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Name
Class
Index Number
PIONEER JUNIOR COLLEGE
JC2 Preliminary Examination
PHYSICS
Higher 2
9646/02
Paper 2 Structured Questions
12 September 2012
1 hour 45 minutes
Candidates answer on the Question Paper.
No Additional Materials are required.
READ THESE INSTRUCTIONS FIRST
Write your name, class and index number on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams, graphs or rough working.
Do not use staples, paper clips, highlighters, glue or correction fluid.
Answer all questions.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part question.
For Examiner’s Use
1
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10
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8
3
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6
4
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7
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Total
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This document consists of 20 printed pages.
2012/PJC/PHYSICS/9646
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Data
speed of light in free space,
c  3.00  10 8 m s–1
permeability of free space,
 0  4  10 7 H m–1
permittivity of free space,
 0  8.85  10 12 F m–1
 1 36   10 9 F m–1
elementary charge,
e  1.60  10 19 C
the Planck constant,
h  6.63  10 34 J s
unified atomic mass constant,
u  1.66  10 27 kg
rest mass of electron,
me  9.11 10 31 kg
rest mass of proton,
mp  1.67  10 27 kg
molar gas constant,
R  8.31 J K–1 mol–1
the Avogadro constant,
N A  6.02  10 23 mol–1
the Boltzmann constant,
k  1.38  10 23 J K–1
gravitational constant,
G  6.67  10 11 N m2 kg–2
acceleration of free fall,
g  9.81 m s–2
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Formulae
uniformly accelerated motion,
1 2
at
2
v 2  u 2  2as
s  ut 
work done on/by a gas,
W  pV
hydrostatic pressure,
p  gh
gravitational potential,

displacement of particle in s.h.m.,
x  x 0 sin t
velocity of particle in s.h.m.,
v  v 0 cos t
Gm
r
  x 0  x 2
2
mean kinetic energy of a molecule
E
3
kT
2
of an ideal gas,
resistors in series,
R  R1  R 2  ...
resistors in parallel,
1/ R  1/ R1  1/ R 2  ...
electric potential,
V 
alternating current/voltage,
x  x 0 sin t
transmission coefficient,
T  exp  2kd  where k 
radioactive decay,
x  x 0 exp( t )
decay constant,

