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01 AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
2001 Structural Question
1. (a) Figure 1.1 shows a man of mass 70 kg standing against the wall of a
cylindrical compartment called a ‘rotor’. The level of the rotor’s floor can be
adjusted. The diameter of the rotor is 5.0 m.
Figure 1.1
The rotor is spun at a certain speed about its central vertical axis so that, at this
angular speed, the man remains ‘pinned’ against the wall even if the floor of
the rotor is pulled downwards.
(i) Name the forces FA and FB acting on the man.
(2 marks)
(ii) It is known that the maximum value of FA equals 0.4 FB. Find the
minimum angular speed, in rads-1, of the rotor needed to keep the man
‘pinned’ against the wall.
(3 marks)
(iii) If the mass of the man is greater than 70 kg, would the result in (a)(ii)
increase, decrease or remain unchanged? Explain briefly.
(2 marks)
(b) Figure 1.2 shows a donut-shaped space station that is far from any planetary
objects. It is designed such that the astronauts live at the periphery 1.0 km
from the centre. Describe how an ‘artificial gravity’ of 10 Nkg-1 can be
created at the periphery.
(3 marks)
Figure 1.2
01 AL/Structural Question/P.2
2. Figure 2.1 shows a small bead of mass m connected by two identical elastic light
strings to points A and B respectively, with A vertically above B. The separation
between A and B is 1.0 m. The bead is at rest when it is 0.45 m above B and both
strings are taut.
A
1.0 m
Figure 2.1
m
0.45 m
B
(a) (i) Write down an equation relating the tensions in the strings with the
weight of the bead.
(1 mark)
(ii) If each string has an unstretched length of 0.4 m and a force constant of
0.6 Nm-1, find m.
(2 marks)
(b) The bead is now displaced vertically a small distance y from its equilibrium
position and is then released from rest. (Neglect air resistance and assume that
both strings are always taut.)
(i) What is the maximum allowed value of y such that the strings remain taut
when the bead oscillates?
(1 mark)
(ii) Show that the restoring force is given by -1.2 y and calculate the period of
oscillation of the bead.
(3 marks)
(c) With the bead resting at its equilibrium position, the lower string is cut. Find
(i) the initial acceleration of the bead;
(2 marks)
(ii) the new equilibrium position of the bead and its maximum speed in the
subsequent motion.
(5 marks)
01 AL/Structural Question/P.3
3. Figure 3.1 shows a thin horizontal wire attached to a fixed point A at one end. The
wire passes over a smooth light pulley, and is kept taut by a mass M hanging down
at the other end. Movable wooden wedges B and B’ are placed beneath the wire.
A sinusoidal alternating current of variable frequency is passed into the wire.
Strong magnets are placed midway between B and B’ such that the magnetic field
is perpendicular to the wire. As a result the wire is set into vertical vibration.
a.c.
S
A
Figure 3.1
B
B’
N
M
(a) Briefly explain how the vibrations are produced. Name this kind of vibration.
(2 marks)
(b) When the frequency of the current is 75 Hz and the length of the wire between
BB’ is 1.2 m, the appearance of the wire is as shown.
B
B’
(i) Find the fundamental frequency and the speed of the waves in the wire.
(3 marks)
(ii) With the length of the wire between BB’ unchanged, the frequency of the
current is increased to a value slightly higher than 75 Hz. Explain how to
restore the pattern of stationary waves shown.
(2 marks)
(c) Would the speed of the waves in the wire increase, decrease or remain
unchanged when the frequency of the current is decreased gradually. Explain
briefly. (No mathematical derivation is required.)
(2 marks)
01 AL/Structural Question/P.4
4. Figure 4.1 shows a solenoid of diameter 5.0 cm and length 50 cm. The solenoid
has 1.0  103 turns and it carries a current of 60 mA. (Given: permeability of free
space = 4  10-7 Hm-1)
50 cm
Figure 4.1
O
60 mA
solenoid
(a) (i) Calculate the magnetic field strength at the centre O of the solenoid.
Justify the major assumption you made in the calculation.
(3 marks)
(ii) Calculate the magnetic flux linkage through the solenoid. Hence or
otherwise find the inductance of the solenoid. (Assume that the flux
leakage of the solenoid is negligible.)
