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CCC Hoh Fuk Tong College
Mock Examination 2011-2012
Physics Paper I
Secondary : 7
Time allowed : 3 hours
Date : 7 / 2 / 2012
Marks : 108
( 8:15 – 11:15 )
Name : ______________________________
Class : 7S
Number : ______
1. Answer ALL questions.
2. Write your answers in the spaces provided in the question paper. In calculations
you should show all the main steps in your working.
3. Assume:
velocity of light in air = 3 x 108 m s-1
acceleration due to gravity = 10 m s-2
electronic charge = 1.6 x 10-19 C
Questions No.
Marks
1
15
2
15
3
13
4
13
5
13
6
15
7
13
8
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1. A spacecraft is launched with 31.3 MJ of kinetic energy per unit mass vertically
upwards from the Earth surface. When the spacecraft is instantaneously at rest at
the highest position, the rocket engine exerts an impulse of force parallel to the
Earth’s surface below setting the spacecraft to move in a circular orbit round
Earth.
Given that:
G
M
GM
R
=
=
=
=
gravitational constant
mass of earth
4 x 1014 J kg-1 m-1
radius of earth = 6.4 x 106 m
2
a.
What is the radius r of the circular orbit?
( 2 marks )
b. Find the gravitational force acting on an astronaut of mass 60 kg in the
spacecraft.
( 2 marks )
c.
The final mass m of the spacecraft ( with the astronaut ) when it is orbiting
round the Earth is 5000kg.
i. Find the orbiting speed v of the spacecraft ( with the astronaut ) in this
circular orbit.
( 2 marks )
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ii. Find the sum of potential and kinetic energy (E0) of the orbiting
spacecraft?
( 2 marks )
iii. The speed of the spacecraft in this orbit is increased to v’ such that it can
leave the earth permanently. Find the minimum value of v’ . ( 2 marks )
iv.
Owing to air resistance, the spacecraft loses mechanical energy at a rate
of 1.4x106 J per complete orbital revolution. Adopt the reasonable
approximation that the trajectory is a “circle of slowly diminishing
radius”
(1) Determine its height h above the Earth’s surface at the end of its
6000th orbital revolution.
( 2 marks )
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(2) What is the magnitude of the average retarding force F acting on
the spacecraft?
( 3 marks )
2. A light spring is fixed vertically to a trolley and a light platform is attached to its
upper end. A small block of mass m is placed on this horizontal platform.
When the system achieves static equilibrium, the spring is compressed by 0.08 m
as shown in Figure 2.1
Figure 2.1
The block is released from the uncompressed position of the spring. The trolley
is then given a push so that it moves together with the block at a uniform velocity
on a smooth horizontal surface. Neglect air resistance and assume that there is
no slipping between the block and the platform.
(a)
Find the period of the vertical oscillation of the block.
( 3 marks )
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(b) Figure 2.2 represents the stroboscopic photograph of the motion of the block.
Figure 2.2
Use the result in (a) to find
(i) the frequency of the stroboscope,
( 2 marks )
(ii) the speed of the trolley.
( 2 marks )
(iii) Suppose the mass of the block is halved and the force constant of the
spring is doubled while its natural length remains unchanged. If the
block is again released from the same position and the trolley is given
the same uniform velocity as before, find the block’s period of
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oscillation and draw the corresponding stroboscopic photograph in
Figure 2.2. Use x to indicate the position of the block.
( 5 marks )
(c) The trolley is stopped suddenly when the block is just at its lowest position.
The block slips on the platform and then moves off from it. Describe and
explain the subsequent motion of the block as seen by a stationary observer
on the ground.
( 3 marks )
3. Longitudinal waves can be produced in a metallic slinky spring and the
propagation speed of the waves is approximately given by
where
k = force constant of the slinky spring
L = length of the slinky spring
M = mass of the slinky spring
Figure 3.1
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A student conducts an experiment to verify this relationship.
The spring is
stretched to a length of 2.2 m as shown in Figure 3.2. A battery is connected
across the spring and two search coils are placed at A and B which are at a fixed
distance 1.0 m apart. The search coils are connected to the respective Y- inputs
of a dual trace CRO.
Figure 3.2
A sharp push is made at the left end of the slinky spring so that a compression
pulse travels along the spring. When the compression pulse passes the search
coil at A, the following trace is described on the screen of the CRO.
(a) State the purpose of connecting the slinky spring to a battery.
(b) Explain how the trace is formed.
( 1 mark )
( 3 marks )
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(c) The time interval for the pulse to travel from A to B can be found from the
corresponding traces registered by the search coils. The experiment is
repeated with slinky spring stretched to different lengths and the
corresponding time intervals found are tabulated below.
(i) Complete the table by choosing a suitable physical quantity and plot a
straight line graph to verify the given relationship.
( 4 marks )
Length of the slinky
spring L / m
2.2
2.0
1.8
1.6
1.4
Time interval for
0.51
0.56
0.62
0.70
0.79
the pulse to travel
from A to B t /s
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(ii) Calculate the slope of the graph obtained. Hence, estimate a value for
the force constant k when the mass of the spring is 0.3 kg.
( 3 marks )
(iii) Another student wants to verify whether the propagation speed of the
waves is inversely proportional to the square root of the spring’s mass.
He suggests using slinky springs of different masses stretched to the
same length to repeat the experiment. Explain whether he can verify
this relationship by plotting a suitable straight line graph. ( 2 marks )
4. A rectangular slice, of width d = 2.0 mm and thickness t = 0.5 mm, carries a
current I = 16 A in the direction as shown in Figure 4. A uniform magnetic field B
= 0.1 T is applied in the direction shown. The Hall voltage is measured between X
and Y. Given that there are 1.0 1029 charge carriers per cubic metre and each
carries a charge of 1.6  1019 C.
