Revision Package for H2 J1

Revision Package for JC One H2 Physics

Section 1 Measurement

1. When expressed in terms of base units, the units of torque are the same as those of energy. Explain why it would nevertheless be inappropriate to measure torque in joules.

2. Why is it that, in the SI system of units, power cannot be defined using the equation

power = potential difference x current

3. A student wishes to determine the density ρ of a cylinder of mass M, height h and diameter of cross-section d, using the following formula:

M =

If the percentage of uncertainties of his measurements of M, d and h are ±4%, ±1% and ±0.5% respectively, what will be the percentage uncertainty of ρ?

A 1.5% B 2.5% C 5.5% D 6.5%

4 (a) Explain what is meant by a random error and give an example of a random error. [2]

(b) A student measured the internal diameter of a capillary tube using a travelling microscope. Explain why taking the mean of several microscope readings of the diameter tends to reduce random error. [2]

(c) Another student determined the internal diameter d of the same capillary tube by using a different approach. He introduced a thread of mercury into the capillary tube and measured the mass and length of the thread to be m = (2.23 ± 0.04)g and l = (19.8 ± 0.1)cm respectively. The density of mercury was assumed to be ρ = (13 600 ± 100)kg m-3.

(i) Calculate the value of d [2]

(ii) Determine the uncertainty in d [3]

(iii) Express d together with its uncertainty to the correct number of significant figures [1]

5. The radiancy RT is defined as the total energy emitted per unit time per unit area from a blackbody at thermodynamic temperature T. It was first stated empirically in 1879 in the form given by RT = σT4, where σ is called the Stefan-Boltzmann constant. Which of the following is a unit for σ?

A W m-2 K4 B J s m-2 K4 C kg s-3 K-4 D J s-1 m-2 K4

Section II Newtonian Mechanics

Kinematics

6 The graph shows how the velocity of a moving body varies with time.

Which one of the displacement-time graphs below could represent the same pattern of motion?

7

A ball-bearing X is projected horizontally from a certain point at the same time as a ball-bearing Y of the same size but twice the mass is released from rest and allowed to fall vertically from the same level. Which of the following will occur? (Air resistance may be neglected.)

A X and Y will hit the floor at the same time.

B X hits the floor while Y is halfway to the floor.

CY hits the floor while X is halfway to the floor.

DY will hit the floor just before X.

8 A body is accelerated from rest by a constant force.

Which graph best represents the variation of the body’s kinetic energy Ek with time t?

Floor

XY

9 The diagram shows the path of a ball.

Which pair of the following graphs best represents the variations of the horizontal and vertical speeds vH and vv of the ball with time t, assuming that air resistance is negligible?

Dynamics

10 The figure below shows a graph of the horizontal force applied to an object of mass 2 kg initially at rest on a smooth horizontal surface.

What is the speed of the object, in m s-1, after 1 second?

A 7.5 B 12.5 C 15.0 D 25.0

11 A helicopter of mass 5000 kg is rising with an acceleration of 2.4 m s 2. What thrust must be exerted on it by its rotor?(Assume g = 10 m s2)

A 6000 N B 12000 N C 17000 N D 62000 N

12 The graph shows the variation of force F acting on a body with time t.

The change in momentum of the body during this 4 s period is

A 2.5 N s B 5.0 N s C 7.5 N s D 12.5 N s

13 The diagram shows two masses, 10 kg and 20 kg respectively, joined by a light string which passes over a light frictionless pulley. The acceleration of free fall is g.

The acceleration of the masses is

B C g D

14. A student, holding a ball, is standing on a trolley moving at constant speed v towards the right on a frictionless surface. He conducts the following experiments

separately:(i) He throws the ball to the left and the final speed of the trolley is vA

(ii) He throws the ball to the right and the final speed of the trolley is vB

(iii) He drops the ball from rest and the final speed of the trolley is vC

Assuming there is negligible air resistance, which of the following best describes the relationship between vA ,vB, vC and v?

A vA = vB = vC = vB vA > vB > v > vC

C vA > vC > vB, v = vA

D vA > vC > vB, v = vC

15 The diagram shows a strobe photograph of a mark on a trolley X, moving from right to left, in collision with another trolley Y which had no mark on it.

After the collision both trolleys are in motion together.