(4 marks)
(b) The solenoid is now connected with a resistor R0 and a 3 V battery as shown in
Figure 4.2. When switch S is opened the variation of the current I through R0
with time t for the first 30 s is as shown.
A
R0
I/mA
B
60
solenoid
D
C
Figure 4.2
41
3V
S
0
30
t/s
According to textbooks, the current would decrease exponentially as I =
 Rt
I 0 e L , where R and L are the resistance and inductance of the circuit ABCD
respectively.
(Given: e  x can be approximated to 1 - x for small x)
(i) Explain why the graph in Figure 4.2 appears to be a straight line. (2 marks)
(ii) Find the experimental values of R and L.
(4 marks)
(iii) Account for the difference between the experimental value of L in (b)(ii)
and its theoretical value in (a)(ii).
(1 mark)
01 AL/Structural Question/P.5
5. A simple electric motor has a rectangular coil of 120 turns, each of area 0.002 m2,
and of total resistance 0.8 . It is connected to a 12 V d.c. supply of negligible
internal resistance. The strength of the uniform magnetic field in the region of the
coil is 0.5 T. Figure 5.1 shows the variation of current I with time t when the
motor is switch on.
I
P
Imax
Not to scale
Figure 5.1
Q
C
2.0 A
t
0
t1
(a) (i) Estimate the maximum value of the current Imax.
(2 marks)
(ii) When the motor is switched on, the current is so large that it may burn out
the coil. Explain how this can be avoided.
(2 marks)
(b) Explain why the current
(i) does not rise immediately to its maximum value;
(ii) drops gradually from P to Q and becomes steady along QC.
(3 marks)
(c) (i) What is the maximum torque acting on the coil due to the current when it
is rotating at constant speed?
(2 marks)
(ii) For the motor running at constant speed, calculate
(I) the back e.m.f. developed across the coil;
(II) its efficiency in converting electrical power to mechanical power.
(4 marks)
01 AL/Structural Question/P.6
6. The map in Figure 6.1 shows two radio transmission stations P and Q, which are
about 15 m apart. Both stations emit radio waves of frequency 60 MHz and with
vertical electric fields in phase with each other.
S
P
A
B
Figure 6.1
O
Q
R
Sea
When an electric field detector is moved steadily along line POQ, alternate
maximum and minimum signals are received.
(a) Describe the variation of the signals along line ROS, which is perpendicular
bisector of POQ. Account for the difference(s) compared to the variation of
the signals along POQ.
(2 marks)
(b) The signal is minimum at points A and B on line POQ. Find the wavelength of
the radio waves and deduce the least separation between A and B.
(3 marks)
(c) On Figure 6.1, draw a few lines of the minimum intensity of the received
signal on both sides of ROS.
(2 marks)
(d) If the transmission station at Q is temporarily suspended, the signal at A would
increase. Account for the observation with reference to energy consideration.
(3 marks)
01 AL/Structural Question/P.7
7. An earthquake propagates in the form of waves. The quake centre produces both
longitudinal and transverse waves, which are known as P waves and S waves
respectively. The two types of wave propagate at different speeds in the earth’s
crust. Figure 7.1 shows distance-time graphs for these two waves.
Figure 7.1
(a) With reference to the vibrations of particles, state the difference between
longitudinal and transverse waves.
(1 mark)
(b) (i) Find the speed of the P waves and of the S waves.
(2 marks)
E
where E and  are

respectively the Young modulus and the average density of the earth’s
crust. Estimate E if  = 2.5  103 kgm-3.
(2 marks)
(ii) The speed of the P waves can be approximated by
Three detecting stations A, B and C are located at the vertices of an equilateral
triangle as shown in Figure 7.2. Their mutual separation is 600 km. Figure 7.3
shows the records (seismograph traces) of an earthquake recorded by these
stations. Due to the difference in speeds, the P and S waves are detected at
different times. Such a time difference is called the S-P interval. The S-P
intervals are respectively 45 s, 27 s and 18 s for stations A, B and C.
01 AL/Structural Question/P.8
Figure 7.2
Figure 7.3
(c) (i) What evidence in the records shows that station C is closest to the quake
centre?
