This document consists of 21 printed pages MERIDIAN JUNIOR COLLEGE Preliminary Examinations Higher 2 ___________________________________________________________________ H2 Physics 9646/3 Paper 3 15 September 2010 2 hours ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST Class Reg Number Candidate Name _____________________________ This booklet contains Sections A and B of the Preliminary exam paper 3. Do not open this booklet until you are told to do so. Section A Answer all questions. Section B Answer any two questions. In the event that all 3 questions are attempted, only the first 2 questions will be marked. You are advised to spend about one hour on each section. Write your answers on this question booklet in the blanks provided. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. Marks will be deducted if units are not stated where necessary or if answers are not quoted to the appropriate number of significant figures. All working for numerical answers must be shown. You are reminded of the need for good English and clear presentation of your answers. Examiner’s Use Section A Q1 /8 Q2 /10 Q3 /6 Q4 /8 Q5 /8 Section B Circle the questions you have attempted Q6 /20 Q7 /20 Q8 /20 Deductions Total /80
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___________________________________________________________________ READ THESE INSTRUCTIONS FIRST
Class Reg Number
Candidate Name _____________________________ This booklet contains Sections A and B of the Preliminary exam paper 3.
Do not open this booklet until you are told to do so. Section A Answer all questions.
Section B Answer any two questions.
In the event that all 3 questions are attempted, only the first 2 questions will be marked. You are advised to spend about one hour on each section. Write your answers on this question booklet in the blanks provided.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question. Marks will be deducted if units are not stated where necessary or if answers are not quoted to the appropriate number of significant figures. All working for numerical answers must be shown. You are reminded of the need for good English and clear presentation of your answers.
Examiner’s Use
Section A
Q1 /8
Q2 /10
Q3 /6
Q4 /8
Q5 /8
Section B
Circle the questions you have attempted
Q6 /20
Q7 /20
Q8 /20
Deductions
Total /80
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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DATA AND FORMULAE Data speed of light in free space c = 3.00 x 108
m s-1
permeability of free space µo = 4π x 10-7 H m-1 permittivity of free space ε0 = 8.85 x 10-12 F m-1
= (1/(36π)) x 10-9 F m-1
elementary charge e = 1.60 x 10-19 C
the Planck constant h = 6.63 x 10-34 J s
unified atomic mass constant u = 1.66 x 10-27 kg
rest mass of electron me = 9.11 x 10-31 kg
rest mass of proton mp = 1.67 x 10-27 kg
molar gas constant R = 8.31 J K-1 mol-1
the Avogadro constant NA = 6.02 x 1023 mol-1
the Boltzmann constant k = 1.38 x 10-23 J K-1
gravitational constant G = 6.67 x 10-11 N m2 kg-2
acceleration of free fall g = 9.81 m s-2
Formulae uniformly accelerated motion
s = ut + 1
2at2
v2 = u2 + 2as
work done on/by a gas W = p∆V hydrostatic pressure p = ρgh gravitational potential φ = -Gm/r
displacement of particle in s.h.m. x = xo sin ωt velocity of particle in s.h.m. v = vo cos ωt
= ± ω 2 2o -x x
resistors in series R = R1 + R2 + …
resistors in parallel 1/R = 1/R1 + 1/R2 + …
electric potential V = Q/4πεor alternating current/voltage x = xo sin ωt
transmission coefficient T = exp(-2kd)
where k = π −2
2
8 ( )m U E
h
radioactive decay x = xo exp(-λt ) decay constant
λ
= 1
2
0.693
t
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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Section A
Answer all the questions in this section.
1 (a) A charged body falls vertically in a vacuum near the Earth’s surface. The variation with time t of its vertical speed v is shown in Fig. 1.1 below.
Fig. 1.1 An electric field induces a horizontal force on the body that causes the body to accelerate horizontally at 2.25 m s-2. Calculate the displacement of this body after 0.50 s falling from rest.
displacement = ................................m
angle = ........................... [4]
v/ m s-1
t/ s 0
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(b) Another object moving in a straight line has a graph of the variation with time of its
velocity shown in Fig. 1.2.
Fig. 1.2
(i) Sketch on Fig. 1.2, a graph of the variation of the acceleration with
time for the same object within the same time frame.