Which one of the following is consistent with the photograph?

A Trolley Y had the same mass as trolley X and was initially stationary

B Trolley Y had a smaller mass than X and was initially moving from right to left

C Trolley Y had the same mass and was initially moving from left to right at the same speed as trolley X

D Trolley Y had the same mass and was initially moving from left to right at a higher speed than trolley X

Forces

16 A light shelf holds a weight W. The shelf is supported by a string and by the hinge R at the wall.

Which diagram, A, B, C or D, shows the direction of the force exerted on the hinge by the shelf?

17 A smooth sphere of weight W is suspended from a smooth wall by a string equal in length to its radius as shown in the diagram below.

The tension in the string is equal to

B C D

18 A uniform beam of length l is supported by two forces FA and FB.

The ratio of forces FA : FB is

A 1 : 4 B 1 : 2 C 1 : 1 D 2 : 1

·

W

T

Work, Energy and Power

19 An escalator can carry a maximum of 40 people of average weight 720 N. Each person is raised through a vertical height of 10 m in 40 s.

Neglecting friction, what minimum power, in kW, is required for the driving motor?

A 0.18 B 0.72 C 3.6 D 7.2

20 A trolley of mass 60 kg moves on a frictionless horizontal surface and has kinetic energy 120 J. A mass of 40 kg is lowered vertically onto the trolley. The total kinetic energy of the system is now

A 60 J B 72 J C 120 J D 144 J

21 A ball falls freely under gravity after being released from rest. A short time later it hits the ground. Neglecting air resistance, which graph best represents the variation of potential energy Ep

with time t?

22 A crate is pushed 10 m along a horizontal surface by a force of 80 N. The frictional force opposing the motion is 60 N.

What are the correct values for the increase in internal energy of the system and the additional kinetic energy of the crate?

Increase inInternal energy/J

Additional kinetic energy/J

ABCD

200200600600

600800200800

23 A body of mass m moves at constant speed v for a distance s against a constant force F. What is the power required to sustain this motion?

A mv B ½ mv2 C Fs D Fv

Structured Questions

24 (a) Define displacement, velocity and acceleration. [3]

(b) Derive, using your definitions of velocity and acceleration, (i) v = u + at(ii) v2 = u2 + 2as,

where v is the final velocity, u the initial velocity, a the acceleration, t the time and s the displacement travelled. State the assumptions made about a in these equations. [4]

(c) A rocket accelerates from rest at ground level at 7.0 m s for 30 s vertically. Calculate,

(i) the speed and height of the rocket 30 s after launch,

(ii) the maximum height if its fuel is used up after 30 s,

(iii) the speed of impact when it hits the ground,

(iv) the total time of flight. [6]

(d) A train has a normal operating speed of 50.0 m s. Assume that the train starts from rest and has a constant acceleration and deceleration of 0.400 m s-2 and 0.733 m s

respectively.

It can be shown that the time required to reach its normal operating speed and the time required for a train travelling at its operating speed to go to rest are respectively 125.0 s and 68.22 s.

The inhabitants of a certain town would like trains to make an additional stop at their station. The train would stand for two minutes to allow passengers to get on and off and further delay would be caused by having to slow down and speed up.

(i) Sketch speed-time graphs for a train that stops at the town and for a train that does not on the same axes.

(ii) Using your graphs, determine the additional distance travelled by the train that did not stop compared to the train that stops at the town.

(iii) Hence determine the total delay caused by making the additional stop. [7]

25 (a) (i) Define acceleration

(ii) Explain how it is possible for a body to undergo acceleration although its speed remains constant [3]

(b) A tile of mass 270 g, initially at rest, slides down a roof for a distance of 3.8m before falling off the roof. The tile experiences a resistive force of 0.40N while sliding. The roof is inclined at an angle of 25° to the horizontal, and its edge is 12.3m above the ground as shown below.

(i) Determine the speed of the tile just as it leaves the roof.

(ii) Determine how long it takes to hit the ground after leaving the roof.

(iii) Determine the horizontal distance from the edge of the roof at which the tile lands. [9]

(c) Car A stops at a red light. As the light turns green, it accelerates forward at 2.4 m s-2. At the exact same instant, car B passes by travelling at a constant speed of 60 km h-1.

(i) Determine the time taken for the cars to meet again

(ii) How far down the road will they meet?

