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04 AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
2004 Structural Question
1. Two particles of masses M and m are attached to the ends of a rigid rod of
negligible mass. The rod is pivoted as shown such that Ml > mx.
m

x
pivot
Figure 1.1
l
M
(a) When the system is displaced a small angle  from the vertical and then
released from rest, a net torque acts upon the system and tends to restore it to
the vertical position. Express this restoring torque in terms of m, M, x, l,  and
g.
(2 marks)
(b) The system then oscillates about the pivot.
(i) Write down an expression describing the moment of inertia of this system
about the pivot.
(1 mark)
(ii) Show that the oscillation of this system is simple harmonic.
(iii) Show
that
the
 Ml  mx
T  2 
 Ml  mx
2
period
2
of
oscillation
of
this
1
 .
g
(2 marks)
system
is
(2 marks)
(c) (i) This system exhibits 36 complete oscillations in one minute. Given that l
= 3 cm, x = 10 cm and m = 20 g, determine the mass M of the lower
particle.
(2 marks)
(ii) State and explain what will happen to the period of oscillation of the
system if
(I) the upper particle is removed;
(II) m is increased such that mx is close but not equal to Ml.
(4 marks)
04 AL/Structural Question/P.2
2. A student studies the harmonics of the guitar string AB shown in Figure 2.1. He
uses a personal computer and a datalogger to obtain the waveform of the openstring note (i.e. played without pressing the string).
Figure 2.1
(a) Determine the fundamental frequency of the open-string note shown above.
(2 marks)
(b) If the length of the string AB is L (in m) and its mass is m (in kg), find the
tension (in N) in the string, in terms of m and L.
(4 marks)
Figure 2.2 shows the waveform of an unknown harmonic of this open-string note.
Figure 2.2
04 AL/Structural Question/P.3
(c) Determine the frequency of the harmonic shown in Figure 2.2 and find the
integral ratio of this harmonic’s frequency to the fundamental frequency.
Sketch in the figure below the standing wave along the string AB that
corresponds to this harmonic.
(3 marks)
A
B
(d) The student describes a way to produce the harmonic shown in Figure 2.2 as
follows:
Touch the string lightly at C with your fingertip, then pluck the string at D
where AB = 3AC = 6AD.
Explain why this method predominantly produces the above harmonic.
(2 marks)
3.
Figure 3.1
Figure 3.1 shows a ship equipped with a sonar to detect objects in the sea.
Ultrasonic waves of frequency 25 kHz are sent towards the seabed. The waves,
which propagate at an angle of 50 to the sea surface, are reflected from a
submarine back to the ship after 0.15 s.
Given: speed of sound in air = 340 ms-1
speed of sound in sea water = 1500 ms–1
(a) Find the wavelength of the ultrasonic waves in sea water.
(2 marks)
04 AL/Structural Question/P.4
(b) Calculate the vertical distance of the submarine beneath the sea surface.
(2 marks)
(c) Some of the ultrasonic waves reflected by the submarine propagate along the
dotted line and emerge into the air at X. Calculate the angle of refraction in air.
(3 marks)
(d) Is it possible for ultrasonic waves, at certain angles of incidence, to undergo
total internal reflection when they go from sea water to the air? Explain.
(2 marks)
(e) Explain why microwaves are not suitable for detecting objects in sea water.
(1 mark)
4. (a) A high-pitch note of frequency 4 kHz is amplified to a r.m.s. voltage of 4 V and
the output is fed to a tweeter (high frequency speaker) circuit as shown in
Figure 4.1. The capacitance of capacitor C is 50 F. Assume that the tweeter
can be regarded as a resistor R of resistance 8 .
A
C
Figure 4.1
Audio
amplifier
R
Tweeter
B
(i) Find the impedance between A and B to 3 significant figures.
(3 marks)
(ii) Find the r.m.s. current passing through the tweeter. Hence, calculate the
average power consumption of the tweeter when the note is being played.
(3 marks)
(b) A low-pitch note of frequency 80 Hz is also amplified to a r.m.s. voltage of 4 V
and the output is fed to the tweeter circuit in Figure 4.1.
(i) Find the phase difference between the current passing through the tweeter
and the voltage across AB. Draw a phasor diagram to represent their
relationship.
(3 marks)
(ii) Find the average power consumption of the tweeter in this case. (2 marks)
(c) The two notes now sound together at 80 Hz and 4 kHz respectively. They are
both amplified to the same r.m.s. voltage and the output is fed to a 2-way
speaker, which consists of a woofer (low frequency speaker) and a tweeter
04 AL/Structural Question/P.5
crossover network as shown in Figure 4.2. Assume that the woofer can also be
regarded as a resistor R of resistance 8 .
C
X
Figure 4.2
Audio
amplifier
R
R
Tweeter
Woofer
The function of component X is to block high frequency signals. Suggest what
component X should be and explain how it works.
(3 marks)
5. (a) (i) Several energy levels of a mercury atom are shown in Figure 5.1.
