Name: ____________________________________
Class: 13S ___________
VICTORIA JUNIOR COLLEGE
2014 JC2 PRELIMINARY EXAMINATIONS
PHYSICS
Higher 2
Paper 2 Structured Questions
15/9/2014
Monday
READ THESE INSTRUCTIONS FIRST
Answer all questions.
Write your answers in the spaces provided.
The number of marks is given in brackets [ ]
at the end of each question or part question.
9646/02
1400 h – 1545 h
(1 h 45 min)
For marker’s use
1.
2.
3.
4.
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7.
8.
9.
sf
units
Total (72)
This paper contains 17 printed pages
DATA
speed of light in free space,
c = 3.00 x 108 m s-1
permeability of free space,
µo = 4 x 10-7 H m-1
permittivity of free space,
o = 8.85 x 10-12 F m-1
(1/(36)) 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 mol-1 K-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
2
Formulae
uniformly accelerated motion,
s = ut + (½) at2
v2 = u2 + 2as
work done on/by a gas,
W = p V
hydrostatic pressure,
p = hg
gravitational potential,
 
displacement of particle in s.h.m.,
x = xo sin  t
velocity of particle in s.h.m.,
v  vo cos t
GM
r
  ( xo2  x 2 )
mean kinetic energy of a molecule of an
ideal gas,
E=
resistors in series,
R = R1 + R2 + …
resistors in parallel,
1/R = 1/R1 + 1/R2+ …
electric potential,
V = Q/4or
alternating current/voltage,
x = xo sin  t
transmission coefficient,
T  exp(-2kd)
3
kT
2
8 2 m(U  E )
where k 
h2
radioactive decay,
x = xoexp(-t)
decay constant,

0.693
t1
2
3
1.
A mass of mass m was suspended from the bottom of a vertical spring, and set into
oscillation with a period T. Measurements were made, and the resultant force F acting
on the mass, and its velocity v were obtained. The graphs below were then plotted to
show how F and v vary with the displacement x of the mass from its equilibrium
position.
v/ m s‐1 F/ N 1.2 0.63 0.45 0.45 ‐0.45 0 x/m ‐0.63 ‐0.45 0 x/m ‐1.2 Calculate:
(a)
the period of the oscillation, and
(b)
the mass m.
[4]
4
2.
An ideal gas in a container with a movable piston is heated. At the same time, the
piston is pulled out in such a way that the temperature of the gas remains constant at
all times.
(a)
Use the First Law of Thermodynamics to explain why the temperature of the gas
remains constant, even though it is heated.
[3]
(b)
Fig 2.1 below shows how the pressure p of the gas varies with its volume V as the gas
is changed from state A to state B isothermally. The volume of the gas at state A is VA,
and at state B is VB, while the pressure of the gas at state A is pA and its pressure at
state B is pB:
p pA A pB B VB VA V Fig. 2.1
In a separate experiment, the same gas also starts from state A. However, the
container is now completely insulated, and the piston is pulled out until the volume of
the gas is VB again, without it being heated.
(i)
Use the First Law of Thermodynamics to explain whether the final pressure is
higher or lower than pB.
[2]
(ii)
Sketch in Fig. 2.1 a curve to show how the pressure of the gas in the insulated
container changes with volume as the piston is pulled out.
[1]
5
3
A communications satellite of mass 2000 kg is to be put into an equatorial orbit so that
the satellite remains above the same point on the Earth’s surface and is travelling from
west to east.
[The mass of the Earth is 5.98 x 1024 kg.]
(a)
Calculate the radius of the satellite’s orbit.
(b)
Explain whether all orbits around the Earth with a period of 24 hours are geostationary.
[1]
6
[3]
4 (a)
Four parallel, vertical metal plates of negligible thickness, A, B, C and D are arranged
as shown in Fig 4.1 below. The distance between the adjacent plates is 15 mm. The
outer plates A and D are earthed, B is maintained at a potential of -50 V and C is
maintained at a potential of + 30 V.
A
C
B
D
15 mm 15 mm 15 mm
+30V
-50V
Fig. 4.1
Sketch graphs (with axes labelled with appropriate values) to show how the following
varies along a line through the centre of the plates perpendicular to their planes.
1. The electric potential.
[2]
2. The electric field strength.
[3]
7
(b)
A battery of e.m.f. 25 V is connected across two parallel, vertical metal plates as
shown.
Parallel plates vacuum electron path
X
Y
15mm
25V
Fig. 4.2
An electron travels in a vacuum and passes through holes X and Y, which are at the
centre of each plate. The separation of the plates is 15 mm.
