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00 AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
2000 Structural Question
1. In December 1998, a serious car accident happened on the Lantau Link. The car
sped up the concrete ramp and took off from the ramp. It then hit the top of a road
sign of height 5 m above the road and 30 m away from the ramp as shown in
Figure 1.1.
road sign
Figure 1.1
5m
ramp
30 m
(a) Sketch in Figure 1.1 the possible trajectories of the car in the air for a certain
take-off speed.
(2 marks)
(b) Assume that the car hit the road sign at the highest point in its trajectory.
Estimate
(i) the take-off speed of the car;
(ii) the projection angle of the car; and
(iii) the time of flight before the car hit the road sign.
(You may neglect the air resistance and the size of the car.)
(5 marks)
(c) Barking marks of 39 m long was found on the road in front of the ramp.
Forensic measurements on the marks by the police indicated that the braking
force was about 8000 N on the car of mass 1000 kg. Estimate the speed of the
car just before applying the brakes.
(2 marks)
(d) A report on this accident appeared in a local newspaper in which the take-off
speed of the car, u, is state as
u
2  10  5
sin 2 9.5
5m
9.5
30 m
Referring to the relation, the angle of elevation of the road sign from the ramp
is taken as the angle of projection. Comment on the appropriateness of such
an assumption.
(2 marks)
00 AL/Structural Question/P.2
2. Two identical pans, each of mass 150 g, are connected by a light string which
passes over a light pulley suspended from the ceiling. The pulley can rotate
smoothly about a horizontal axis through its centre. Two identical weights m1 and
m2, each of mass 10 g, are placed on the pans as shown in Figure 2.1. (Neglect air
resistance.)
Figure 2.1
m1
pan
m2
(a) In the space provided below, sketch and label all the forces acting on both m1
and the pan supporting it. Identify an action and reaction pair.
(3 marks)
pan
m1
(b) Write down all the possible state(s) of motion that the system can take.
(1 mark)
00 AL/Structural Question/P.3
Initially the separation between the pans is 0.72 m. Now m2 is removed from the
lower pan and the system accelerates from rest.
Figure 2.1
m1
0.72 m
O
x
mg
where m and M are
m  2M
the masses of the weight and the pan respectively. Calculate the tension in the
string.
(3 marks)
(c) Show that the acceleration of m1 is given by a =
(d) Find the speed of the pans when they are at the same level.
(2 marks)
(e) A light spring of force constant 4 Nm-1 is fixed vertically below the
descending pan as shown in Figure 2.2. A light plate is attached to the upper
end of the spring. The descending pan comes into contact with the plate when
the two pans are at the same level. The motion of the system becomes simple
harmonic until it comes to rest momentarily. With the contact point taken as
the origin, find the equilibrium position and the angular frequency of the
motion. (Assume that the pan moves together with the plate once they are in
contact and the string does not slack throughout.)
(4 marks)
00 AL/Structural Question/P.4
3. Figure 3.1 shows a circuit used for measuring the capacitance of a capacitor C.
Y
Figure 3.1
A
X
Lead Z
C
100 k
Lead Z is first connected to X, which is the positive terminal of the battery. After
about one minute, lead Z is disconnected from the battery and is then connected to
Y. The stop watch is started when the current through the microammeter drops to
50 A. The variation of the current I with time t is recorded.
t/s
0
2
5
9
17
22
26
34
I/10-6 A
50
40
30
20
10
6
4
2
(a) Explain why it is better to take readings of time for pre-selected current values
(e.g. 50, 40, 30, …) rather than trying to read current values at pre-selected
times (e.g. 0, 5, 10, …)?
(1 mark)
(b) State TWO uncertainties associated with the experiment.
(2 marks)
(c) The experiment is repeated to measure the variation of current with time.
Explain the advantage of doing so.
(1 mark)
(d) Deduce whether the e.m.f. of the battery used is 3 V, 4.5 V or 6 V.
(2 marks)
00 AL/Structural Question/P.5
(e) A graph of ln I against t is plotted. The slope of the graph is –9.4  10-2 s-1.
