................................

...............................................................................................................................................(2)

(Total 5 marks)

178. The ‘London Eye’ is a large wheel which rotates at a slow steady speed in a vertical plane about a fixed horizontal axis. A total of 800 passengers can ride in 32 capsules equally spaced around the rim.

A simplified diagram is shown below.

G rou n d

P assen g erca p su le

B

C

D

6 0 m

0 .2 0 m s –1

A

On the wheel, the passengers travel at a speed of about 0.20 m s–1 round a circle of radius 60 m. Calculate how long the wheel takes to make one complete revolution.

...............................................................................................................................................

...............................................................................................................................................

Time = ..........................(2)

What is the change in the passenger’s velocity when he travels from point B to point D?

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...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

When one particular passenger ascends from point A to point C his gravitational potential energy increases by 80 kJ. Calculate his mass.

...............................................................................................................................................

...............................................................................................................................................

Mass =..........................(3)

On the axes below sketch a graph showing how the passenger’s gravitational potential energy would vary with time as he ascended from A to C. Add a scale to each axis.

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(3)

Discuss whether it is necessary for the motor driving the wheel to supply this gravitational potential energy.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

(Total 12 marks)

179. Define linear momentum.

...............................................................................................................................................

...............................................................................................................................................(1)

The principle of conservation of linear momentum is a consequence of Newton’s laws of motion. An examination candidate is asked to explain this, using a collision between two trolleys as an example. He gives the following answer, which is correct but incomplete. The lines of his answer are numbered on the left for reference.

1. During the collision the trolleys push each other.

2. These forces are of the same size but in opposite directions.

3. As a result, the momentum of one trolley must increase at the same rate as the momentum of the other decreases.

4. Therefore the total momentum of the two trolleys must remain constant.

In which line of his argument is the candidate using Newton’s second law?

.............................................(1)

In which line is he using Newton’s third law?

..............................................(1)

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The student is making one important assumption which he has not stated. State this assumption. Explain at what point it comes into the argument.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(2)

Describe how you could check experimentally that momentum is conserved in a collision between two trolleys.

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................(4)

(Total 9 marks)

180. One way of producing neutrons for experiments is to fire a beam of protons at a target of lithium metal. The interaction between a proton and a lithium nucleus produces a beryllium nucleus.

Complete the nuclear equation shown below which describes this reaction.

73 Li + p Be + n

(2)

Useful data:

Accelerating voltage for protons = 2.8 MVBeam current = 2.0 mAArea of lithium target = 1.2 × 10–3m2

All protons are stopped within 280 m of the target surface.

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Calculate the rate at which energy is transferred by the beam of protons to the target.

………………………………………………………………………………………………

………………………………………………………………………………………………

Rate of energy transfer = …………………………(2)

Show that energy is absorbed in the surface layer at the rate of 17 GW per cubic metre.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(2)

Suggest a problem this may cause.

………………………………………………………………………………………………

………………………………………………………………………………………………(1)

(Total 7 marks)

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181. Liquid crystal (LC) displays are found in digital watches and calculators. The display is made from two parallel pieces of glass separated by 1.0 × 10–5m with liquid crystal molecules between them. The glass is coated with conducting material.

The LC molecules have a permanent dipole - that is, they are positive at one end of the molecule and negative at the other. The normal state of these molecules is to be aligned parallel with the glass surfaces as in diagram A. If a voltage of 1.5 V is applied as shown, the molecules align with the electric field.

G lass p la te

G lass p la te

M ole cu les

1 .5 V

S

1 0 m + –+ –

A B

On diagram A, show the forces acting on the molecule as the switch S is closed.(1)

Explain why the molecules align with the field.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(2)

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On diagram B, draw field lines to represent the electric field in the central region of the plates.(2)

Calculate the strength of the electric field.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

Field strength = …………………………(2)

(Total 7 marks)

182. Fast modern passenger and car ferries are often twin-hull boats, propelled using water jets instead of conventional propellers. A pumping system throws water out backwards at speed. One such ferry is the Stena Lynx II, which sails between Fishguard in Wales and Rosslare in Ireland.

Some data about the Stena Lynx II:

Resistive forces at cruising speed = 8.0 × 105 NMass of water per second ejected by the jets = 60 000kg s–1

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Show that water must be thrown backwards at about 13 m s –1 while the boat is maintaining cruising speed.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(3)

The pumping system converts energy which is expended in two main ways: working against resistive forces and giving kinetic energy to the water thrown backwards.

