PHYSICS PAPER 2 9646/02 - A Level Tuition

This booklet consists of 18 printed pages, inclusive of this page.

For Examiner’s Use

Paper 2

Q 1 / 11

Q 2 / 10

Q 3 / 6

Q 4 / 7

Q 5 / 9

Q 6 / 10

Q 7 / 9

Q 8 /18

Deductions

Total / 80

HWA CHONG INSTITUTION

JC1 Promotional Examination

Higher 2

CANDIDATE NAME

CT GROUP 13S

TUTOR NAME

PHYSICS PAPER 2

Candidates answer on the Question Paper. No Additional Materials are required.

9646/02

01 October 2013

1h 50 minutes

INSTRUCTIONS TO CANDIDATES

1) Write your name, CT class and tutor’s name clearly in the spaces at the top of this page.

2) Answer all questions in the spaces provided in this Question Booklet.

3) For numerical answers, all working should be shown. You may use a soft pencil for any diagrams, graphs or rough working. Do not use paperclips, highlighters, glue or correction fluid.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question.

A Data and Formula list is provided on page 2.

You are reminded of the need for good English and clear presentation in your answers.

2013 HWA CHONG INSTITUTION (COLLEGE SECTION) C1 H2 PHYSICS

Page 2 of 18

Data Formulae

speed of light in vacuum,

c = 3.00 108 m s

-1

permeability of free space,

o = 4 10-7 H m

-1

permittivity of free space,

o = 8.85 10-12

F m-1

= (1/(36)) 10-9 F m

-1

elementary charge,

e = 1.60 10-19

C

the Planck constant,

h = 6.63 10- 34

J s

unified atomic mass constant,

u = 1.66 10-27

kg

rest mass of electron,

me = 9.11 10-31

kg

rest mass of proton,

mp = 1.67 10-27

kg

molar gas constant,

R = 8.31 J K-1 mol

-1

the Avogrado constant,

NA = 6.02 1023

mol-1

the Boltzmann constant,

k = 1.38 10-23

J K-1

gravitational constant,

G = 6.67 10-11

N m2 kg

-2

acceleration of free fall,

g = 9.81 m s-2

uniformly accelerated motion,

work done on/by a gas,

hydrostatic pressure,

gravitational potential,

displacement of particle in s.h.m.,

velocity of particle in s.h.m.,

mean kinetic energy of

a molecule of an ideal gas

resistors in series,

resistors in parallel,

electric potential,

alternating current / voltage,

transmission coefficient,

where

radioactive decay,

decay constant,

2

2

1atuts

asuv 222

VpW

ghp

r

GM

txx o sin

tvv o cos

22xxv o

kTE2

3

...21 RRR

.../1/1/1 21 RRR

r

QV

o4

txx o sin

)2exp( kdT

2

2 )(8

h

EUmk

)exp( txx o

2

1

693.0

t


Page 3 of 18

1 A small ball P, illuminated by a lamp flashing at a constant frequency, is rolling along a smooth horizontal table towards the edge. Fig. 1 shows part of a multi-flash photography of the motion of ball P with square grids drawn onto the photograph for ease of reference.

At the instant when P reaches the edge of the table, another ball Q is dropped from rest. At the next two flashes of the lamp, ball Q appears at positions Q1 and Q2, respectively.

Fig. 1

(a) On Fig. 1, indicate accurately

(i) the position of ball Q for the next flash of the lamp. Label this position as Q3. [1]

(ii) the corresponding positions of ball P when ball Q is at positions Q1, Q2 and Q3. Label these positions as P1, P2 and P3, respectively.

[1]

(b) The stroboscopic lamp flashes at a rate of 8.0 Hz.

(i) Determine the time taken for ball Q to fall from rest to position Q2.

Time = s [1]

Table Ball Q

Q1

Floor

Q2

Ball P


Page 4 of 18

(b) (ii) Hence, determine the length of each square grid that is drawn on the figure.

Length = m

[2]

(c) (i) Determine the horizontal velocity of ball P just before it hits the floor.

Horizontal velocity = m s-1 [1]

(ii) With the aid of Fig. 1 and using the value found in (c)(i), further determine the final velocity ball P just before it hits the floor.

