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97/AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
1997 Structural Question
1. Figure 1.1 shows a smooth box in which a small block of mass m is connected by
two identical light springs to opposite sides, A and B, of the box.
box
m
A
B
x
Figure 1.1
m
T1
T2
Initially both springs are stretched an equal amount e and the force constant is 10
Nm-1 each. The block is now displaced a small distance along AB from the
equilibrium position and is released from rest. (Assume that both springs are
always in tension.)
(a) When the block is at a distance x from the equilibrium position, write down
the expressions for the tensions, T1 and T2, in the springs. Show that the
motion of the block is simple harmonic.
(4 marks)
(b) Figure 1.2 shows the time variation of the potential energy of one of the
springs.
potential energy
Figure 1.2
0
0.2
0.4
0.6
0.8
time / s
(i) Using crosses, indicate on the graph the points corresponding to the time
at which the block is at its extreme positions.
(1 mark)
(ii) Find the period of oscillation and the mass of the block.
(4 marks)
(c) State the change, if any, in the period of oscillation if
(i) the box is tilted at a small angle to the horizontal;
(1 mark)
(ii) a larger box with greater separation AB is used.
(1 mark)
97/AL/Structural Question/P.2
2. A small source emitting electromagnetic waves of frequency 1010 Hz is placed
some distance, say 100 m, from a 1 m  1 m square metal plate. The line joining
the source and the centre of the plate is perpendicular to the plate. Figure 2.1
shows part of the wavefronts emitted from the source towards the plate.
plate
source
Figure 2.1
(a) Name the electromagnetic waves emitted.
(1 mark)
(b) (i) In Figure 2.1, sketch the reflected wavefronts and indicate the position S’
where the reflected wavefronts appear to come from.
(2 marks)
(ii) A detector registers a non-zero reading when it is placed some distance
behind the plate on the line joining the source and the centre of the plate.
Briefly explain this observation with the aid of a diagram.
(2 marks)
plate
source
(c) (i) If the plate is now moving towards the source at a speed of 20 ms-1, what
would the speed of position S’ in (b)(i) be? Hence or otherwise calculate
the change in frequency of the reflected waves.
(3 marks)
(ii) A typical radar speed trap employs similar principles by sending some
electromagnetic waves towards a moving car. To deduce the speed of the
car, the reflected waves received are compared with the emitted waves in
such a way that the beat frequency between them can be measured.
Explain why the beat frequency is measured instead of the frequency of
the reflected waves being directly measured.
(2 marks)
97/AL/Structural Question/P.3
3. Figure 3.1 shows a uniform wire which is held taut but unstretched between a
fixed point and a smooth cylindrical peg of radius 1 cm. The force constant of the
wire is 9.6  102 Nm-1. The tension in the wire can be increased by rotating the
peg about its fixed axis so that some wire is wound onto the peg.
wire
Figure 3.1
peg
(a) When the peg is rotated through an angle of 2, calculate
(i) the tension in the wire.
(2 marks)
(ii) the work done in rotating the peg.
(2 marks)
(b) The above wire is part of a musical instrument. Two knife edges, A and B, are
placed 0.36 m apart under the stretched wire as shown in Figure 3.2. The mass
of the wire between A and B is 6.4  10-4 kg. (Assume that the presence of the
two knife edges would not affect the tension in the wire.)
A
B
wire
Figure 3.2
0.36 m
peg
(i) Calculate the frequency of the fundamental note emitted when the wire
between A and B is plucked.
(3 marks)
(ii) State THREE differences between the waves in the wire and the
fundamental note emitted.
(3 marks)
(iii) Draw a diagram to show the vibration of the wire between A and B when
it is vibrating at the third harmonic.
(1 mark)
A
B
97/AL/Structural Question/P.4
4. (a) Figure 4.1 shows three identical cells connected with a 10-k resistor. A
student uses a CRO and a moving-coil voltmeter in turn to measure the
potential difference across PQ, the readings being 4.5 V and 4.1 V
respectively.
10 k
X
Figure 4.1
P
Q
(i) Account for the difference in the readings.
(3 marks)
(ii) Estimate the resistance of the voltmeter. What would the reading be if the
voltmeter is connected across XQ?
(3 marks)
(b) Figure 4.2 shows part of the internal structure of a typical multimeter. It has a
coil connected to a shunt built from resistors R1 and R2, and a series of voltage
multipliers R3 and R4. The resistances of R1, R2 and R3 are 9.8 k, 200  and
48 k respectively. A rotary switch S enables the various full-scales values of
current or voltage to be chosen.
