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07 AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
2007 Structural Question
1. (a)
Jacky, an American football player, is subject to a horizontal push at his
shoulders, which are at a distance 0.47 m from his centre of gravity G as
shown in Figure 1.1. His contact point O on the ground is at a distance 1.18 m
from G. In order to balance the push, he leans forward at an angle  to the
vertical.
(i) Draw and label the force(s) acting on Jacky in Figure 1.1.
(2 marks)
Figure 1.1
(ii) Suppose Jacky is at equilibrium and the friction between his feet and the
ground is at a maximum, and is equal to 0.25 times the normal reaction
acting on him from the ground. Find the value of . Assume that Jacky
keeps this posture like a rigid body in your calculation.
(4 marks)
07 AL/Structural Question/P.2
(b) Jacky tries to make a long pass to his teammate, Roy, standing 38 m away
from him. He passes the ball by throwing it from a point 2 m above the
ground with an initial speed 20 ms-1 at an angle of elevation 35. The mass of
the ball is 0.42 kg. Neglect air resistance and the size of the ball.
Figure 1.2
(i) Find the work done on the ball by Jacky, assuming the throwing action
starts from rest and the gain in gravitational potential energy of the ball
during the throwing action can be neglected. If the throwing action lasts
for 0.15 s, estimate the average power that Jacky delivers to the ball.
(4 marks)
(ii) At what height h should Roy place his hands so as to catch the ball? Show
your calculation.
(3 marks)
2. A thin wedge of an air-film is formed by placing a piece of foil between two
microscope slides at one end Y with the slides in contact at the other end X as
shown in Figure 2.1. (Figures 2.1 and 2.2 are NOT drawn to scale.)
Figure 2.1
foil
air-film
Y
microscope slides
X
When the set-up is illuminated by monochromatic light of wavelength  at normal
incidence, straight bright and dark fringes can be observed from above. The
fringe at the line of intersection X of the slides is dark and the rest of the fringes
are parallel to it.
07 AL/Structural Question/P.3
(a) What is the condition for a bright fringe to be observed, say, at O where the
air-film thickness is t? Explain briefly with the aid of drawing a ray diagram
in Figure 2.2.
(4 marks)
Figure 2.2
monochromatic light
O
Y
X
(b) The length of each slide is 60 mm and the wavelength  of the monochromatic
light used is 560 nm. The separation of the bright fringes observed is 1.0 mm.
(i) Estimate the thickness of the foil.
(3 marks)
(ii) If the foil is replaced by a piece of paper, the fringe separation becomes
smaller. Explain what can be deduced from this observation. (3 marks)
(iii) Figure 2.3 shows the positions of some of the bright fringes observed.
Sketch in the same figure the expected positions of the bright fringes if
monochromatic light of longer wavelength is used.
(2 marks)
TOP VIEW
Figure 2.3
X
bright fringes
3. Figure 3.1 shows a current balance which consists of a copper wire frame PQRS
balanced on two razor blades. Two identical solenoids, each of 1500 turns, are
placed coaxially such that one arm RS of the current balance is in the narrow gap
between the two solenoids. Each solenoid is 30 cm long and has a square crosssection of 3 cm  3 cm.
07 AL/Structural Question/P.4
Figure 3.1
When a current of 2.0 A flows in the arm RS of the current balance, and the same
current flows in the two solenoids in the same direction (not shown in the figure),
placing a rider of mass 0.072 g on the arm RS can restore the balance. (Given:
permeability of free space = 4  10-7 H m-1.)
(a) (i) Indicate in Figure 3.1 the direction of the magnetic force acting on the
arm RS and the direction of the current in the solenoids.
(2 marks)
(ii) Use the experimental result to estimate the average magnetic flux density
B in the gap between the solenoids. Calculate also the theoretical value
B’ of the magnetic flux density using the current in the solenoids and state
TWO possible reasons to account for the discrepancy between the two
values.
(6 marks)
(iii) If one of the solenoids is removed, what should be the average magnetic
flux density B on the copper wire that originally lied in the gap between
the solenoids?
(2 marks)
(b) Is it justifiable to treat either of the solenoids as a ‘long’ one in practice?
Explain.
(1 mark)
4. A system consists of 2.5 moles of neon gas at a pressure of 100 kPa and a
temperature of 273 K. Given that the molar mass of neon is 0.0202 kg mol-1, the
Boltzmann constant is 1.38  10-23 J K-1 and the Avogadro constant is 6.02  1023
mol-1. Neon gas is monatomic and assume that it can be treated as an ideal gas.
(a) Determine
(i) the average kinetic energy of the gas atoms;
(ii) the root-mean-square speed of the gas atoms; and
(iii) the internal energy of the gas.
(6 marks)
(b) The system undergoes the cycle XYZ via the processes a, b and c shown in
Figure 4.1 and the change from state X to state Y is isothermal at 273 K. p0 =
100 kPa.
07 AL/Structural Question/P.5
Figure 4.1
(i) Find the volume V0 of the gas at state X.
(2 marks)
(ii) Calculate the work done on the gas in the process c.
(2 marks)
(iii) Use the answer in (a)(iii), or otherwise, to determine the internal energy
of the gas at states Y and Z.
(4 marks)
(iv) Calculate the work done by the gas in the process a. Hence, find the heat
x2 1
x
flowing into the gas in the process a. (Given:  dx  ln[ 2 ] ) (4 marks)
x1 x
x1
5. A student performs an experiment on an optical bench to measure the focal length
of a convex lens. He places a lamp behind a sheet of cardboard with a circular
hole covered by a piece of translucent paper and tries to locate a sharp image of
the edge of the hole on a screen. The object distance and image distance are
denoted by u and v respectively.