(iii) Sketch the displacement-time graph for each car on the same axes, indicating the values you have obtained for (i) and (ii)

(iv) What was the average speed of car A for this time interval?

25

12.3m

ground

tile

roof

(v) Compare your answer in (iv) with the speed of car B and explain the result. [8]

26 A model rocket of initial mass 1.3 kg is fired vertically into the air. Its mass decreases at a constant rate of 0.23 kg s−1 as the fuel burns. The final mass of the rocket is 0.38 kg. The rocket rises to a height such that, during the flight, the gravitational field strength of the Earth may be considered to have the constant value of 9.8 N kg−1.

(a) Calculate

(i) the initial weight of the rocket,

(ii) the final weight of the rocket,

(iii) the time taken for the fuel to be burned. [3]

(b) The variation with time t of the upward force on the rocket during the first 3 seconds after firing is shown in Fig.25.

(i) On Fig.25, use the same scales to draw a line to represent the variation with time t of the total weight of the rocket during the first 5 seconds after firing.

(ii) Hence read off from Fig.25 the time delay between firing the rocket and the lift-off. [3]

(c) (i) Write down an equation to represent the relation between the resultant force F on the body, the time t for which the force acts and the change in momentum p of the body.

(ii) On Fig.25, shade the area of the graph which represents the change in momentum of the rocket during the first 3 seconds after the rocket is fired.

[3]

Fig.25

27 (a) A conveyor belt travelling at a speed of 3.0 ms-1 and at an angle of 20o to the horizontal has 18 kg of sugar dropped on to it each second as shown in Fig. 27

Fig. 27

Assuming that the sugar has negligible speed before reaching the belt, calculate

(i) the momentum gained in each second by the sugar, (ii) the force which the belt must exert on the sugar to accelerate it to the speed

of the belt, (iii) the work done per second by the belt on the sugar in exerting this force, (iv) the potential energy gained in each second by all the 36 kg of the sugar which

is on the belt. [6]

(b) From your answers to (a) find the extra power required by the driving motor when the belt is loaded rather than unloaded. [2]

28 (a) Starting with the definition of work, deduce the change in the gravitational potential energy of a mass, m when moved a distance h upwards against a gravitational field strength g. [3]

(b) By using the equations of motion, show that the kinetic energy EK of an object of mass m travelling with a speed v is given by

EK = ½ mv2

[3]

(c) A cyclist, together with his bicycle, has a total mass of 90 kg and is travelling with a constant speed of 15 m s-1 on a flat road at A, as illustrated in Fig. 28 He then goes down a small slope to B so descending 4.0 m.

Fig. 28

Calculate

(i) the kinetic energy at A,

(ii) the loss of potential energy between A and B,

(iii) the speed at B, assuming that all the lost potential energy is transformed into kinetic energy of the cyclist and bicycle. [3]

(d) (i) A cyclist travelling at a constant speed of 15 m s-1 on a level road provides a power of 240 W.

Calculate the total resistive force.

(ii) The cyclist now travels at a higher constant speed. Explain why the cyclist needs to provide a greater power. [3]

(e) It is often stated that many forms of transport transform chemical energy into kinetic energy. Explain why a cyclist travelling at constant speed is not making this transformation. Explain what transformations of energy are taking place. [3]

Circular Motion

29 A body of mass m moves in a horizontal circle of radius r at constant speed v (Fig. 29). Which pair of values correctly gives (i) the work done by the centripetal force, (ii) the change in linear momentum of the body, when it moves from X to Y (where XY is a diameter)?

Fig. 29

(i) work done (ii) change in linear momentumA 2mv2 2mvB 2mv2 2mvC 0 2mvD 2mv2 0

30 A motor-cyclist moving sufficiently fast may travel in a horizontal circle on the inside surface of a vertical cylindrical wall (a “wall of death”). Which one of the diagrams below, which are vertical sections, correctly shows the orientation of the motor-cycle and the rider at any instant, and the directions of the forces acting?

(In the diagrams, F is a fractional force, W is the total weight of rider and motor-cycle, N is the normal reaction of surface on the motor-cycle, and P is an outward force.)

A B C D

31 A straight length of tape winds on to a roll rotating about a fixed axis with constant angular velocity, the radius of the roll increasing at a steady rate.