(Given: electronic charge = 1.6  10-19 C;
Planck constant = 6.63  10-34 Js )
Energy in eV
Figure 5.1
n=
0
n=4
- 1.57
n=3
- 3.71
n=2
- 5.52
n=1
- 10.38
Diagram NOT to scale
In a fluorescent tube, atoms in the mercury vapour are excited to the first
excited state from its ground state by the bombardment of energetic
electrons. Determine the wavelength of the radiation emitted by the
excited mercury atom as it returns to the ground state. In which part of the
electromagnetic spectrum does this radiation belong to?
(4 marks)
04 AL/Structural Question/P.6
(ii) The radiation in (a)(i) is then absorbed by the coating on the inner surface
of the fluorescent tube. Figure 5.2 shows some of the energy levels of a
coating atom.
Energy in eV
n=
Figure 5.2
0
C
- 2.66
B
A
- 3.81
- 4.86
n=1
- 7.52
Diagram NOT to scale
(I) After the absorption of the radiation in (a)(i), which energy levels, A,
B or C, would the ground state coating atom be excited to? (1 mark)
(II) The excited coating atom returns to the ground state through various
intermediate states. State the TWO transitions of the coating atom
that emit visible light. (Given: The visible spectrum runs from 400
nm to 700 nm approximately. A photon of wavelength 400 nm has
3.11 eV of energy.)
(3 marks)
(b) Fluorescence occurs when an electron of a fluorescent coating atom is excited
to an excited state, the excited electron will return to the ground state through
various intermediate states and these transitions will emit photons.
The screen of a colour television emits light of different colours also by
fluorescence. On the inner surface of the screen, there are three kinds of
coatings arranged as dots that emit red, green and blue light. Inside the
cathode-ray tube of a television, three beams of electrons are accelerated to high
speeds before they strike the corresponding coatings and excite the coating
atoms.
Energy in eV
n=
0
n=3
n=2
Energy in eV
n=
0
n=
0
n=3
n=2
- 1.35
- 2.31
n=3
- 1.35
n=2
- 3.06
n=1
- 4.86
- 3.65
- 4.89
n=1
n=1
Energy in eV
- 5.06
- 7.20
Atom X
Atom Y
Figure 5.3
Atom Z
04 AL/Structural Question/P.7
(i) Figure 5.3 shows the energy levels of the coating atoms, namely atoms X, Y
and Z. Write the name of the coating atom that corresponds to each colour
in the following table.
(2 marks)
Colour of visible light
emitted
Energy of emitted
photon / eV
Red
1.80
Green
2.31
Blue
2.75
Name of coating atom
(Atoms X, Y or Z)
(ii) The excitation energies of the three kinds of coating atoms are different.
Can a single electron beam carrying a sufficient amount of energy excite
these coating atoms? Explain briefly.
(2 marks)
6. Figure 6.1 shows a regulator for adjusting the angular speed of an engine. A
vertical shaft is driven into rotation about its axis by the engine. Two identical
rigid rods, each of length L and of negligible mass, are hinged together at one end.
A counterweight of mass m is attached to the hinge. The upper rod is hinged to the
shaft while the lower rod is hinged to a collar which can move freely along the
shaft. The mass of the collar is m’. The angular speed of the engine could be
indicated by the collar's equilibrium position. All moving parts are assumed to be
smooth.
Figure 6.1
(a) The upper and lower rods exert forces T1 and T2 respectively on the
counterweight. Why does T2 act in a direction parallel to the lower rod? Mark
in Figure 6.1 the force(s) acting on the collar.
(3 marks)
(b) (i) At a certain angular speed , the counterweight performs uniform circular
motion. Write down two equations describing the vertical equilibrium of
04 AL/Structural Question/P.8
the collar and that of the counterweight. Write down one equation
describing the horizontal circular motion of the counterweight. (3 marks)
(ii) Hence, use the equations in (b)(i) to show that  and  are related as
follows:
(2 marks)
2 cos  = (1 
2m' g
)
m L
(iii) State and explain the change in the collar’s position if the mass of the
counterweight is increased while keeping the angular speed unchanged.
(2 marks)
(c) Given L = 0.5 m, the angles  for various angular speeds  are measured:
/rad s-1

13.6
64
12.6
60
11.5
53
10.5
43
9.4
26
Plot a suitable straight line graph, find the slope and hence calculate m’: m.
(7 marks)
7. Figure 7.1 shows an earth leakage circuit breaker installed in a domestic circuit.
The live and the neutral wires pass through the centre of a soft iron ring of mean
radius 1 cm. A 100-tum coil C with cross-section area 0.8 cm2 is wound on the rim
of the ring. In case of an earth leakage in the domestic circuit such that the currents
flowing in the neutral and live wires differ by a value of 0.5 A, the relay switch S of
this device will open so as to switch off the mains supply. The relay switch has to
be reset mechanically in order to resume the supply.