20
30
10
40
0
50
coil
Figure 4.2
R1
R3
R2
2.5 mA
50  A
S
0.1 V
R4
2.5 V
10 V
X
input terminals
+
_
(i) Calculate the resistance of the coil and the current flowing through it for
full-scale deflection. Show your working.
(4 marks)
(ii) Calculate the resistance of R4.
(2 marks)
(iii) In the spaces provided in Figure 4.2, add two components to the circuit so
that the multimeter can be used to measure resistance between its input
terminals when switch S is set at X. Describe briefly how to adjust for
zero ohm position.
(3 marks)
97/AL/Structural Question/P.5
5. An iron-cored inductor L, a milliammeter A and a 9 V d.c. supply of negligible
internal resistance are connected as shown in Figure 5.1. The graph shows the
variation of current with time during the first few milliseconds, OA, and a few
seconds later, BC, after closing switch S.
current/mA
B
C
500
L
Figure 5.1
S
A
9V
A
10
O
0
2
(a) What is meant by the inductance of an inductor?
2500
3000
time/ms
(1 mark)
(b) (i) Explain why the current cannot rise instantaneously to the final steady
value.
(2 marks)
(ii) Find the inductance of L.
(2 marks)
(iii) Calculate the resistance of the circuit.
(2 marks)
(iv) If the soft iron core of inductor L is removed, sketch on the same graph
the parts corresponding to OA and BC.
(2 marks)
(c) When the circuit is broken by opening switch S, sparking occurs at the
contacts of the switch.
(i) Where does the energy for the sparks come from?
(1 mark)
(ii) In order to prevent sparking, a capacitor is now connected in parallel with
the switch. It is known that sparking occurs when the voltage across the
contacts of the switch exceeds 350 V. Assuming that the energy loss due
to the resistance of the circuit is negligible, calculate the minimum
capacitance required to prevent sparking.
(3 marks)
6. (a) Figure 6.1 shows the apparatus for investigating the transmission and reception
of 1 GHz radio waves. A transmitting aerial connected to a signal generator
emits plane-polarized radio waves. An antenna connected to a microammeter
is used for receiving the radio waves. The antenna can be rotated about its
centre in the plane containing it as shown.
97/AL/Structural Question/P.6
Figure 6.1
(i) What do you understand by ‘plane-polarized’ radio waves?
(1 mark)
(ii) Describe how you would use the apparatus to show the transverse nature
of radio waves. Explain briefly.
(3 marks)
(iii) A metal plate is now placed vertically to one side of the aerial and the
antenna such that it is very close to the antenna but without touching it.
Explain carefully the change, if any, in the microammeter reading after
the plate is placed.
(3 marks)
metal plate
top view
Figure 6.2
aerial
antenna
(b) Figure 6.3 shows a simplified tuning circuit for a radio receiver.
antenna
Figure 6.3
L’
L
C
To receiver
earth
(i) Explain the function of coil L’.
(2 marks)
97/AL/Structural Question/P.7
(ii) Explain how a radio signal of a particular frequency can be picked up by
the LC circuit though radio signals of various frequencies are received by
the antenna.
(2 marks)
(iii) It is preferable to keep the length of the wire for making coil L as short as
possible. Briefly explain why this is so.
(2 marks)
6V
S1
7. (a)
Figure 7.1
A
C
R
A
B
S2
Figure 7.1 shows a circuit used for investigating the charging process of a
capacitor.
Before the experiment, push-button switch S2 is closed
momentarily. With switch S1 closed, the charging process starts. The
ammeter readings, I, at various times, t, are taken. The results are plotted on
the graph below.
I / mA
80
70
60
50
40
30
20
10
0
1
2
3
4
5
t /s
(i) Explain why the ammeter reading decreases with time.
(ii) What is the physical meaning of the area under the curve?
(2 marks)
(1 mark)
(iii) Sketch on the same graph to show how the current varies with time when
the experiment is repeated with
(I) a second identical capacitor connected in parallel with C, (label it as
curve (I))
97/AL/Structural Question/P.8
(II) a second identical resistor connected in series with R (label it as
curve (II)).
(4 marks)
(b) Two parallel-plate capacitors, C1 and C2, formed by identical metal plates are
connected in series with an E.H.T. of 1.5 kV as shown in Figure 7.2. Point R
of the circuit is earthed. The plate separation of C2 is double that of C1.
+
Figure 7.2
1.5 kV _
E.H.T.
C1
C2
R
P
Q
S
T
(i) Sketch a graph to show the variation of electric potential with position
along PQRST. Label both axes.