Which one of the graphs below correctly shows how the speed v at which the tape moves towards the roll varies with time?

32 An artificial satellite travels in a circular orbit about the Earth. Its rocket engine is then fired and produces a force on the satellite exactly equal and opposite to that exerted by the Earth’s gravitational field.

The satellite would then start to move

A along the line joining it to the centre of the Earth (i.e. radially) B along a tangent to the orbit C in a circular orbit with a longer period D in a circular orbit with a shorter period

33 A particle travels in uniform circular motion.

Which of the following correctly describes the linear velocity, angular velocity and linear acceleration of the particle?

linear velocity angular velocity

linear acceleration

A constant constant varyingB constant constant zeroC constant varying constantD varying constant varying

34 (a) In a ride at an entertainment park, two people, each of mass 80 kg, sit in cages which travel at constant speed in a vertical circle of radius 8.0 m as shown in Fig. 34. Each revolution takes 4.2 s. When a cage is at the top of the circle (position A) the person in it is upside down.

Fig. 34

For the person in cage A calculate the magnitudes of

(i) the angular velocity,

(ii) the linear speed,

(iii) the centripetal acceleration. [3]

(b) (i) Draw a vector diagram to show the directions of the following forces acting on the person in cage A in Fig. 34

the weight W of the person, the force F exerted by the cage on the person.

(ii) Draw the corresponding diagram for the person at the bottom of the circle (position B).

(iii) What must be the value of the resultant of these two forces at both A and B?

(iv) Explain why the person remains on the floor of the cage at the top of the circle.

(v) State the position of the cage at which the force it exerts on the person has its maximum value. Calculate the magnitude of this force. [7]

(c) Draw a vector diagram showing W, F and their resultant when the line joining the cages is horizontal. Numerical values are not required for this part of the question, but the force vectors should be drawn so that they have approximately correct relative sizes. [2]

Gravitational Field

35 A communications satellite which takes 24 hours to orbit the Earth is replaced by a new satellite which has twice the mass of the old one. The new satellite also has an orbit time of 24 hours.

What is the value of ?

A B C D

36 A satellite is in circular orbit 144 km above the Earth. Assuming the radius of the Earth to be 5760 km, the gravitational force on the satellite compared with that when it is at the Earth’s surface is (approximately)

A greater by 10%

B greater by 5%

C less by 5%

D less by 10%

37 Which one of the following graphs best indicates the relationship between V, the change in gravitational potential energy of the hull of a spacecraft, and x, its height above the surface of the Earth, during the first few hundred metres after launch?

38 A certain star of mass M and radius r rotates so rapidly that material at its equator only just remains on its surface. Given that the gravitational constant is G, the period of rotation is

A B C D

39 A body is moved from a point P on the Earth’s surface to another point Q further the Earth’s centre. Which one of the following statements about the gravitational potential energy of the body at the two points is correct? [Take the gravitational potential energy of the body as zero when it is at an infinite distance from the Earth.]

A It is positive at both points and numerically greater at Q than at P.

B It is positive at both points and numerically less at Q than at P.

C It is negative at both points and numerically greater at Q than at P.

D It is negative at both points and numerically less at Q than at P.

40 An Earth satellite is moved from on stable circular orbit to another stable circular orbit at a greater distance from the Earth. Which one of the following quantities increases for the satellite as a result of the change?

A gravitational force

B gravitational potential energy

C angular velocity

D linear speed in the orbit

41 A planet of mass P moves in a circular orbit of radius R round a sun of mass S with period T. Which one of the following correctly shows how T depends on P, R, S?

A B C D

42 Assuming the Earth to be a uniform sphere rotating about an axis through the poles, the weight of a body at the Equator compared with its weight at a pole would be

A greater, because the angular velocity of the Earth is greater at the Equator than at a pole.

B greater, because the weight at the Equator is given by the sum of the gravitational attraction of the Earth and the centripetal force due to the circular motion of the body.

C the same, because the weight is the gravitational attraction of the Earth and for a uniform sphere, even when rotating, this is independent of the body’s position on the Earth.

D smaller, because the gravitational attraction of the Earth must provide both the weight and the centripetal force due to the circular motion of the body.

43 According to one model X, the Earth is a solid sphere of uniform density. On another model Y, the Earth has a very dense core surrounded by less dense material.