0
ln I
10
20
30
40
-9.0
-10.0
-11.0
-12.0
-13.0
-14.0
(i) Write down the relation between I and t. Hence find the capacitance of C.
(3 marks)
(ii) Explain why the capacitor is practically fully charged when lead Z has
been connected to the positive terminal of the battery for one minute.
(2 marks)
(iii) If another 100 k resistor is connected in parallel with the one in the
circuit, state one possible change on the graph. (No mathematical
derivation is required.)
(1 mark)
time/s
00 AL/Structural Question/P.6
4. A metal cylinder of volume 0.5 m3 contains some compressed gas at an initial
pressure of 16  105 Pa. The gas is used to inflate identical non-elastic balloons,
each to a volume of 1.2 m3 at atmospheric pressure of 105 Pa. Assume that the
balloons are inflated slowly so that the temperature of the gas does not change and
the pressure in the balloons is always equal to the atmospheric pressure. (You
may assume that the equation of state for an ideal gas in the calculation.)
(a) The density of the gas in the cylinder is 1.57 kgm-3 at room temperature.
Estimate the r.m.s. speed of the gas molecules.
(2 marks)
(b) Find the work done against atmospheric pressure in inflating one balloon.
(2 marks)
(c) (i) Calculate the decrease in gas pressure in the cylinder after inflating one
balloon.
(3 marks)
(ii) Find the number of balloons that can be inflated before the gas pressure in
the cylinder drops below 10  105 Pa.
(2 marks)
(d) Briefly explain whether there is heat transfer between the cylinder and the
surroundings when the balloons are being inflated in the way described in this
question.
(2 marks)
5. Figure 5.1 shows an ionization chamber that can be used to estimate the activity of
a sample of uranium-238. The sample is placed inside a metal can held at a
negative potential. Electrons produced inside the metal can migrate to the sample
while positive ions migrate to the wall of the can. The sample is connected to the
ground via a 109  resistor. The potential difference across the 109  resistor is
measured by an op-amp circuit.
ionization chamber
(metal can)
U-238 sample
Figure 5.1
insulator
power supply
109 
V
0V
(a) Name the op-amp circuit used in Figure 5.1.
(1 mark)
00 AL/Structural Question/P.7
(b) Figure 5.2 shows the variation of the voltmeter reading with the potential
difference across the metal can and the sample.
voltmeter
reading/mV
100
80
Figure 5.2
60
40
20
p.d. across the metal can
and the sample/V
0
5
10
15
Explain the variation of the voltmeter reading.
20
25
30
(3 marks)
(c) In the sample, uranium-238 decays into thorium-234 by emitting an -particle.
This nuclear reaction can be represented as:
Given: Mass of one nuclide of U-238 = 238.0508 u
Mass of one nuclide of Th-234 = 234.0436 u
Mass of one nuclide of He-4 = 4.0026 u
1 u (atomic mass unit) = 1.660  10-27 kg, which corresponds to
934 MeV
(i) Calculate the energy, in MeV, released in this nuclear reaction. (2 marks)
(ii) From the information provided in Figure 5.2, calculate the number of air
particles being ionized per second inside the metal can. Assume that each
ionized air particle carries one electronic charge. (electronic charge = 1.6
 10-19 C)
(2 marks)
(iii) If the energy required to produce an ion-electron pair is 30 eV, estimate
the activity, in disintegrations per second, of the U-238 sample. State the
assumption(s) in your calculation.
(3 marks)
(iv) Is this experimental method suitable for estimating the activity of a
sample emitting -particles? Give TWO reasons to support your answer.
(2 marks)
00 AL/Structural Question/P.8
6. (a) Two conductors, a metal rod and a hollow cylinder conductor, are arranged
coaxially. Figure 6.1 shows their cross-section. The inner and outer
conductors are charged with +Q and –Q respectively, which is distributed
uniformly on their surfaces. Draw the resulting electric field lines.