(3 marks)
(ii) Describe and explain what would be observed if a positively-charged foil
strip is moved between the plates of C1 without touching them. (3 marks)
(iii) Comparing with (b)(ii), state the change(s), if any, when the foil strip is
placed between the plates of C2.
(1 mark)
8. Figure 8.1 shows a device for accelerating protons to a high speed in a vacuum. It
consists of two semi-circular chambers within which a uniform magnetic field, B,
is present (not shown in the diagram). A potential difference, V, is set up across
the narrow gap between the chambers such that its polarities reverse every time
the proton goes from one chamber to the other.
High frequency
alternating p.d.
+V
Figure 8.1
-V
narrow gap of
negligible width
0V
When a proton of negligible speed is injected into the centre of the device, it is
accelerated by the potential difference towards one chamber and describes a semicircle inside that chamber due to the magnetic field present. The proton is then
97/AL/Structural Question/P.9
accelerated across the gap through a potential difference of V and describes
another semi-circle of greater radius in the other chamber since its speed has
increased. This process is repeated and the path of proton is shown in Figure 8.1.
(a) (i) Indicate in Figure 8.1 the direction of the magnetic field in the chambers.
(1 mark)
(ii) For a proton of mass m and charge q moving with speed v in a circle of
radius r in one of the chambers, express v in terms of r. Explain why the
proton does not gain kinetic energy in the chambers.
(3 marks)
(iii) Show that the time spent by the proton in describing any semi-circle is
independent of v and r.
(2 marks)
(b) It is known that the strength of the magnetic field, B, is 1.5 T and the
alternating potential difference, V, is 10 kV.
(Given: electronic charge = 1.6  10-19 C; mass of a proton = 1.66  10-27 kg)
(i) Find the gain in kinetic energy, in eV, of the proton in each complete
revolution.
(1 mark)
(ii) Calculate the time taken for a proton to gain a kinetic energy of 1 MeV.
(3 marks)
9. (a) An operational amplifier of open-loop voltage gain 105 operates with supply
voltage 15 V. What is the voltage across its input terminals when it has just
been saturated?
(1 mark)
(b) (i) In the space provided, draw the circuit of a voltage follower using an ideal
operational amplifier.
(2 marks)
(ii) Explain why, for a voltage follower, the output voltage follows the input
voltage exactly. State one application of such a circuit.
(3 marks)
(c) Figure 9.1 shows the essential parts of a light-operated alarm circuit. The
operational amplifier in the circuit acts as a voltage comparator so that the
LED is on as soon as light is detected by the LDR. The resistance of the LDR
drops from 100 k to 10 k in the presence of light.
97/AL/Structural Question/P.10
+ 15 V
15 k
LDR
X
Figure 9.1
LED
Y
50 k
30 k
0V
- 15 V
(i) Briefly explain the operation of the circuit.
(3 marks)
(ii) State the minimum potential at Y for switching on the LED and calculate
the minimum value of the resistance of the 50-k rheostat below which
the circuit will fail to operate.
(3 marks)
10. In an experiment to investigate the absorption of  and  rays by materials, a
source emitting  and  rays is placed at a distance of about 5 cm from a G-M tube
as shown in Figure 10.1.
ratemeter
source
G-M tube
Figure 10.1
absorbers
The count rates, N, are measured for different thicknesses, d, of absorber plates.
The results are shown in Figure 10.2, with curve A corresponding to the
measurements using aluminium absorber plates while curve B corresponds to
those using lead absorber plates.
97/AL/Structural Question/P.11
N / s-1
60
(A)
50
40
(B)
30
aluminium
20
lead
10
0
2
4
6
8
d / mm
10
Figure 10.2
(a) (i) Curve A shows a considerable decreased in count rates up to a thickness
of 7 mm; a further increase in d only results in a slight decrease in count
rates. Explain why this is so.
(2 marks)
(ii) From the graphs in Figure 10.2, estimate the minimum thickness of lead
needed to absorb most of the  rays.
(1 mark)
(iii) The source also emits -particles.
neglected in this experiment.
Explain why their effects can be
(1 mark)
(b) The count rates, N’, corrected for background, corresponding to different
thickness, d, of lead absorber plates are tabulated as follows:
d / mm
N’ / s-1
ln N’
1
28.0
2
24.8
3
22.0
4
20.0
5
18.2
6
16.8
7
15.7
97/AL/Structural Question/P.12
(i) What is meant by the count rates being ‘corrected for background’?
(1 mark)
(ii) Complete the table on the previous page and plot a graph of ln N’ against
d.
(4 marks)
(iii) Write down a relation between N’ and d.
- End of Paper -
(2 marks)