The models are adjusted so that they give the same values of g, the acceleration of free fall at the Earth’s surface. The value gh at height h above the surface and gd at depth d below the surface are also calculated on both models. Which one of the following correctly describes the results?

gh gd

A same for both models greater for X than Y

B same for both models smaller for X than Y

C greater for X than Y same for both models

D smaller for X than Y same for both models

44 In two widely-separated planetary systems whose suns have masses S1 and S2, planet P1

of mass M1 and planet P2 of mass M2 are observed to have circular orbits of equal radii. If P1 completes an orbit in half the time taken by P2 it may be deduced that

A S1 = S2 and M1 = 0.25 M2

B S1 = 4 S2 only

C S1 = 4 S2 and M1 = M2

D S1 = 0.25 S2 and M1 = M2

45 The gravitational potential energy Ep of a body varies with its distance r from the centre of a planet as shown in the diagram below.

What does the gradient at any point on the curve represent?

A the gravitational field strength at that value of r

B the force pulling the body towards the planet

C the acceleration of the body towards the planet

D the potential energy of the body at that value of r

46 A stationary object is released from a point P a distance 3R from the centre of the Moon which has radius R and mass M.

Which one of the following expressions gives the speed of the object on hitting the Moon?

A B C D

47 A satellite of mass m is placed in an equatorial orbit so that it remains vertically above a fixed point on the Earth’s surface. If is the Earth’s angular velocity of rotation and M is the Earth’s mass, what is the radius of the satellite’s orbit?

A B C D

48 A satellite of mass 50 kg moves from a point where the gravitational potential due to the Earth is 20 MJ kg1, to another point where the gravitational potential is 60 MJ kg1.

In which direction does the satellite move and what is its change potential energy?

A closer to the Earth and a loss of 2000 MJ of potential energy.B closer to the Earth and a loss of 40 MJ of potential energy.C further from the Earth and a gain of 2000 MJ of potential energy.D further from the Earth and a gain of 40 MJ of potential energy

49 An experimental satellite is found to have a weight W when assembled before launching from a rocket site. It is placed in a circular orbit at a height h = 6R above the surface of the Earth (of radius R).

What is the gravitational force acting on the satellite whilst in orbit?

A B C D

50 The Earth experiences gravitational forces from the Sun, mass Ms, and from the Moon, mass Mm. The distance of the Sun from the Earth is rs and the distance of the Moon from the Earth is rm.

What is the ratio ?

A B

C D

51 The figure below shows two identical stars each of mass 4.0 × 1030kg moving with a constant speed v in a circular orbit of radius 1.0 × 1011m about their common centre of mass.

You may assume each star to be a uniform sphere with its mass concentrated at the centre of the sphere.

(a) (i) Explain and state the point X, where the gravitational field strength is zero.[2]

(ii) Determine the gravitational potential at X. [2]

(b) (i) Calculate the net force acting on each star [2]

(ii) Calculate the linear speed v of each star in the system [2]

(iii) Determine the period of rotation [2]

52 (a) (i) State in words the relationship between gravitational potential and gravitational field strength. [2]

(ii) Explain why gravitational potential has a negative value [2].

1.0 × 1011 m

v

v

Star

(b) The variation of gravitational potential near a certain plane of radius 10 000 km is shown by the graph below.

Use the graph to determine

(i) the gravitational potential energy of a 2.0kg mass at P, a distance of 20 000 km from the centre of the planet, [1]

(ii) the gravitational field strength at P, [2]

(iii) the difference in gravitational potential between the planet's surface and infinity. Hence, find the escape velocity for an object at the surface of the planet. [3]

53 (a) A satellite of mass m moves in a circular orbit of radius r about the Earth.

(i) Derive expression for its kinetic energy T, in terms of G, ME, m and the radius of the orbit.

(ii) Hence state the relationship between T and U and T and E where U is the potential energy and E, the total energy of the satellite respectively when in orbit.

(iii) Sketch on the same axes showing the variation of T, U and E with r. [7]

(b) If due to atmospheric friction, the total energy of the satellite decreases.

(i) Using your graph in (a)(iii) or otherwise explain what happens to the radius, T and U of the satellite.