(1 mark)
-Q
Figure 6.1
+Q
(b) Figure 6.2 shows a coaxial cable. The cable consists of an inner conductor, an
insulating layer, an outer conductor and a protective layer.
protective
layer
Figure 6.2
inner
conductor
outer
conductor
insulating
layer
(i) The cable can be represented as conductors AB and A’B’ in a circuit
diagram. The cable can be treated as a capacitor when the inner and outer
conductors are taken as the positive and negative plates. To measure its
capacitance per unit length C0, the cable is connected in series with an a.c.
source and a 10 k resistor as shown in Figure 6.3. The frequency of the
source is 100 kHz. The r.m.s. voltage across the resistor is found to be
1.80 V when that of the source is 2.00 V.
A
Figure 6.3
B
A’
a.c. source
100 kHz
B’
10 k
(I) Find the r.m.s. voltage across the inner and outer conductors of the
cable, that is the voltage across AA’.
(2 marks)
(II) If the cable is 3.0 m long, find its capacitance per unit length, C0.
(3 marks)
00 AL/Structural Question/P.9
(ii) The cable can also be treated as an inductor (single loop) when the inner
and outer conductors are connected (i.e. B is connected to B’).
(I) The separation between the inner and outer conductors is so small
that it is negligible when compared with the distance from the cable
to a point outside it. What is the magnetic field outside the cable
when it is treated as an inductor carrying a current?
(1 mark)
(II) It is known that the inductance per unit length of the cable, L0, is of
the order 10-7 Hm-1. With the 10 k resistor replaced by a 2  one,
the circuit in Figure 6.3 can now be used to measure L0. There are
two frequencies, 100 kHz and 1 MHz, that can be chosen for the
measurement. Which one is a better choice? Explain briefly.
(2 marks)
7. (a) You are a member of a project group. Your group has planned a project to
investigate the magnetic field pattern around two parallel wires carrying
currents in opposite directions. The project would include measuring and
comparing the field strength at different points around the two wires.
Conducting wire
Figure 7.1
Electric Current
(i) A steady d.c. current is passed through the wires. Sketch in the space
below the magnetic field pattern around the two wires.
(2 marks)
(ii) With reference to Figure 7.2, if the current flowing through both wires is
5 A and the separation between them is 0.05 m, predict the magnitude of
the magnetic field strength due to these two wires at point X, which is
00 AL/Structural Question/P.10
0.02 m from wire Q. (The diameters of the wires are negligible.) Given:
permeability of free space = 4   10-7 Hm-1
(2 marks)
5A
5A
Figure 7.2
X
0.02 m
P
0.05 m
Q
(iii) Name the apparatus that you would use to measure the magnetic field in
this experiment.
(1 mark)
(b) Your group then submits the plan to the teacher. However, the teacher
disagrees with the use of d.c. in this experiment and he points out that the
measuring apparatus available in the school laboratory is not sensitive enough
to measure even the earth’s magnetic field, which is about 50 T. He further
suggests that since the plan is to compare the magnetic field strength at
different positions, absolute measurement of field strength is not necessary.
(i) Suggest TWO reasons why the teacher disagrees with the use of d.c. in
this experiment.
(2 marks)
(ii) Your group then decides to investigate the magnetic field pattern around
two parallel current-carrying wires by using a modified experiment. The
set-up is shown in Figure 7.3. With the time base of the CRO switched
off, a vertical trace is observed on the screen of the CRO.
signal generator
long parallel wires
A
a.c. ammeter
search coil
Figure 7.3
CRO
00 AL/Structural Question/P.11
(I) Explain what is represented by the length of the trace observed on the
CRO and state TWO advantages of this modified experiment.
(3 marks)
(II) State TWO necessary precautions for carrying out the experiment.
(2 marks)
8. (a)
X
uniform magnetic
field (into paper)
Figure 8.1
v
l
+Q
Y
Figure 8.1 illustrates a though experiment. A metal bar XY of length l is pulled
through a uniform magnetic field B with a velocity v. The direction of the
velocity is perpendicular to the bar and they are both perpendicular to the
magnetic field.
