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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 70kg standing against the wall of a cylindrical
compartment called a ‘rotor’. The level of the floor can be adjusted. The
diameter of the rotor is 5.0m.
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.
(1) Name the force FA and FB acting on the man.
(2) It is known that the maximum value of FA equals 0.4FB. Find the minimum
angular speed, in radian per second, of the rotor needed to keep the man
pinned against the wall.
(3) If the mass of the man is greater than 70kg, would the result in (a)(2) increase,
decrease or remain unchanged? Explain briefly.
Figure 1.2
(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 center. Describe how an ‘artificial gravity’ of 10 Nkg-1 can be created at the
01 AL/Structural Question/P.2
periphery.
2. Figure 2.1 shows a small bead of mass m connected by two identical elastic light
strings to point A and B respectively, with A vertically above B. The separation
between A and B is 1.0m. The bead is at rest when it is 0.45 above B and both
strings are taut.
Figure 2.1
(a) (1) Write down an equation relating the tension in the strings with the weight
of the bead.
(2) If each string has an unstretched length of 0.4m and a force constant of
0.6Nm-1, find m.
(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.)
(1) What is the maximum allowed value of y such that the strings remain taut
when the bead oscillates?
(2) Show that the restoring force is given by –1.2y and calculate the period of
oscillation of the bead.
(c) With the bead resting at its equilibrium position, the lower string is cut. Find
(1) the initial acceleration of the bead.
(2) The new equilibrium position of the bead and its maximum speed in the
subsequent motion.
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.
01 AL/Structural Question/P.3
Figure 3.1
(a) Briefly explain how the vibrations are produced. Name this kind of vibration.
(b) When the frequency of the current is 75Hz and the length of the wire between
BB’ is 1.2m, the appearance of the wire is as shown.
(1) Find the fundamental frequency and the speed of the waves in the wire.
(2) With the length of the wire between BB’ unchanged, the frequency of the
current is increased to a value slightly higher than 75Hz. Explain how to
restore the pattern of stationary waves shown.
(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.)
4. Figure 4.1 shows a solenoid of diameter 5.0cm. 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)
Figure 4.1
(a) (1) Calculate the magnetic field strength at the center O of the solenoid. Justify
the major assumption you made in the calculation.
(2) 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.)
(b) The solenoid is now connected with a resistor R0 and a 3V battery as shown in
01 AL/Structural Question/P.4
Figure 4.2. When switch is opened the variation of the current I through R0
with time t for the first 30μs is as shown.
Figure 4.2
According to the textbooks, the current would decrease exponentially as
I  I0e
 Rt
L
, where R and L are the resistance and inductance of the solenoid
respectively. Assume that the resistance of R0is much smaller than R. (Given:
e-x can be approximated to 1-x for small x)
(1) Explain why the graph in Figure 4.2 appears to be a straight line.
(2) Find the experimental values of R and L.
(3) Account for the difference between the experimental value of L in (b)(2)
and its theoretical value in (a)(2).
5. A simple electric motor has a rectangular coil of 120 turns, each of area 0.002m2,
and of total resistance 0.8Ω. It is connected to a 12V d.c. supply of negligible
internal resistance. The strength of the uniform magnetic field in the region of the
coil is 0.5T. Figure 5.1 shows the variation of current with time t when the motor
is switched on.
01 AL/Structural Question/P.5
Figure 5.1
(a) (1) Estimate the maximum value of the current Imax.
(2) When the motor is switched on, the current is so large that it may burn out
the coil. Explain how this can be avoided.
(b) Explain why the current
(1) does not rise immediately to its maximum value;
(2) Drops gradually from P to Q and becomes steady along QC.
(c) (1) What is the maximum torque acting on the coil due to the current when it is
rotating at constant speed?
(2) 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.
01-1B
6. The map in Figure 6.1 shows two radio transmission stations P and Q, which are
about 15m apart. Both stations emit radio waves of frequency 60 MHz and with
vertical electric fields in phase with each other. The waves are of the same
amplitude.
01 AL/Structural Question/P.6
Figure 6.1
When an electric field detector is moved steadily along line POQ, alternate
maximum and minimum signals are received.