(1 mark)
(ii) Use Figure 7.1 or otherwise to find the distances of stations A and B from
the quake centre. Which position in Figure 7.2, X, Y or Z, is the
approximate location of the quake centre?
(3 marks)
(d) The frequency of the quake waves is approximately 5 Hz. It is known that the
natural frequencies of bridges F and G are respectively 6 Hz and 12 Hz.
Explain why bridge F would collapse more easily in an earthquake. (2 marks)
8. Figure 8.1 shows a circuit for investigating the current delivered by a battery and
its terminal voltage. A battery of e.m.f.  and internal resistance r is connected
through an ammeter to a variable resistor R. The terminal voltage is measured by
a high-resistance voltage. The resistance of the ammeter is negligible compared to
that of R.
A
Figure 8.1
, r
V
R
01 AL/Structural Question/P.9
The ammeter reading I and voltmeter reading V for different values of R are
tabulated as follows:
I (A)
V (V)
V/I ()
1/I (A-1)
0.80
3.52
0.50
4.46
0.40
4.76
0.32
5.02
0.25
5.23
(a) Express V in terms of , I and r. Explain why V increases as I decreases.
(2 marks)
(b) Complete the above table and plot a graph of V/I against 1/I in order to
determine the e.m.f. and the internal resistance of the battery.
(6 marks)
(c) Suggest a graphical method to determine the resistance value of R necessary
for the battery to deliver maximum output power.
(2 marks)
Both the ammeter and voltmeter used are converted from the same kind of basic
meter, which has a scale with 100 divisions; its current sensitivity is 0.01 mA per
division and the voltage sensitivity is 1.0 mV per division.
(d) Find the resistance of the basic meter and describe how to convert such a meter
into
(i) an ammeter of full-scale deflection 1 A; and
(ii) a voltmeter of full-scale deflection 6 V.
Give the value(s) of the component(s) you would use.
(5 marks)
(e) Figure 8.2 shows a circuit in which the converted meters in (d) are used for
measuring a resistance R1 of 1 k. Would the measured value of R1 obtained
from the meter readings be smaller than, close to or greater than the actual
value? Find the percentage error in the measured value.
(3 marks)
A
Figure 8.2
V
R1
01 AL/Structural Question/P.10
9. (a) Figure 9.1 shows a circuit in which a light dependent resistor (LDR) is
connected in series with a 8 k resistor and a 6 V battery. The resistance of
the LDR is 500 k in the dark.
8 k
6V
Figure 9.1
(i) When the LDR is in the dark, the voltage across the LDR is
approximately 6 V, which takes the same value as the e.m.f. of the
battery. Briefly explain the result and suggest a suitable instrument for
the measurement of this voltage.
(2 marks)
(ii) The voltage across the LDR is 2 V when the illumination is high. Find
the resistance of the LDR at this level of illumination.
(1 mark)
(b) (i) Describe the difference in function between an operational amplifier used
as an amplifier and one used as a comparator.
(2 marks)
(ii) With an operational amplifier used as a comparator, draw a switching
circuit for a street light powered by 220 V a.c. main which allows both
manual and automatic operation. Briefly describe how the circuit works.
(6 marks)
10. Two containers A and B with volumes 100 cm3 and 500 cm3 respectively are
connected by a tube of negligible volume as shown in Figure 10.1. The tap T for
controlling gas flow is closed initially. Container A contains an ideal gas at a
pressure of 12  105 Pa while there is a vacuum in container B. The temperature
of the two containers is maintained at 0C by two separate water baths with
melting ice.
T
Figure 10.1
A
B
01 AL/Structural Question/P.11
(Given: Universal gas constant = 8.31 JK-1mol-1
Avogadro constant = 6.02  1023 mol-1
Mass of a molecule of the ideal gas = 4.52  10-26 kg)
(a) Calculate the number of moles of gas in container A.
(2 marks)
(b) When tap T is open and steady state is reached, find
(i) the work done by the gas;
(ii) the root-mean-square speed of the gas molecules in B.
(3 marks)
(c) The water bath for container A is heated until the water boils. The tap T
remains open. Calculate
(i) the equilibrium pressure of the gas in the two containers; and
(ii) the net amount of gas, in moles, that passed through the connecting tube
during the heating process.
(5 marks)
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