(ii) If the decrease in energy is E and it changes gradually such that the orbit remains circular, determine the corresponding change in T and U in terms of E. [5]

Section V – Electricity and Magnetism

Electric Field

54 An electric field exists in the space between two charged metal plates.

Which of the following graphs shows the variation of electric field strength E with distance d from A along the line AB.

A B

C D

55 A thundercloud and the Earth’s surface may be regarded as a pair of charged parallel plates separated by a distance h as shown in the diagram. The capacitance of the system is C where C is the ratio of the charge stored in the clouds over the potential difference between the cloud and earth.

When a lightning flash of mean current I and time duration t occurs, the electric field strength between cloud and Earth is reduced by

A CIt B C D

A

B

E

d

E

d

E

d

E

d

cloud

Earth

h

0 0

00

56 A metal sphere of radius 0.10 m was insulated from its surroundings and given a large positive charge. A small charge was brought from a distant point to a point 0.50 m from the sphere’s centre.

The work done against the electric field was U and the force on the small charge in its final position was F. If the small charge had been moved to only 1.0 m from the centre of the sphere, what would have been the values of the work done and the force?

Work done forceA U/4 F/4B U/4 F/2C U/2 F/4D U/2 F/2

57 Which of the following statements about an electric field or electric field line is incorrect?

A The electric field strength at a point is a measure of the potential gradient at that point.

B The electric field strength is zero at all points where the potential is zero.C In the direction indicated by an electric field line, the potential must decrease.D The electric field strength due to a point charge varies as 1/r2 where r is the

distance from the charge.

58 Four identical point charges are arranged at the corners of a square as shown.

Which statements about the values of the electric field strength E and the potential V at point X in the middle of the square is true?

E V

A non zero zeroB non zero non zeroC zero zeroD zero non zero

Q

QQ

Q

X

59 (a) State Coulomb’s law. [1]

(b) Two identical small charged spheres, each having a mass of 3.0 x 10-2 kg hangs in equilibrium as shown below. The angle is 5.0o and the charges are 13 mm apart at equilibrium.

(i) Sketch a free-body diagram for the forces acting on one of the spheres.

(ii) Calculate the magnitude of the electric force between the spheres.

(iii) Hence calculate the magnitude of the charge on each sphere. [5]

60 (a) Define electric potential at a point and distinguish it clearly from electric potential energy. [2]

(b) Three point charges, q1 = + 1C, q2 2C, and q3 = + 3C are fixed at the position as shown in the Fig 60 below.

(i) Find the potential at point P at the corner of the rectangle?

(ii) Calculate the amount of work needed to bring a charge 2.5C from infinity and place it at P?

(iii) Calculate the resultant electric field at P. [9]

q1

q2

q2

P

q3

3m

4mFig 60

61 (a) Define electric field strength and electric potential at a point. [2]

(b) State the relationship between electric field strength and electric potential gradient.[1]

(c) Hence state how the electric field strength at a point may be determined from a graph of the variation of electric potential with distance from the point. [1]

(d) The electric potentials V are measured at distances x from P along a line PQ. The results are summarised in the table below.

x/m V/V0.020 130.030 150.040 180.050 210.060 23

(i) State the direction of the component of the E-field at 0.040 m along PQ.

(ii) Calculate an approximate value of the magnitude of the E-field component at x = 0.040 m. [3]

62 An electron is moved in a vacuum through a uniform electric field of 2.7 x 105 N C-1 from A to B, a distance of 0.0078 m such that it experiences a loss of kinetic energy.

(a) State whether A or B is at the higher potential. [1]

(b) Determine the magnitude of the electric force exerted on the electron and state its direction. [2]

(c) Calculate the work done by the field on the electron to bring it from A to B? [2]

(d) State the change in potential energy of the electron as it moves from A to B. [1]

(e) Deduce the change in the kinetic energy of the electron. State whether is it a gain or loss. [2]

(f) Determine the difference in potential from A to B. [2]

A

B

63 (a) An isolated, positively charged conducting sphere is situated above a large flat metal plate which is earthed as shown below.

(i) Sketch the pattern of electric field lines in the region surrounding the sphere. [2]

(ii) Explain the sign of the charge on the metal plate in terms of charge flow. [2]

(b) Sketch a diagram showing electric field lines near a conductor of square cross-section that is charged positively. [2]