[2]
(ii) Explain your sketch in (i) between time t1 and t2.
…………………………………………………………………………………………........
………………………………………………………………………………………….......
……………………………………………………………………………………..... [2]
0 t2 t1
v/ ms-1
t/ s
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2 (a) It is often assumed that air resistance acting on a moving object will result in the
object slowing down. Air resistance can however indirectly make an object speed up. Consider a 1000 kg satellite orbiting at 280 km above the Earth’s surface. A small force of air resistance makes the satellite descend into a circular orbit with an altitude of 100 km. [Radius of Earth = 6.37 x 106 m, mass of Earth = 5.98 x 1024 kg]
(i) By calculating the speed of the satellite at both orbits, show that the satellite
is indeed travelling faster at the lower orbit. [3]
(ii) Show that the total mechanical energy of the satellite, E can be expressed
as:
E s
o2= −
GM mE
R where ME is the mass of earth, ms is the mass of satellite and, Ro is the
radius of orbit. [2]
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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(iii) Explain the significance of the negative sign in the expression for the total
mechanical energy of the satellite.
…………………………………………………………………………………........
…………………………………………………………………………………........
…………………………………………………………………………….....
[1]
(iv) Hence, calculate the change in mechanical energy due to air resistance.
change in mechanical energy = ……………….. J [2] (c) Black holes are formed when massive stars collapse towards a singularity i.e. a
point mass. There exist a boundary, known as the event horizon, surrounding a black hole where a even body travelling at the speed of light (if it is possible) can barely escape. Consider the gravitational potential energy of the body at the event horizon, deduce an expression for the radius of the event horizon, event horizonR in terms of
the mass of the black hole, M and speed of light c.
event horizonR = ……………….. [2]
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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3
(a) A thin layer of copper is deposited uniformly on the surface of an iron wire of radius 0.60 mm and length 3.0 m shown in Fig. 3.1.
Fig. 3.1 (Not to scale) Determine the effective resistance between the ends of the copper-plated wire, given that the thickness of the copper is 1.78 x 10-5 m. [Resistivity of iron = 8.90 x 10-8 Ω m; resistivity of copper = 1.60 x 10-8 Ω m]
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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(b) Fig. 3.2 shows a system in which an unmodulated audio frequency signal is
transmitted from the transmitter to the receiver through a cable. The cable consists of two strands of insulated copper wire.
Fig. 3.2 The power output of the transmitter is 12.5 mW and the corresponding current in each wire is 2.5 mA. Power is lost to the surroundings due to the rise in temperature produced by this current. For transmitted signal to be detected the power input to the receiver must be at least 1.5 mW. The resistance of each 1.0 m of the copper wire used in the cable is 0.27 Ω.
Calculate the maximum distance between the transmitter and receiver at which the
transmission can be detected successfully. maximum distance = ……………………m [3] 4 (a) State Faraday’s law of electromagnetic induction.
………………………………………………………………………………………….......
………………………………………………………………………………………….......
……………………………………………………………………………………...... [1]
I
insulation
transmitter 12.5 mW
receiver
copper wire
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(b) A long straight wire carries a direct current. A rigid loop of conducting wire is
placed near the wire such that the wire is in the plane of the loop. The loop is moved at constant speed away from the wire as shown in Fig. 4.1.
(i) Explain why an e.m.f. is induced in the loop.
…………………………………………………………………………………………........
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………...... [2]
(ii) On Fig. 4.1, draw an arrow to indicate the direction of the current induced in
the loop and explain your answer below.
…………………………………………………………………………………………........
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………...... [2]
(iii) It was found that energy is dissipated in the wire loop. Explain how the
movement of the loop gives rise to energy dissipation.
………………………………………………………………………………………….........
…………………………………………………………………………………………........
………………………………………………………………………………………….......
………………………………………………………………………………………….......
……………………………………………………………………………………...... [3]
wire
current
conducting loop
direction of motion of loop
Fig. 4.1
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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5 (a) Explain what is meant by internal energy of a system.
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………...... [2]
(b) The temperature, T of an ideal gas at pressure p is defined by the equation
p = nkT
(i) Identify the quantity n.
……………………………………………………………………………………...... [1]
(ii) State an equation relating k and R, molar gas constant.
