Checker’s Use Only

Checker No.

香港考試局 保留版權 Hong Kong Examinations Authority All Rights Reserved 2002

Total

2002-AL-PHY 1B–1

HONG KONG EXAMINATIONS AUTHORITY

HONG KONG ADVANCED LEVEL EXAMINATION 2002

PHYSICS A-LEVEL PAPER 1 Question-Answer Book B

8.30 am – 11.30 am (3 hours)

This paper must be answered in English

INSTRUCTIONS

1. Write your Candidate Number, Centre Number and Seat Number in the spaces provided on the covers of Question-Answer Books A and B.

2. Question-Answer Books A and B must be

handed in separately at the end of the examination.

3. Supplementary answer sheets will be supplied

on request. Write your Candidate Number on each sheet and fasten them with string inside this book.

Candidate Number

Centre Number

Seat Number

Marker’s Use Only

Examiner’s Use Only

Marker No. Examiner No.

Question No. Marks Marks

6

7

8

9

Total

2002-AL PHY PAPER 1 (SECTION B)

B

2002-AL-PHY 1B–2 –1– 保留版權 All Rights Reserved 2002

SECTION B i Answer ALL questions. ii Write your answers in the spaces provided in this question-answer book. In calculations you should show

all the main steps in your working. iii Assume : speed of light in air = 3 × 108 m s–1 acceleration due to gravity = 10 m s–2

Question No. 6 7 8 9

Marks 14 13 17 16

6. A space shuttle is launched into a circular orbit around the earth at an altitude of 2.4 × 105 m. (Given : radius of the earth = 6.4 × 106 m) (a) (i) Find the orbital speed of the shuttle. Show your working. (3 marks)

(ii) Calculate the gravitational force acting on an astronaut of mass 60 kg in the shuttle. (2 marks)

2002-AL-PHY 1B–3 –2– 保留版權 All Rights Reserved 2002

(b) Two astronauts A and B, each of mass 60 kg, float in the cabin of the shuttle. They approach each other in opposite directions with the same speed of 1 m s–1. Astronaut A carries with him a toolbox of mass 30 kg.

(i) Explain why the astronauts appear to be ‘weightless’ in the cabin. (1 mark)

(ii) In order to avoid colliding head-on with B, A throws the toolbox to B, and B grasps the box

once it reaches him. How can a collision be avoided by so doing ? (2 marks)

(iii) Calculate the minimum speed that the toolbox should have when it reaches B in order to

avoid a collision. (4 marks)

(iv) Use the result in (b)(iii) to find the corresponding work that is done on the toolbox by A.

(2 marks)

Go on to the next page

2002-AL-PHY 1B–4 –3– 保留版權 All Rights Reserved 2002

7. In this question you are asked to estimate the lifetime of the sun (i.e. How long can the sun shine ?) based on some theories of physics, standard constants and given information.

(a) Given : Universal gravitational constant = 6.7 × 10–11 N kg–2 m2 1 year = 3.2 × 107 s The surface area of a sphere of radius r is 4πr2 (i) Solar radiation takes about 8 minutes 20 seconds to reach the earth. Estimate the

sun-earth separation to 2 significant figures. (1 mark)

(ii) Calculate the mass of the sun to 1 significant figure. (3 marks)

(iii) The intensity of the solar radiation when it reaches the earth is 1.35 kW per unit area.

Estimate the total power of the solar radiation from the sun. Assume that the sun radiates evenly in all directions. (2 marks)

2002-AL-PHY 1B–5 –4– 保留版權 All Rights Reserved 2002

(b) The energy released by the sun is the result of thermonuclear fusion in its core, where protons are fused together into helium nuclei through a complicated process. The overall reaction can be represented by the following equation :

H11

4 He24

+ + energy

(i) Why is the above process of forming helium nuclei from protons very difficult to achieve

on earth, but easily achieved at the sun’s core ? (2 marks)

(ii) Given : mass of proton = 1.007 28 u mass of helium nucleus = 4.001 50 u 1 u = 1.66 × 10–27 kg Calculate the energy released by the sun for every kilogram of protons fused to form

helium nuclei. (3 marks)

(c) Estimate the lifetime, in years, of the sun assuming that it initially consists mainly of hydrogen and

it ‘burns’ at a constant rate until all its hydrogen is consumed. (2 marks)

other particles of negligible mass

Go on to the next page

2002-AL-PHY 1B–6 –5– 保留版權 All Rights Reserved 2002

8. Figure 8.1 shows a circuit consisting of a resistor R and an inductor L connected in series with a sinusoidal a.c. supply. The supply delivers constant r.m.s. voltage V of variable frequency f and its internal impedance is negligible. When f is set to 100 Hz, the peak current in the circuit is 50 mA.