(i) Draw on Figure 8.1 all the forces acting on the positive charge +Q in the
bar. Label the forces.
(1 mark)
(ii) Describe the movement of the charges in the bar and show that the e.m.f.
induced across the ends XY is given by  = Blv.
(3 marks)
00 AL/Structural Question/P.12
(b) In 1996 astronauts on the space shuttle Columbia performed an experiment to
test an idea for generating electricity in the upper ionosphere. In the
ionosphere, the ultraviolet radiation from the Sun or other radiations causes
the air particles to undergo ionization, and they tend to remain ionized as the
chance of recombination is small. Once in orbit, Columbia released a satellite
attached to it by a 20 km long conducting cable. With the satellite vertically
above the shuttle, the two moved together around the earth above the equator.
Figure 8.2
Given: Magnetic field strength in the orbital region = 30  10-6 T
Orbital position of the shuttle = 6.8  106 m from the centre of the
earth
Mean radius of the earth = 6.4  106 m
(i) Calculate the orbital speed of the shuttle at the orbital position. (3 marks)
(ii) Estimate the e.m.f. induced across the cable. State the assumption(s) that
you have made in the calculation.
(3 marks)
(iii) The experiment was in fact successful and a steady current was detected
in the cable. Indicate the direction of the current in the cable and explain
why a current can be sustained.
(3 marks)
9. A diffraction grating is used to study the hydrogen spectrum from a discharge
tube. The first-order diffraction angles of some of the various discrete lines are
tabulated below.
First-order diffraction angle /
Wavelength /nm
23.19
656.3
16.96
486.1
15.09
434.0
14.25
410.2
12.64
364.6
(a) Plot a suitable graph to find the grating spacing, in lines per mm, of the
diffraction grating.
(5 marks)
00 AL/Structural Question/P.13
(b) (i) Which line corresponds to blue light?
(1 mark)
(ii) One of the lines cannot be seen by naked eyes. Name the region in the
electromagnetic spectrum to which this line belongs.
(1 mark)
(c) What activity within an atom gives rise to these emission lines? What is the
physical significance of the spectrum consisting of discrete lines?
(2 marks)
(d) In fact, the wavelengths of the emission lines satisfy the formula of the Balmer
series:
n2
 = (364.6 nm ) 2
, where n = 3, 4, 5, …
n 4
1 1
 ) , where 
n2 4
represents the frequencies of the emission lines, h is the Planck constant
and K is a constant.
(1 mark)
(i) Show that the formula can be transformed into h = K (
(ii) Find K in units of eV. State the physical significance of the sign and the
K
magnitude of the term 2 in the formula of h.
n
(Planck constant = 6.626  10-34 Js; electronic charge = 1.6  10-19 C)
(4 marks)
10. Figure 10.1 shows an operational amplifier circuit.
Rf = 100 k
Figure 10.1
Vin
10 k
+ 15 V
Vout
- 15 V
0V
(a) (i) What is meant by negative feedback in an operational amplifier circuit?
State TWO effects of using negative feedback.
(3 marks)
(ii) What will be the effect on the above circuit if Rf increases?
(iii) Find Vout when Vin equals (I) 10 mV;
(II) 2 V.
(1 mark)
(2 marks)
00 AL/Structural Question/P.14
(iv) The graph below represents the variation of the input voltage Vin with
time. Sketch the corresponding variation of the output voltage Vout.
(2 marks)
Vin / V
2
1
0
time
-1
-2
(b) (i) The circuit in Figure 10.1 can be used to amplify the signals of the order
of 10 mV from an electronic stethoscope monitoring heart beats. An
earphone requiring a peak voltage of at least 0.5 V to operate is connected
to the output of the circuit. What should be the minimum resistance value
of the feedback resistor Rf?
(2 marks)
(ii) Although a step-up transformer can give a larger output voltage from a
small input voltage, it cannot serve the same purpose as the amplifier
circuit in Figure 10.1. Explain briefly.
(2 marks)
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