……………………………………………………………………………………...... [1]
(c) State the process and give one practical example of each of the following : (i) a process in which heat is supplied to a system without causing an increase
in temperature.
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………...... [2]
(ii) a process in which no heat enters or leaves a system but the temperature
changes.
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………...... [2]
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Section B
Answer two questions in this section. 6 (a) (i) State Newton’s 1st law of motion and show it leads to the concept of force.
…………………………………………………………………………………………........
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………....... [2]
(a) (ii) Express the unit of force in terms of S.I. base units.
S.I. base units of force is ….....……………
[1] (b) Michael drove a car of mass 1200 kg which had a maximum speed of 150 km h-1.
During a driving test, it was found that the average retarding force from the air and ground added up to 1200 N when the car was accelerating uniformly.
(i) Calculate the forward driving force when the car accelerated uniformly from rest to the maximum speed in 11.0 s under driving test conditions.
forward driving force= ……………… N [3]
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(ii) Hence, find the maximum power delivered by the engine.
maximum power = ……………… W [2] (c) Michael wishes to find out how his car will fare during a car crash. He visited a
laboratory where several cars like his own were used in controlled car crash testing. The magnitude F of the force required to crush the barrels was shown below in Fig. 6.1 as a function of the distance x the automobile had moved into the cushion. In a particular crash test, the car was travelling at 100 km h-1 before it struck a crash cushion in which the car was brought to rest by successively crushing steel barrels.
(i) Neglecting friction, predict by using the Work Energy Theorem the distance the car would move into the cushion of steel barrels before coming to rest.
distance = ……………… m [4]
y
x
Fig. 6.1
170
130
90
0.0 1.5 4.0
F / kN
x/ m
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(ii) State and explain in terms of energy considerations whether the actual
distance will be longer or shorter than the value in (c)(i).
…………………………………………………………………………………………........
…………………………………………………………………………………………........
…………………………………………………………………………………………........
……………………………………………………………………………………....... [2]
(d) Michael parked his 1200 kg car at an underground carpark in Orchard Road. It
started to rain very heavily and rainwater quickly entered and filled the underground carpark such that Michael’s car is floating in the water as shown in Fig. 6.2. The total volume of the car is 6.43 m3 and the volume of air space in the car is 5.50 m3. [Density of rainwater = 1000 kg m-3]
(i) State Archimedes’ principle.
…………………………………………………………………………………………........
……………………………………………………………………………………...... [1]
(ii) Initially, no water enters the passenger compartment. Determine the volume
of car below the water surface when the car is floating as shown in Fig. 6.2.
volume of car = …………………….. m3 [2]
Fig. 6.2
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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(iii) Water slowly enters the car. Determine the volume of water in the car at the
point when it first disappears completely below the water surface. (Assuming that the car remains horizontal throughout the sinking process)
volume of water = …………………… m3 [3]
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7 (a) Define the Tesla.
………………………………………………………………………………………….......
………………………………………………………………………………………….......
……………………………………………………………………………………...... [2]
(b) Fig. 7.1 shows an arrangement used to accelerate an initially stationary alpha
particle and make it travel in a uniform magnetic field.
Fig. 7.1
(i) On Fig. 7.1, draw a possible trajectory of the alpha particle in the uniform
magnetic field. [1] (ii) Explain whether the force experienced by the alpha particle due to the
magnetic field changes its kinetic energy.
………………………………………………………………………………….........
…………………………………………………………………………………........
………………………………………………………………………………….........
…………………………………………………………………………………........
……………………………………………………………………………........ [3]
Vacuum
B
alpha emitter
A
4.0 kV Uniform magnetic field of 2.00 T directed into the
plane of the paper
Path of alpha particle
Region W
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(iii) Show that the alpha particle will attain a speed of 6.21 x 105 m s-1 when it
reaches the slit opening of plate B. [ 27Mass of alpha particle 6.644 10 kg−= × ] [1]
(iv) Calculate the electric field that needs to be applied in Region W for the
alpha particle to pass through the uniform magnetic field undeflected.
Magnitude of electric field = ………………..
[2]
Direction of Electric Field = ………………..
[1]
(c) Suppose that the arrangement in Fig. 7.1 is now modified so that the alpha particle
enters the uniform magnetic field at an angle of o30 to the horizontal as shown in Fig. 7.2 below.
