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98 AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
1998 Structural Question
1. A space shuttle crew is sent to service the Hubble Space Telescope H which is in a
circular orbit 6.0  105 m above the earth’s surface. The crew succeed in moving
the space shuttle S into the same orbit as H and its thrust rockets are shut down.
The telescope is positioned a few kilometers in front as shown in Figure 1.1. Let
G be the gravitational constant and ME the mass of the earth.
(Given: radius of earth = 6.4  106 m )
Figure 1.1
(a) What is the apparent weight of an astronaut of mass of 70 kg inside the
shuttle?
(b) (1) Calculate the value of the gravitational field strength in the orbit.
(2) Calculate the speed and period of the shuttle in the orbit.
(c) (1) Show that the total mechanical energy of the shuttle is proportional
to –1/r, where r is the radius of its orbit.
(2) In order to overtake the telescope, the shuttle must first spiral into an orbit
of a smaller radius in which it would have a larger angular speed. Using the
result in (c)(1), determine whether the shuttle should increase or decrease its
original speed so that it can get into a lower orbit. Explain your answer.
2. A boy of mass 50 kg performs a bungee jump from a bridge 40 m above a river.
An elastic rope outstretched length 15 m is tied round his legs at one end while the
other end is fixed on the bridge at A. The boy then drops off the bridge and
reaches the lowest point D just clear of the water surface. Assume that the rope
obeys Hooke’s law throughout the motion. (Neglect the air resistance, the size of
the boy and also the mass of the rope.)
98 AL/Structural Question/P.2
(a) (1) Find the elastic potential energy stored in the rope when the boy is at D.
(2) What is the force constant of the rope?
(b) The variation of the speed of the boy, v, with the distance fallen, s, is shown
below. The boy attains his greatest speed at point C.
(1) Comment on the force(s) acting on the boy while he is in motion
between AB, BC and CD.
(2) The motion of the boy can be considered as simple harmonic once the
rope s stretched, and down to the lowest point D. How far is his
equilibrium position fro the bridge? Find his amplitude of oscillation.
(3) Calculate the time taken for the boy to go from C to D.
3. A monochromatic light rays enter a glass sphere of radius 5.0cm from air as
shown in Figure 3.1. The incident ray is parallel to the diameter AOB with a
separation of 4.5 cm. After entering the glass sphere, the ray crosses the diameter
AOB at a certain point between center O and point B.
98 AL/Structural Question/P.3
Figure 3.1
(a) Mark on Figure 3.1 the angle of incident I and angle of refraction r.
(b) Calculate the angle of incident i.
(c) If the angle of refraction is 28.6°, calculate the refractive index of the glass
sphere.
(d) If the frequency of the light ray is 5.4  1014 Hz , find its wavelength inside
the glass sphere.
(e) If the glass sphere is immersed in water (refractive index = 1.33), would be
the light ray intersect the diameter AOB before it leaves the sphere? Explain
briefly.
4. A sheet of carbon paper of uniform conductivity has been painted with two
parallel, rectangular silver strips as shown in Figure 4.1. Points A0 and B0 on the
two strips are connected to a battery of e.m.f. 6V. The negative terminal of an
ideal voltmeter is connected to A0 and its positive terminal is a probe P.
Figure 4.1
(a) What is the voltmeter reading when P is connected to B1? What would be
observed when P is moved along B1B2?
(b) Now the probe is moved along A0B0 and the voltage reading V recorded is
plotted against the distance x of the probe from A0.
98 AL/Structural Question/P.4
(1) Explain the variation of V along A0B0.
(2) Find the electric field strength at point X. State it direction.
(3) Neglect edge effect, sketch on Figure 4.1 the equipotential lines at 1 V
intervals between the two silver strips.
(c) An additional silver strip is now painted in between the two strips present as
shown in Figure 4.2.
Figure 4.2
(1) Sketch on the graph in (b) the variation of voltage V with distance x of
the probe from A0.
(2) State and explain the change, if any, in the electric field strength at point
X.
5. A reaction which takes place in the core of a nuclear reactor is described by the
following equation:
235
92
91
1
U  01n 142
56 Ba  36 Kr 30 n  174.4MeV
Mass of one nuclide of
235
92
U = 235.0439u
Mass of one nuclide of
142
56
Ba = 141.9164 u
98 AL/Structural Question/P.5
Mass of one nuclide of
91
36
Kr = 90.9234 u
1 u (atomic mass unit) = 1.660  1027 kg , which corresponds to 934MeV
(electronic charge = 1.6  10 19 C )
(a) (1) Calculate the mass, in atomic mass unit, of a neutron.
(2) The fuel rods in the reactor contain 1.0  104 kg of U-235 isotope.
Calculate the total energy released from the complete fission of all the U-235
nuclei in the fuel rods.
(3) If the mean power output of the reactor is 500MW and the efficiency of
conversion of nuclear energy to electrical energy is 40%, estimate the time for
which the fuel rods can be used.
(4) Explain why the fuel rods are usually replaced well before the time
estimated in (a)(3) has elapsed.
(b) In an emergency, explain how the reactor can be shut down immediately.