Figure 5.1
(a) Suggest ONE way to make it easier to focus the image on the screen. (1 mark)
(b) For a certain object distance, the student cannot obtain an image on the screen
no matter how he adjusts the screen’s position. What would most likely be the
reason? Explain briefly.
(2 marks)
(c) If the centre of the lens is covered by a small coin, what would be the effect on
the image formed on the screen? Explain briefly.
(2 marks)
07 AL/Structural Question/P.6
(d) The positions of the cardboard and the screen are varied such that a real image
is always formed on the screen. The corresponding object distance and image
distance are obtained for plotting a graph of (u + v) against u.
(i) Estimate the image distance for which (u + v) is a minimum and find the
corresponding magnification of the image.
(3 marks)
(ii) Draw a ray diagram corresponding to the situation when (u + v) is a
minimum. Hence, estimate a value for the focal length of the lens.
(3 marks)
6. (a) A parallel-plate capacitor is formed by two square metal plates. The plates are
kept apart by four small polythene spacers at the comers.
07 AL/Structural Question/P.7
The set-up shown in Figure 6.1 is used to investigate the relation between the
capacitance C of the capacitor and the separation d of the plates when their
area of overlap is kept constant.
Figure 6.1
The frequency f of the reed switch is 400 Hz and the voltmeter reading V is 25
V. By varying the separation d of the plates, the corresponding galvanometer
readings I are obtained. A graph of I against 1/d is plotted below.
(i) Write down an expression of C in terms of f, I and V. Use the graph to
deduce a numerical relation between C (in F) and d (in m).
(5 marks)
(ii) Give a possible reason to explain why the graph does not pass through the
origin.
(1 mark)
(iii) The current measured by the light-beam galvanometer is zero for very
high switching frequencies (~2 kHz). Explain.
(1 mark)
(b) A capacitor is formed by using the two square metal plates with 6 mm
separation. It has capacitance 92.2  10-12 F and is connected to a d.c. source
as shown in Figure 6.3. Another 2 mm thick metal plate of the same area is
inserted mid-way between the parallel plates of the capacitor as shown. The
voltage of the d.c. source is maintained at 100 V.
07 AL/Structural Question/P.8
Figure 6.3
100 V
d.c. source
+
6 mm

2 mm
(i) Calculate the increase in the following physical quantities.
(I) the capacitance of the capacitor
(II) the charges on the capacitor plates connecting to the source
(III) the energy stored in the capacitor
(6 marks)
(ii) Calculate the work done by the d.c. source in moving the charges from
one plate to another when inserting the 2 mm metal plate. Compare your
result with that of (b)(i)(III) and account for the difference.
(4 marks)
7. A coil is made by winding a few hundred turns of insulated copper wire around a
paper cone. The coil and a 100  resistor are connected to an a.c. source of peak
value 6 V as shown in Figure 7.1. A student uses the set-up to investigate the
properties of the coil.
Figure 7.1
When the source frequency f is below 50 kHz, the peak voltage across the resistor
is approximately the same as the peak value of the source voltage VS.
(a) Figure 7.2 shows the variation of VS with time t at 50 kHz.
VL or I
(arbitrary
units)
VS
0
Figure 7.2
0
20 t / s
Figure 7.3
20 t / s
07 AL/Structural Question/P.9
(i) If the coil has negligible resistance, sketch in Figure 7.3 the time variation
of the voltage VL across the coil and the current I in the circuit. (2 marks)
(ii) State ONE change in your sketch if the coil has significant resistance.
(1 mark)
(b) (i) Describe how the inductive reactance of the coil varies with f .
(1 mark)
(ii) How does the magnitude of the inductive reactance of the coil compare to
100 k for f below 50 kHz? Hence, estimate the peak current I0 in the
100  resistor.
(3 marks)
(iii) The peak value of VL is measured at various source frequencies f below
50 kHz. Show that the peak value of VL is given by 2fLI0, where L is
the inductance of the coil. Plot a suitable graph and use it to estimate L.
(6 marks)
Source frequency f / kHz
10
20
30
40
50
Peak value of VL / mV
2.1
4.0
5.9
7.9
9.9
8. (a) Show that the pressure due to a liquid column of density  and height h is
given by gh, where g is the acceleration due to gravity.
(2 marks)
liquid column
of density 
h
Figure 8.1
(b) Figure 8.2 shows a rigid rectangular block completely submerged in a liquid
of density . The upper and lower surfaces of the block are at depths h1 and h2
respectively from the liquid surface. The atmospheric pressure is p0.
liquid of density 
Figure 8.2
h2
h1
block
07 AL/Structural Question/P.10
(i) State the respective pressure acting on the upper and lower surfaces of the
block and hence show that the pressure difference between the two
surfaces is given by g(h2 – h1).
(2 marks)
(ii) If the block is submerged slightly deeper into the liquid, would this
pressure difference change? Explain.
(1 mark)
(iii) Show that the pressure difference found in (b)(i) is consistent with the
result deduced from Bernoulli’s principle.
(2 marks)
(c) A rectangular aluminium block with a cavity at its centre is completely
submerged in water as shown in Figure 8.3. The dimensions of the block are
10 cm  8 cm  6 cm. The densities of aluminium and water are 2700 kg m-3
and 1000 kg m-3 respectively. The mass of air in the cavity can be neglected.
water of density 1000 kg m-3
aluminium block
submerged in
water
Figure 8.3
6 cm
cavity at the
block’s centre
10 cm
8 cm
The block is able to stay at rest uprightly in water as shown in Figure 8.3.
(i) Draw and label the force(s) acting on the aluminium block in Figure 8.3.
(2 marks)
(ii) Deduce the weight of the aluminium block using the pressure difference
found in (b)(i). Hence, find the volume of the cavity.
(4 marks)
END OF PAPER