The figure on the graph paper is a phasor diagram (drawn to scale) for the circuit. Line AB represents the

peak voltage across L, AC the peak voltage of the supply and AD the peak voltage drop across R. (a) (i) What feature of the phasor diagram indicates that L is not a ‘pure’ inductor ? (1 mark)

(ii) What is the peak voltage of the a.c. supply ? (1 mark)

(iii) Find the resistance of the resistor R. (2 marks)

(iv) Calculate the resistance and inductance of the inductor L. (4 marks)

D

CB

A

X Y

L R

Figure 8.1 1 V

2002-AL-PHY 1B–7 –6– 保留版權 All Rights Reserved 2002

(v) Calculate the power factor of this circuit. Give its physical meaning and state in what way it is affected by the frequency of the supply. (3 marks)

(b) Figure 8.2 shows the variation of the potential VX at point X in the circuit against time t. On the

same figure, add a graph to show the variation of the potential VY at Y against time t. (2 marks)

Figure 8.2

Go on to the next page

2002-AL-PHY 1B–8 –7– 保留版權 All Rights Reserved 2002

8. (c) If the frequency f is increased from a small value to a large value, sketch a graph to show how each of the following varies with f.

(i) the peak current I in circuit (ii) the peak voltage VL across the inductor (4 marks)

f / Hz 0

I/mA

100

VL/V

f / Hz 0 100

2002-AL-PHY 1B–9 –8– 保留版權 All Rights Reserved 2002

(Blank page)

Go on to the next page

2002-AL-PHY 1B–10 –9– 保留版權 All Rights Reserved 2002

9. In a model of a molecule consisting of two atoms P and Q at a distance r apart, the interatomic force that P

exerts on Q is given by F =32 r

bra+− where a = 2 × 10–30 J m, b = 2 × 10–40 J m2, as shown in Figure 9.1.

(a) (i) Find the equilibrium separation ro of the two atoms. (2 marks)

(ii) State the physical meaning of the terms 32

andrb

ra

− in the expression. (2 marks)

Figure 9.1 ro

r0

F

U

ro r0

QP

r

2002-AL-PHY 1B–11 –10– 保留版權 All Rights Reserved 2002

(b) The interatomic potential energy U of the two atoms is taken to be zero when they are very far apart.

(i) Show explicitly that U = 22r

bra+− . (2 marks)

(ii) Sketch a graph of U against r below the F-r graph. (2 marks) (iii) Calculate the magnitude of the molecular binding energy of the molecule. (2 marks)

(c) Atom P is so massive that it can be considered as fixed at the origin and atom Q oscillates about the

equilibrium position ro if it is displaced slightly from ro. (i) What features of the F-r graph show that the motion of Q is simple harmonic ? (2 marks)

(ii) If the mass of atom Q is 3.2 × 10–27 kg, find the frequency of atomic vibration of the

molecule. (4 marks)

END OF PAPER

保留版權 All Rights Reserved 2002

2002 A Physics 1 B 6. (a) (i) 7.9 × 103 m s–1

(ii) 5.6 × 102 N

(b) (iii) 2.6 m s–1

(iv) 86 J

7. (a) (i) 1.5 × 1011 m

(ii) 2 × 1030 kg

(iii) 3.8 × 1026 W

(b) (ii) 6.2 × 1014 J kg–1

(c) 1 × 1011 years

8. (a) (ii) 7.1 V

(iii) 80 Ω

(iv) 20 Ω, 160 mH

(v) 0.7

9. (a) (i) 10–10 m

(b) (iii) 10–20 J

(c) (ii) 4 × 1012 Hz