Figure 7.1
(a) (i) Explain the working principle of the circuit breaker when there is a leakage
of current from the load to the ground.
(3 marks)
(ii) Would the circuit breaker respond if a leakage to the ground occurs at P?
Explain.
(1 mark)
04 AL/Structural Question/P.9
(b) Suppose there is a leakage of current of 0.5 A from the load to the ground.
(i) It is known that the flux density of the magnetic field due to a currentcarrying conductor will be 1500 times larger in the presence of soft iron.
Calculate the magnetic flux density B through coil C. (Given: permeability
of free space 0 = 4  10-7 H m-l)
(3 marks)
(ii) If the leakage develops steadily from 0 A to 0.5 A within a time interval of
0.03 s, determine the e.m.f. induced in the coil C. (Neglect the inductance
of the solenoid.)
(2 marks)
(c) Electrical appliances are usually equipped with fuses. What would happen to
the fuse and the earth leakage circuit breaker if short circuit occurs between live
and neutral in an appliance? Explain.
(4 marks)
8. Figure 8.1 shows the apparatus using crossed magnetic and electric fields to
measure the charge-to-mass ratio of electron. The cathode-ray tube has a cathode C
and an anode A with a horizontal collimating slit, from which the electrons emerge
in a narrow beam.
Figure 8.1
(a) Describe how electrons are emitted from the cathode.
(2 marks)
(b) The Helmholtz coils, Xl and X2, are to provide a uniform magnetic field over
some distance around their common axis midway between the two. The e.h.t. is
set at voltage V and a direct current I flows round the Helmholtz coils.
(i) State the direction of the magnetic field if the current flows round each coil
in a clockwise direction. Suggest a piece of apparatus for measuring the
flux density of the magnetic field due to the Helmholtz coils.
(2 marks)
(ii) Sketch and describe the trail of the electron beam between the deflecting
plates Yl and Y2 if each of the following changes is made independently:
(I) Both Y1 and Y2 are connected to the positive terminal of the e.h.t.
(2 marks)
04 AL/Structural Question/P.10
(II) The current in the Helmholtz coils is switched off.
(2 marks)
(c) The Helmholtz coils, each of diameter 30 cm, are connected in series to a d.c.
power supply. The coils are parallel and 15 cm apart. Each coil has 130 turns.
The flux density B of the magnetic field midway between the coils near the axis
is given by
N 0 I
B=
(1.25) 3 / 2 a
where I is the current through the Helmholtz coils
N is the number of turns on each coil
a is the radius of the coils
0 = 4  10-7 Hm-1
The e.h.t. is now set at 3 kV and a direct current of 1.6 A flows round the
Helmholtz coils. The electron beam, which is perpendicular to both the
magnetic field and the electric field, emerges from between the deflecting plates
Y1 and Y2 without deflection.
(i) Calculate the flux density B of the magnetic field between the coils near
the axis.
(2 marks)
(ii) If the separation between Y1 and Y2 is d, derive an expression for the
charge-to-mass ratio of electron in terms of B, V and d. Calculate the
measured charge-to-mass ratio if d is 0.07 m.
(4 marks)
(iii) The accepted value of the charge-to-mass ratio of electron is 1.76  1011
Ckg-1. Suggest a cause that may lead to the discrepancy between the
accepted value and the experimental value obtained in (c)(ii).
(1 mark)
9. A student measures the specific heat capacity of water by the set-up shown in
Figure 9.1. A cylindrical drum, wrapped with a stationary band of silk, is being
driven into steady rotation about a vertical axis through its centre. The silk band is
held taut at the two ends by the spring balances S1 and S2. Work is therefore done
against friction produced by the silk band and heat is generated. The drum is rotated
in a clockwise direction when viewed from above.
Figure 9.1
04 AL/Structural Question/P.11
The drum of diameter 15.00  0.01 cm is hollow and it contains 220.0  0.1 g of
water, which is initially at 20.4  0.1 C. The difference in readings between spring
balances S1 and S2 takes a steady value of 41.6  0.2 N.
After the rotation stops, the maximum temperature reached by the water inside the
drum is 28.2  0.1 C and the revolution counter registers 400.0  0.5 revolutions.
(a) Suggest a piece of apparatus to measure the diameter of the drum.
(1 mark)
(b) (i) Explain why there is a difference in spring balance readings when rotating
the drum. State which spring balance gives a larger reading.
(2 marks)
(ii) Determine the work done against friction in this experiment.
(2 marks)
(iii) Hence, determine the specific heat capacity of water found in this
experiment. State the assumption(s) in your calculation.
(3 marks)
(c) (i)
Calculate the maximum possible percentage errors in measuring the work
done, the mass of water and the temperature change. State which
measurement most likely leads to the dominating source of error in this
experiment.
(4 marks)
(ii) Compared with the accepted value of the specific heat capacity of water
4200 J kg-1 K-1, discuss whether the discrepancy in the experimental value
can be explained solely by random errors.
(3 marks)
- END OF PAPER -