Figure 4
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a. Determine the sign of the charge carriers in the slice.
( 1 mark )
b. Calculate the drift velocity of the charge carriers.
( 2 marks )
c. Calculate the electric force on each charge carrier.
( 2 marks )
d. i. Calculate the value of the electric field between X and Y.
( 2 marks )
ii. Hence, using the answer of (d)(i), determine the Hall voltage between X
and Y.
( 2 marks )
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e.
State one precaution in the process of measuring the Hall voltage.
( 1 mark )
f.
Suggest any THREE modifications to the process of measurement so that
the value of the Hall voltage can be increased.
( 3 marks )
5. In Figure 5.1, a 47 µF capacitor, an inductor L and a 1 Ω resistor are connected
with a cell of e.m.f. 3V and negligible internal resistance. The inductor L is of
inductance 54 mH and resistance 0.5 Ω. Initially the capacitor is uncharged.
Figure 5.1
(a)
Find the current flowing in the 1 Ω resistor
(i) when the switch S is just closed;
(ii) a few minutes after the switch S is closed.
Explain briefly.
( 4 marks )
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(b) (i) Calculate the maximum p.d. across the capacitor.
(ii) Find the energy stored in the inductor at the steady state.
(iii)
( 2 marks )
( 2 marks )
If switch S is now opened, sketch the time variation of the p.d. Vc
across the capacitor.
( 2 marks )
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(c) State how you would modify the circuit so as to demonstrate that a large
induced e.m.f. is produced across the inductor when switch S is suddenly
opened. Explain briefly.
( 3 marks )
6. (a) A parallel-plate capacitor is formed by two square metal plates. The plates
are kept apart by four small polythene spacers at the corners.
The set-up shown in Figure 6.1 is used to investigate the relation between the
capacitance C of the capacitor and the separation d of the plates when their
area of overlap is kept constant.
Figure 6.1
The frequency f of the reed switch is 400 Hz and the voltmeter reading V is
25 V. By varying the separation d of the plates, the corresponding
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galvanometer readings I are obtained. A graph of I against 1/d is plotted
below.
(b) Write down an expression of C in terms of f, I and V. Use the graph to
deduce a numerical relation between C (in F) and d (in m).
( 5 marks )
(b)
A capacitor is formed by using the two square metal plate 6 mm
separation. It has capacitance 92.2 x 10-12 F and is connected to a d.c.
source as shown in Figure 6.3. Another 2 mm tick metal plate of the
same area is inserted mid-way between the parallel plates of the
capacitor as shown. The voltage of the d.c. source is maintained at
100 V.
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Figure 6.3
(i) Calculate the increase in the following physical quantities.
( 6 marks )
(I) the capacitance of the capacitor
(II) the charges on the capacitor plates connecting to the source
(III) the energy stored in the capacitor
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(ii) Calculate the work done by the d.c. source in moving the charges
from the plate to another when inserting the 2 mm metal plate.
Compare your result with that of (b)(i)(III) and account for the
difference.
( 4 marks )
7.
A cylinder fitted with a movable piston contains 1.00 mole of a monatomic gas
at a pressure of 1.00 x 105 Pa and a temperature of 200 K. The gas in first heated
at constant pressure to 350 K. Take the gas constant. R = 8.31 mol-1 K-1.
a. Find the volume of the gas
i.
before heating
ii. after heating.
b. Determine the change in internal energy of the gas.
( 3 marks )
( 2 marks )
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c. Determine the heat input to the cylinder.
( 3 marks )
The gas is then compressed isothermally to its initial volume. Afterward, it is
cooled at constant volume to its initial temperature.
d. Sketch the changes happened to the gas on a p-V diagram, inserting all the
initial and final pressure and volume values for all the processes described
in this question.
e. What does the area bounded by the curves represent?
( 3 marks )
( 1 marks )
f. Mark on your curves in (d) the state of the gas when its density is highest.
( 1 mark )
8.
a.
Xenon-139 has a half-life of 41 s and is produced at a constant rate during
the fission of a particular sample of Uranium-235. No Xenon-139 escapes
from the sample and it is found that eventually, the number of Xenon-139
nuclei present becomes constant. (Avogadro’s number = 6.02  1023 mol-1)
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b.
i.
Define half-life.
( 1 mark )
ii.
Suggest why the number of Xenon-139 nuclei in the sample becomes
constant.
( 1 mark )
When the number of Xenon-139 nuclei has become constant, the activity
of the Xenon-139 is 3.4  108 Bq. Calculate the mass of Xenon-139
present in the sample.
( 4 marks )
c.
When Uranium-235 nuclei are fissioned by slow-moving neutrons, two
possible reactions are:
235
reaction 1:
+0n1 → 54Xe139 + 38Sr95 +2 0n1 + energy
92U
235
reaction 2:
+ 0n1 → 2 46Pd116 + n X + energy
92U
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The binding energy per nucleon E for a number of nuclides is given in the
following table.
Nuclide
E / MeV
95
38Sr
8.74
54
Xe139
235
92U
(i)
8.39
7.60
State what is meant by the binding energy per nucleon
of a nucleus.
( 1 mark )
(ii)
Calculate the energy, in MeV, released in reaction 1.
( 2 marks )
(iii)
The energy released in reaction 2 is 163 MeV. Suggest,
with a reason, which one of the two reactions is more
likely to occur.
( 2 marks )
*** END OF PAPER ***
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