Calculate the power expended against the resistive forces at the cruising speed of 20 ms–1.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

Power = …………………………(2)

Calculate the rate at which the water in the jets gains kinetic energy.

………………………………………………………………………………………………

………………………………………………………………………………………………

Rate = …………………………(2)

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Hence show that the overall efficiency of the pumping system at cruising speed is about 40%.

Data:

Fuel consumption of pumping system at cruising speed = 1.6 litres/second1 litre of fuel provides 3.4 × 107 J of energy when burnt

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(3)

(Total 10 marks)

183. Rahal is choosing a capacitor to use in an electronics project. From a catalogue she finds this information about the range of capacitors for sale

Catalogue letter Capacitance/F Maximum voltage/VU 15000 16V 33000 16W 68000 16X 220 400Y 470 400Z 1000 400

Which of the six capacitors above can store the greatest amount of energy? Justify your answer.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(3)

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The actual value of the capacitor Rahal will receive may be different from the value the catalogue states. The manufacturer guarantees that the maximum percentage difference below/above the catalogue value will be –10% / +50%. Rahal orders one of the 400 V 1000 F capacitors. Within what range will its actual value lie?

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(2)

When a capacitor is charged (with a p.d. across it), there is always a little current through the “insulator” between the plates - that is, the insulator is never perfect.

This current depends on the p.d. and the capacitor value. The catalogue says “Maximum leakage current 0.003 A per F per V”.

The next three questions are about one of the 16 V 68 000 F capacitors which is initially fully charged.

(i) Calculate the charge it stores initially.

………………………………………….……………………………………………

………………………………………….……………………………………………

Charge = ………………………….(1)

(ii) Show that the value of the maximum leakage current is about 3000 A.

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………(2)

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(iii) Make an estimate of the time it would take for this capacitor to discharge fully by leakage.Set out your reasoning clearly.

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………

………………………………………….……………………………………………(2)

(Total 10 marks)

184. Collisions between sub-atomic particles can be observed using a bubble chamber by taking a photograph of the tracks left by the particles as they move through the magnetic field in the chamber. Photons produce very few ions and so they cannot be seen in bubble chamber photographs.

This question is about the interaction between an atomic electron and a photon which has entered the chamber from the left in the direction shown. The photograph shows the result of this interaction.

e – e –

e +

P a th o fp h o to n

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The interaction has caused the release of the atomic electron and the creation of an electron-positron pair. The tracks of these three particles can be seen.

Explain how you can deduce that the magnetic field acts out of the plane of the photograph.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(2)

Explain which e– moves faster.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(1)

Measurements from the photograph show the initial radius of curvature of the positron to be r = 0.048 m. Calculate the momentum of the positron if the magnetic field strength is B = 5.4 × 10–3T.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

Momentum = ………………………..(2)

Explain why the path of the positron is a spiral.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(1)

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In interactions such as these, charge, energy and momentum are always conserved. For the interaction shown in the photograph, discuss the conservation of any two of these properties.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(5)

(Total 11 marks)

185. The ignition system in a car requires 25000 V to be applied to the spark plug to produce a spark in the combustion chamber. This voltage is produced from the car’s 12 V d.c. electric supply by using a type of transformer usually called the “ignition coil”. A circuit diagram of such a coil is shown below.

1 2 VS

F e wtu rn s

M an ytu rn s

To d is tr ib u to ran d sp a rk p lu g

In order to generate a pulse of high voltage at the spark plug, the switch S must be closed for a short period and then opened quickly.

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Use Faraday’s law to explain why a large voltage is generated in the secondary circuit when the switch is opened.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

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………………………………………………………………………………………………(Total 6 marks)

186. Read the following paragraph carefully and CIRCLE the correct response to the choices in the brackets.

Geiger and Marsden carried out an experiment to investigate the structure of the atom.

In this experiment

raysGammaparticlesBetaparticlesAlpha

were

scatteredrefracteddiffracted

by thin films of metals such as gold.

The experiment led to the conclusion that the atom had an

chargedpositivelychargednegatively

uncharged

nucleus of

diameter approximately

m10

m1010–

–15

and containing

masstheofmasstheofmost

masstheall

20001

of the atom.

(Total 5 marks)

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187. A small solenoid is placed at the centre of the large solenoid as shown. The small solenoid is connected to a digital voltmeter.

V

State what would be observed on the voltmeter when each of the following operations is carried out consecutively.

(a) A battery is connected across the large solenoid.

.....................................................................................................................................

.....................................................................................................................................

(b) The battery is disconnected.

.....................................................................................................................................