98-IB
6. (a) A cylindrical container of cross-sectional area A contains a liquid of density ρ
up a height h. Show, from first principles, that the pressure resulting from the
liquid column at the bottom of the container is given by  gh .
(b) A non-viscous, incompressible liquid of density 1200kgm-3 flows along a
horizontal tube with two sections X and Y of different cross-sectional area of
4  10 5 m 2 and the velocity of the liquid flowing through that part is 0.8ms-1. The
difference in manometer heights at X and Y is 0.03m. Assume streamline flow.
Figure 6.1
(1) Find the pressure difference between X and Y on the same horizontal
level.
(2) Calculate the velocity of the liquid flow and the cross-sectional area at
X.
(3) What is the rate of work done on the liquid I moving it from X to Y?
(c) With the aid of a diagram, explain why an aircraft wing can generate a ‘lift’
when it moves in air.
7. A solenoid of diameter 0.05m and length 0.45m has 100 turns of wire. A
rectangular coil, of dimensions 0.01m  0.01m and negligible resistance, is
98 AL/Structural Question/P.6
connected by a pair of twisted wires to a resistor of resistance 100Ω. The coil is
placed inside the solenoid as shown in Figure 7.1. The axis of the solenoid is
perpendicular to plane of the coil. The current in solenoid IS varies with time t as
shown. (Given: permeability of free space = 4  107 Hm 1 )
Figure 7.1
(a) If the induced current IC in the coil is 0.01 μA in the first 0.04s,
(1) find the maximum current Imax trough the solenoid;
(2) state TWO assumptions in your calculation;
(3) complete the graph of the induced current Ic in the coil from t = 0.1s.
(b) What is the purpose of twisting the connecting wires?
(c) If an ideal diode is connected in series with the coil and the 100-Ω resistor
so that there is no current flowing in the resistor after t = 0.04s, find (i) the
maximum induced current in the coil, and (ii) the maximum voltage drop across
the diode from t = 0s to t = 0.1s.
8. The equation of state and the internal energy U for n moles of gas X are respectively
given by
p(V  nb )  nRT and U  3nRT / 2 ,
where b is a positive constant. Due to the effect of the repulsive intermolecular
forces between the gas molecules, the ‘free volume’ occupied by the gas is
98 AL/Structural Question/P.7
modified from the measured volume V to ‘V-nb’ in the equation of state.
In an experiment, 0.5 mole of gas X undergoes a cycle ABCDA as shown in the
temperature-volume diagram below. The respective pressure of the gas in the
processes AB and CD are kept constant.
(Given: Universal gas constant = 8.31Jmol-1K-1)
(a) Find, from the graph, the value of b.
(b) Find the difference in internal energy of the gas at states A and C.
(c) (1) Find the pressures of the gas at states A and C.
(2) Draw the pressure-volume diagram for the cycle ABCDA.
(3) Find the work done by the gas in the process CDA.
(d) Find the heat absorbed by the gas during the process CDA.
9. Figure 9.1 show a common-emitter transistor circuit and also its input/output
voltage characteristics.
Figure 9.1
98 AL/Structural Question/P.8
(a) (1) Find the voltage Vc.
(2) What is the voltage between the base and the emitter when Vi = 1.5 V?
(3) Find the voltage gain and the current amplification factor of this transistor
circuit.
(b) In order to amplify the rectified a.c. signal shown in Figure 9.2, two resistors
and two capacitors are added to the circuit as shown in Figure 9.3.
Figure 9.2
Figure 9.3
(1) State the function of the capacitors in the circuit.
(2) What is the maximum value of Vp such that the signal can be amplified
without chopping off the peaks?
(3) Draw the corresponding output signal in the space provided if Vp =
0.2V.
10. A light inextensible string is wound round the periphery of a thick uniform disc of
mass m and radius r. One end of the string is fixed at a point on the ceiling as
shown in Figure 10.1. When the disc is released from rest, it falls while rotating
about the horizontal axis through its center without slipping. Neglect air
resistance.
98 AL/Structural Question/P.9
Figure 10.1
(a) (1) Mark on Figure 10.1 the force(s) acting on the disc and its sense of
rotation during its fall.
(2) It is known that the linear acceleration a of the disc is given by a 
2
g.
3
By considering the total mechanical energy of the disc, show that one-third of the
loss in gravitational potential energy of the energy of the disc is converted to its
rotational kinetic energy during the fall.
(3) Explain why the string keeps vertical instead of leaning to one side when
the disc falls.
(b) To determine the linear acceleration of the disc, a student uses a stroboscope
to take a photograph of its downward motion. The result, drawn to scale, is as
shown. The time interval between successive exposures is 0.1 s and the first
exposure is at t = 0s when the disc is released.
Time t/s
0
0.1
0.2
0.3
Position s/m 0
0.03
0.13
0.29
(1)
0.4
0.52
0.5
0.79
Plot a linear graph of position s against a suitable power of time t.
(Hint: Find the relation between s and t first.)
98 AL/Structural Question/P.10
(2)
Use the graph to find the value of the gravitational acceleration. Show
your working.