Fig 7.2
Uniform magnetic field of 2.00 T directed along the
plane of the paper
Vacuum
B
alpha emitter
A
4.0 kV
300
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The motion of the alpha particle can be described as a helix as shown on Fig. 7.3 below.
Fig. 7.3
(i) Calculate the radius r of the helical path.
radius r = ………………..m [2]
B field
v
300
Helical path of alpha particle in uniform B Field
+qα
Pitch, p
Cross – section of helical path
r Radius, r
B field
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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(ii) Show that the period, T of the helical path can be expressed as:
2 m
Tq B
α
α
π=
where mα and qα is the mass and charge of the alpha particle respectively.
[1]
(iii) Calculate the pitch, p.
pitch, p = ………………..m [3]
(iv) Describe and explain how the helical path will change if a positron, 01e
++ (i.e.
a particle with the mass of an electron and charge 191.6 10 C−+ × ) with the same initial velocity was to be used in the experiment instead. You may quote relevant equations to substantiate your answer.
.......……………………….……………………………………………………….….
.......……………………….……………………………………………………….….
.......……………………….……………………………………………………….….
….………………………………………………………………………………........
........………………………………………………………………………………......
..........…………………………………………………………………………………
……………………………………………………………………………........
[4]
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8 (a) The X-ray spectrum is first produced by an X-ray tube with tungsten (atomic
number, Z = 74) anode. Another X-ray spectrum is then produced using barium (atomic number, Z =56).
Fig. 8.1
(i) Describe how the characteristic X-ray spectrum is formed.
………………………………………………………………………………..…........
………………………………………………………………………………..…........
………………………………………………………………………………..….......
………………………………………………………………………………..…........
………………………………………………………………………………..…........
……………………………………………………………………………........ [4]
(ii) The accelerating potential used to produce the X-ray spectra using tungsten
and barium are the same. Explain how this can be deduced from Fig. 8.1.
…………………………………………………………………………………..........
……………………………………………………………………………........ [1]
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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(iii) Hence calculate the accelerating voltage for the barium spectrum.
accelerating voltage = …………....…. V
[2]
(iv) Explain the difference between the intensity of the Kα- line of the tungsten
and barium spectrum.
…………………………………………………………………………………..........
………………………………………………………………………………….........
……………………………………………………………………………........ [2]
(v) Calculate the minimum accelerating potential to produce Kα – line for
tungsten. Hence sketch on Fig. 8.1 without any additional numerical labels, the spectrum for tungsten if the accelerating potential is reduced to 50 kV.
minimum accelerating potential = …………....…. V
[3]
(b) An X-ray machine is accelerating electrons through a p.d. of 200 kV. The current is 25 mA. The target is a heavy metal mass 1.0 kg, and specific heat capacity 300 J kg K-1 and has a melting point of 3000 K. The machine is at 300 K when it is first started. While the machine is operating, the cooling fails and its temperature increases by 16.5 K within a second.
(i) Calculate efficiency of X-ray production.
efficiency of X-ray production = .....................%
[2]
Preliminary Examination Meridian Junior College 15 September 2010 JC2 H2 Physics 2010
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(c) Fig. 8.2 below shows portions of the energy-level diagrams of the helium (He) and
neon (Ne) atoms. The He atom is excited from its ground state to state of 20.61 eV. The excited level of helium at 20.61 eV is very close to a level in neon at 20.66 eV. Upon collision with a neon atom, the energy can be transferred from the helium to the neon atom. This excites the Ne atoms to the E3 state at 20.66 eV. Lasing action takes place for electron transitions from E3 to E2 in the Ne atoms.
(i) State any two unique characteristics of laser light.
………………..………………………………………………………………….......
…………………………………………………………………………….......
[1]
(ii) Explain what is meant by population inversion and how energy state E3 in Ne enables lasing to occur.
………………..………………………………………………………………….......
………………..………………………………………………………………….......
………………..………………………………………………………………….......
………………..………………………………………………………………….......
…………………………………………………………………………….......
[3]
(iii) Explain why direct optical pumping (the supply of photons) excitation method using photons of energy ∆ E = E3 - E1 on Neon atom, in the absence of He atom, is generally not used.