The electron has a horizontal velocity of 7.0 x 106 ms-1 when it enters hole X. Calculate
the speed of the electron as it leaves hole Y.
[3]
8
5.
A small square coil of 10 turns with sides of length 5.0 cm has its plane set at right
angles to the uniform magnetic field of flux density 2.0 T between the pole pieces of a
horseshoe magnet as shown in Fig. 5.1.
Fig. 5.1
The magnet is rotated at constant angular velocity of 430 rad s-1 about the axis XY.
You should assume that at t = 0, the coil is in the position shown in Fig. 5.1. Draw
sketch graphs in the spaces below, with appropriate values on the time axes, to show
how the magnetic flux, Φ through the coil and the e.m.f., E induced in the coil vary with
time.
[6]
(a)
Graph of magnetic flux, Φ through the coil against time t
(b)
Graph of e.m.f., E induced in the coil against time t
9
6(a)
By reference to the band theory of solids, explain how doping changes the electrical
conduction properties of an n-type semiconductor.
[3]
(b)
Discuss with the aid of diagrams and using the idea of a depletion region, how a p-n
junction can act as a rectifier.
[4]
10
7.
When a particle comes into contact with its anti-particle, the masses of the two
particles will be converted into pure energy, in accordance with Einstein's equation for
mass-energy equivalence. This process is called pair annihilation.
The anti-particle of the electron is the positron, which has the same mass as an
electron. Consider the case where an electron and a positron annihilate each other
and produce photons. Assume that these two particles collide head-on with equal, but
slow speeds.
(a)
Explain why it is not possible for only one photon to be produced.
[2]
(b)
Show that if only two photons are produced, they must have equal energy.
[2]
(c)
Calculate the maximum wavelength of each of the photons in part (b).
[3]
(d)
State the region of the electromagnetic spectrum in which these photons lie.
[1]
11
8.
Solar powered cars are always being advocated as a more efficient way of using
energy resources. Such cars can be run using relatively low voltages that drive direct
current motors and can produce reasonable power at their peak performance. The
voltages are provided by a battery powered by energy collected by the solar cells
mounted on the roof, bonnet and boot of the car.
The specifications for a typical solar car on a 200 km journey between Perth and
Bunbury are as follows
Area of solar cells collecting energy
7.7 m2
Power output at peak performance
4500 W
Average power output of motor
1100 W
Average speed for the journey
67 km h-1
Average solar energy intensity
0.90 kW m-2
Efficiency of motor at average power output
92 %
Electrical efficiency of solar cells
26 %
(ability of cells to convert solar energy to electrical energy)
Charge capacity of car battery
60 A h
Operating voltage of battery
50 V
(a)
Calculate the total solar energy collected by the solar cells during its 200 km journey.
[3]
(b)
Calculate the amount of energy in (a) that was actually converted into electrical
energy.
[2]
12
(c)
Calculate the total amount of energy being consumed per second from the battery
when the motor was operating at average power output.
[2]
(d)
If the solar cell has a surface area of 6.4 x 10-3 m2, calculate the number of cells that
are fitted onto the solar car, and the amount of energy collected during the 200 km
journey by each cell.
[3]
(e)
Consider the car operating at its average power output. At this power, the car travels
at a constant speed of 67 km h-1. Calculate the tractive force and the total resistive
force acting on the car when it is travelling at this speed.
[2]
(f)
By reference to your answer in (c), calculate the discharge current from the fully
charged battery under conditions of darkness.
[1]
13
(g)
Hence calculate the time for the battery to become fully discharged.
(h)
You are told that the average solar energy intensity received is 0.90 kW m-2. Name two
factors which could affect its actual value.
[2]
14
[2]
9.
The presence of ice on the surface of the Moon can be investigated by transmitting a
radio signal from a spacecraft at a target point on the Moon and studying the signal
received on Earth as a result of internal reflection within the ice.
The strength of the reflected signal should depend on the thickness and temperature
of the ice at the target point.
Design an experiment using electromagnetic waves of wavelength 3 cm (microwaves)
to find how the strength of the reflected waves from a sheet of ice depends on the
thickness of the sheet of ice.
The equipment available includes the following:
Calibrated thermocouple
Low voltage power supply
Microammeter
Microwave transmitter
Microwave receiver
Sheets of ice of different thickness
You should draw diagrams to show the arrangement of your apparatus. In your
account you should pay attention to
(a)
(b)
(c)
(d)
(e)
the equipment you would use for the investigation,
the procedure to be followed,
the control of variables,
any safety precautions,
any precautions that you would take to improve the accuracy of the experiment.
Diagram
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