(c) A very low frequency alternating supply is connected across the large solenoid.

.....................................................................................................................................

.....................................................................................................................................(5)

(Total 7 marks)

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Page 302: Phys 4 Qs

188. Magnetic flux density B varies with distance beyond one end of a large bar magnet as shown on the graph below.

0 1 0 2 0 3 0

B /m T60

40

20

0

D is tan ce /m m

A circular loop of wire of cross–sectional area 16 cm2 is placed a few centimetres beyond the end of the bar magnet. The axis of the loop is aligned with the axis of the magnet.

Calculate the total magnetic flux through the loop when it is 30 mm from the end of the magnet.

...............................…............................................................................................................

...............................…............................................................................................................

...............................…............................................................................................................

Magnetic flux =............................................................

Calculate the total magnetic flux through the loop when it is 10 mm from the end of the magnet.

...............................…............................................................................................................

...............................…............................................................................................................

...............................…............................................................................................................

Magnetic flux =............................................................(3)

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Page 303: Phys 4 Qs

The loop of wire is moved towards the magnet from the 30 mm position to the 10 mm position so that a steady e.m.f. of 15 V is induced in it. Calculate the average speed of movement of the loop.

...............................…............................................................................................................

...............................…............................................................................................................

...............................…............................................................................................................

...............................…............................................................................................................

...............................…............................................................................................................

...............................…............................................................................................................

Speed =........................(3)

In what way would the speed of the loop have to be changed while moving towards the magnet between these two positions in order to maintain a steady e.m.f.?

...............................…............................................................................................................(1)

(Total 7 marks)

189. The following statements apply to a body orbiting a planet at constant speed and at constant height. Indicate whether each statement is true () or false (x).

Statement True/False

The body is travelling at constant velocity.

The body is in equilibrium because the centripetal force is equal and opposite to the weight.

The only force acting on the body is its weight.

The body’s acceleration towards the planet equals the gravitational field strength at the position of the body.

(Total 4 marks)

303

Page 304: Phys 4 Qs

190. State Lenz's law of electromagnetic induction

...............................…........................................................................................................…

...............................…........................................................................................................…

...............................…........................................................................................................…(2)

An exhibit at a science centre consists of three apparently identical vertical tubes, T1, T2 and T3, each about 2 m long. With the tubes are three apparently identical small cylinders, one to each tube.

B arm a g ne t

P la stictu b e

C o p p ertu b e

C o p p e rtub e

U n m a g ne tisediro n

B arm a g n et

T T T1 2 3

When the cylinders are dropped down the tubes those in ~T, and ~T2 reach the bottom in less than I second, while that in ~T3 takes a few seconds.

Explain why the cylinder in T3 takes longer to reach the bottom of the tube than the cylinderin T1

...............................…........................................................................................................…

...............................…........................................................................................................…

...............................…........................................................................................................…

...............................…........................................................................................................…

...............................…........................................................................................................…(5)

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Page 305: Phys 4 Qs

Explain why the cylinder in T2 takes the same time to reach the bottom as the cylinder in T1

...............................…........................................................................................................…

...............................…........................................................................................................…

...............................…........................................................................................................…(2)

(Total 9 marks)

191. A light aluminium washer rests on the end of a solenoid as shown in the diagram.

I

I

A lu m in iu mw ash e r

S o len o id

A large direct current is switched on in the solenoid. Explain why the washer jumps and immediately falls back.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………(Total 5 marks)

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Page 306: Phys 4 Qs

192. A satellite orbits the Earth once every 120 minutes. Calculate the satellite’s angular speed.

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

angular speed = .........................................................(2)

Draw a free-body force diagram for the satellite.

(1)

The satellite is in a state of free fall. What is meant by the term free fall? How can the height of the satellite stay constant if the satellite is in free fall?

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................(3)

(Total 6 marks)

193. Define capacitance.

..............................................................................................................................................

..............................................................................................................................................(2)

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Page 307: Phys 4 Qs

An uncharged capacitor of 200 F is connected in series with a 470 k resistor, a 1.50 V cell and a switch. Draw a circuit diagram of this arrangement.

(1)

Calculate the maximum current that flows.

...............................................................................................................................................

...............................................................................................................................................

Current ............................................................(2)

Sketch a graph of voltage against charge for your capacitor as it charges. Indicate on the graph the energy stored when the capacitor is fully charged.

(4)

Calculate the energy stored in the fully-charged capacitor.

...............................................................................................................................................

...............................................................................................................................................

Energy = ............................................................(2)

(Total 11 marks)

307