Q
4 0 r
8 2 mU  E 
h2
0.693
t1
2
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1
(a) State the principle of conservation of momentum.
........................................................................................................................................
................................................................................................................................. [1]
(b) Fig. 1.1 shows momentum against time graphs for two colliding trucks A and B.
30
momentum /
103 kg m s−1
B
20
A
10
0
0
1.0
2.0
3.0
4.0
5.0
time / s
Fig. 1.1
The masses of trucks A and B are 2000 kg and 4000 kg respectively.
(i) Explain why the gradients of the graphs during the collision have opposite sign.
..................................................................................................................................
..................................................................................................................................
........................................................................................................................... [1]
(ii) Show that momentum is conserved when the two trucks collide.
[1]
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(iii) Calculate the force acting on truck A during the collision.
force = ........................................ N [2]
(iv) Using appropriate calculations, determine the type of collision that the trucks
experience.
type of collision: .......................................................................................................
........................................................................................................................... [3]
(c) Discuss how seat belts and air bags ensure greater safety.
........................................................................................................................................
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................................................................................................................................. [2]
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2
(a) Define simple harmonic motion.
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................................................................................................................................. [2]
(b) A rubber duck is floating in a swimming pool. When it is pushed down into the water
without totally submerging it, and released, it bobs up and down in simple harmonic
motion. The variation of the displacement y of the rubber duck with time t is shown in
Fig. 2.1.
y/m
t/s
Fig. 2.1
On Fig. 2.2, sketch a fully labelled graph showing the variation with time t of the
kinetic energy E k of the rubber duck of mass 92.1 g for one period.
Ek / J
t/s
Fig. 2.2
[2]
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(c) The period T of the oscillating rubber duck, measured in s, is given by
T  2
m
k
where m is in kg and k = 21 kg s−2.
(i) Surface water waves of speed v and wavelength 0.28 m are incident on the
rubber duck. It is noted that the rubber duck is oscillating up and down with
maximum amplitude. Determine v.
v = ........................................ m s−1 [2]
(ii) If an oscillator is used such that more water waves of the same amplitude are
incident on rubber duck per unit time, describe and explain what happens to
amplitude of the vertical oscillations of the rubber duck.
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3
(a) Describe briefly how the pattern from the two-source interference of light supports the
wave theory of light.
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................................................................................................................................. [2]
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(b) Two microwave sources S1 and S 2 are situated as shown in Fig. 3.1.
X
S1
O
M
S2
Y
Fig. 3.1
A detector is placed on a line XY which is parallel to the line joining S1 and S 2 . M is
the midpoint of the line joining S1 and S 2 . The line from M, perpendicular to the line
S1S2 , meets XY at O.
S1 and S 2 are switched on together. Fig. 3.2 shows a plot of the intensity of the
signal detected along XOY.
intensity
12
10
8
6
4
2
0
X
O
Y
Fig. 3.2
(i) What evidence from Fig. 3.2 suggests that the two sources S1 and S 2
1. are anti-phase to each other,
..................................................................................................................................
........................................................................................................................... [1]
2. do not have exactly the same amplitude?
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(ii) Calculate the length XY given that S1S2 is 20.0 cm, the distance MO is 10.0 m
and the wavelength used is 2.0 mm.
length XY = ........................................ m [2]
4
(a) With reference to a point in an electric field, define the term electric potential.
........................................................................................................................................
................................................................................................................................. [1]
(b) Two identical negatively charged particles X and Y, each of mass 2.0  1027 kg and
charge 8.0  10 19 C are held at a distance 1.0  10 9 m apart.
(i) Calculate the electric potential energy of the system.
electric potential energy = ........................................ J [2]
(ii) If the charges are released, they will move apart. Show that their speed when
they are very far apart is 5.37  10 4 m s−1.
[3]
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(iii) With the two charges held at rest at 1.0  10 9 m apart, a third charge Z is
placed at the mid-point along XY so that the system of charges is stationary.
1. State and explain the sign of the third charge in order for the system of
charges to be stationary.
..................................................................................................................................
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........................................................................................................................... [2]
2. Calculate the magnitude of charge Z.
magnitude of charge Z = ........................................ C [2]
5
(a) By drawing an energy band diagram, describe how p-type doping affects the number
of mobile charge carriers of an intrinsic semiconductor.
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(b) A junction is formed between slices of p-type and of n-type semiconductor material,
as shown in Fig. 5.1.
p-type material
n-type material
Fig. 5.1
On Fig. 5.1, draw
(i) an arrow to show the direction of movement of electrons as the two slices are
brought into contact,
[1]
(ii) the symbol for a battery, connected so as to decrease the width of the depletion
region.
[1]
(c) Fig. 5.2 shows an ohmic resistor connected in series with a semiconductor diode.
V
V
Vin
Vout
Fig. 5.2
The input signal Vin varies with time as shown in Fig. 5.3.
Vin / V
5.0
0
t/s
0.5
1.0
1.5
2.0
−5.0
Fig. 5.3
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(i) On Fig. 5.4, sketch the variation of the output signal Vout with time t across the
resistor.
Vout / V
0
t/s
0.5
1.0
1.5
2.0
Fig. 5.4
[1]
(ii) On Fig. 5.5, sketch the variation of Vout 2 with time t for the output signal.
Vout 2 / V2
0
t/s
0.5
1.0
1.5
2.0
Fig. 5.5
[1]
(iii) Calculate the average value of Vout 2 across the resistor.
average value of Vout 2 = ........................................ V2 [2]
(iv) Hence, calculate Vr .m.s. , the r.m.s. value of the potential difference across the
resistor.
Vr .m.s. = ........................................ V [1]
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6
A homopolar generator comprises an electrically conductive disc that rotates in a plane
perpendicular to a uniform static magnetic field.
In order to rotate the disc, a d.c. power supply is connected to the disc, as shown in
Fig. 6.1. The disc is placed horizontally in a downward magnetic field and current passes
from the axle to the rim of the conducting disc. Fig. 6.2 shows the top view of the disc.
downward magnetic field
Axle
axle
disc
disc
axle
Fig. 6.1
Fig. 6.2
(a) (i) State the direction of rotation of the disc in Fig. 6.2.
........................................................................................................................... [1]
(ii) As the disc speeds up, there is an increasing e.m.f. induced between the axle
and the rim of the conducting disc. Explain why there is an increasing induced
e.m.f.
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..................................................................................................................................
........................................................................................................................... [2]
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(b) When the power supply is disconnected, this induced e.m.f. can be used to drive a
current through an external resistor, as shown in Fig. 6.3.
downward magnetic field
disc
axle
Fig. 6.3
State whether the output of a homopolar generator is an alternating current or direct
current.
................................................................................................................................. [1]
(c) A large homopolar generator can be designed to produce a large current surge when
it is short-circuited. Fig. 6.4 shows a current surge from a short-circuited homopolar
generator.
2.0
6
I / 10 A
1.5
5
1.0
0.5
0
0
1
2
3
4
t/s
Fig. 6.4
(i) Explain the meaning of the term “short-circuited”, as used in the passage.
..................................................................................................................................
........................................................................................................................... [1]
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(ii) Estimate the charge that flows during this surge.
charge = ........................................ C [3]
(iii) Calculate the maximum power dissipated in the generator when the terminals of
the generator, which has an internal resistance of 0.12 mΩ, are connected
together through a negligible external resistance.
maximum power = ........................................ W [2]
(d) The magnitude of the induced e.m.f. E can be calculated from the relationship


E   rd 2  ra 2 kB
where rd and ra are the radii of the disc and axle respectively, and B is the magnetic
flux density, assumed to be uniform over the surface of the disc.
(i) Determine the units for k.
units for k = ........................................ [3]
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(ii) Hence, suggest what physical quantity may be represented by the symbol k.
........................................................................................................................... [1]
(e) State the energy transformation that takes place in the process shown
(i) in Fig. 6.1,
..................................................................................................................................
........................................................................................................................... [1]
(ii) in Fig. 6.3.
..................................................................................................................................
........................................................................................................................... [1]
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7
The bouncing of a ball is a requirement for some ball games. With all other variables
kept constant, the relation between the first rebound height h of a ball off a surface and
the air pressure p inside the ball is
h  kp n
where k and n are constants.
You are provided with a bicycle pump. You may also use any of the other equipment
usually found in a Physics laboratory.
Design an experiment using different pressures to determine the value of n.
You should draw a labelled diagram to show the arrangement of your apparatus. In your
account you should pay particular attention to
(a) the equipment you would use,
(b) the procedure to be followed,
(c) the control of variables,
(d) how the first rebound height would be measured,
(e) any precautions that would be taken to improve the accuracy of the experiment.
[12]
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Diagram
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2012/PJC/PHYSICS/9646