(a) Describe the variation of signals along line ROS, which is the perpendicular
bisector of POQ. Account for the difference(s) compared to the variation of
the signals along POQ.
(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.
(c) On Figure 6.1, draw a few lines of the minimum intensity of the received
signal on both sides of ROS.
(d) If the transmission station at Q is temporarily suspended, the signal at A would
increase. Account for observation with reference to energy consideration.
7. An earthquake propagates in the form of waves. The quake center 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.
01 AL/Structural Question/P.7
Figure 7.1
(a) With reference to vibrations of particles, state the difference between
longitudinal and transverse waves.
(b) (1) Find the speed of the P waves and of the S waves.
(2) The speed of the P waves can be approximated by
E
where E and ρ

are respectively the Young modulus and the average density of the earth’s
crust. Estimate E if   2.5  103 kgm-3.
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 600km. 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 45s, 27s and
18s for stations A, B and C.
01 AL/Structural Question/P.8
Figure 7.2
(c) (1) What evidence in the records shows that station C is closest to the quake
center?
(2) Use Figure 7.1 or otherwise to find the distances of stations A and B from
the quake center. Which position in Figure 7.2, X,Y or Z, is the
approximate location of the quake center?
(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 6Hz and 12Hz. Explain
why bridge F would collapse more easily in an earthquake.
8. Figure 8.1 shows a circuit for investigating the current delivered by a battery and
its terminal voltage. A battery of e.m.fε and internal resistance r is connected
through an ammeter to a variable resistor R. The terminal voltage is measured by a
high-resistance voltmeter. The resistance of the ammeter is negligible compared to that
of R.
Figure 8.1
The ammeter reading I and voltmeter reading V for different values of R are tabulated
as follows:
I (A)
0.80
0.50
0.40
0.32
0.25
V (V)
3.52
4.46
4.76
5.02
5.23
01 AL/Structural Question/P.9
V/I()
1/I(A-1)
(a) Express V in terms of ε, I, r. Explain why V increases as I decrease.
(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.
(c) Suggest a graphical method to determine the resistance value of R necessary
for the battery to deliver maximum output power.
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 0.01mA per
division and the voltage sensitivity is 1.0mV per division.
(d) Find the resistance of the basic meter and describe how a convert such a meter
into
(1) an ammeter of full-scale deflection 1A; and
(2) a voltmeter of full-scale deflection 6V
Give the value(s) of the component(s) you would use.
(e) Figure 8.2 shows a circuit in which the converted meters in (d) are used for
measuring a resistance R1 of 1kΩ. 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.
Figure 8.2
9. (a) Figure 9.1 shows a circuit in which a light dependent resistor (LDR) is
connected in series with a 8kΩ resistor and a 6V battery. The resistance of the
LDR is 500kΩin the dark.
Figure 9.1
01 AL/Structural Question/P.10
(1) When the LDR is in the dark, the voltage across the LDR is approximately
6V, 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) The voltage across the LDR is 2V when the illumination is high. Find the
resistance of the LDR at this level of illumination.
(b) (1) Describe the difference in function between an operational amplifier used
as an amplifier and one used as a comparator.
(2)With an operational amplifier used as a comparator, draw a switching
circuit for a street light powered by 220V a.c. mains which allows both
manual and automatic operation. Briefly describe how the circuit works.
10. Two containers A and B with volumes 100cm3 and 500cm3 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℃by two separate water baths with
(Given:
melting ice.
Universal gas constant = 8.31JK-1 mol-1
Avogadro constant = 6.02  10 23 mol 1
Mass of a molecule of the ideal gas = 4.52  1026 kg )
Figure 10.1
(a) Calculate the number of moles of gas in container A.
(b) When tap T is open and steady state is reached, find
(1) the work done by the gas;
(2) the root-mean-square speed of the gas molecules in B.
(c) The water bath for container A is heated until the water boils. The tap T
remains open. Calculate
(1) the equilibrium pressure of the gas in the two containers; and
(2) the net amount of gas, in moles, that passed through the connecting tube
during the hearing process.