Magnitude of velocity = m s-1

Direction of velocity =

[3]

(d) Another ball R is launched at the same speed as ball P, but at an angle above the horizontal from the edge of the table. Explain if it is possible for ball R to land at the same spot as ball P.

…………….………………………………………………………………………………….............. …………….………………………………………………………………………………….............. ………………………………………….……………………………………………………………... …………………………………………….……………………………………………………………

[2]


Page 5 of 18

2 (a) State the two conditions necessary for a body to be in equilibrium. [2]

…………………………………………………………………………………………………..….............

…………………………………………………………………………………………………..…............. …………………………………………………………………………………………………..….............

(b) A man supports himself on the centre of a uniform wooden plank by holding onto the ends of two light ropes as shown in Fig. 2.1. The other ends of the two ropes are tied to the wooden plank over two light and frictionless pulleys. The tensions of the left and right ropes are equal in magnitude. The wooden plank remains horizontal at all times. The mass of the man and wooden planks are 70.0 kg and 10.0 kg, respectively.

Fig. 2.1

(i) Draw and label on Fig 2.2 the forces acting on the system comprising of the wooden plank and the man.

Fig. 2.2

[2]

Smooth pulleys

Wooden plank

Right rope Left rope


Page 6 of 18

(ii) Using Fig 2.2, calculate the tension in each of the two ropes.

Tension = ……………………. N [2]

(iii) Hence, determine the normal contact force exerted by the man on the plank.

Normal contact force = …………………….. N [2]

(iv) The man decides to stand away from the centre and move nearer to the left rope (Fig. 2.3).

Fig 2.3

How would this affect the tension in the right rope? Explain.

……………………………………………………………………………………..…………. ………………………………………………………………………………………..………. ………………………………………………………………………………………..……….

…………………………………………………………………………………………...…… [2]

Right rope Left rope


Page 7 of 18

3 Fig. 3 shows David the cyclist rounding a corner. David and his bicycle have a combined total mass of 70 kg. When the road is dry, the maximum friction between the tires and the road is 0.50 R, where R is the normal contact force the road surface exerts on the tyre.

(a) Draw and label on Fig. 3 the forces acting on David and his bicycle as he rounds the corner.

Fig. 3

[2]

(b) Calculate the minimum radius the corner must have for David to round it at 28 km h-1.

minimum radius = ………………….. m

[2]

(c) Explain whether David can round the same corner at the same speed on a rainy day. [2]

…………………………………………………………………………………………………………….…. …………………………………………………………………………………………………………….…. …………………………………………………………………………………………………………….…. …………………………………………………………………………………………………………….…

R


Page 8 of 18

4 Mars has got two moons, Phobos and Deimos. The orbital distances and periods of Phobos and Deimos are 9 378 km and 23 459 km and 7.6 and 30.3 hours, respectively. The radius of Mars is 3 390 km.

(a) Explain what is meant by gravitational potential. [2]

………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

………………………………………………………………………………………………………………..

(b) Use the values for Phobos to show that the mass of Mars is 6.5 x 1023 kg.

[2]

(c) Ignoring the gravitational field of the two moons, calculate the escape velocity, i.e. the minimum speed a body must have in order to escape to an infinite distance from the surface of Mars.

escape velocity = ………………….. m s-1

[3]


Page 9 of 18

5 (a) Define simple harmonic motion. [2]

…………………………………………………………………………………………………..............

…………………………………………………………………………………………………………...

……………………………………………………………………………………………………………

(b) A spring-mass system is placed on a smooth horizontal surface, as shown in Fig. 5. The object of mass 0.30 kg is displaced 5.0 cm to the right of the equilibrium position and then released. The oscillating system has a total energy of 60 mJ.

Fig. 5

(i) Show that the angular frequency of oscillation is 12.6 rad s-1.

[1]

(ii) Determine the following:

1. speed of the mass at a displacement of 3.0 cm from the equilibrium position.

speed = ………………….. m s-1

[1]


Page 10 of 18

2. acceleration of the mass at a displacement of 3.0 cm from the equilibrium position.

acceleration = ………………….. m s-2

[1]

3. the potential energy of the mass at a displacement of 3.0 cm from the equilibrium position.

potential energy = ………………….. J

[1]

(c) Taking into account the effect of air resistance and friction, sketch the variation with time of the potential energy for this system for the first two complete oscillations.

[3]

Potential energy


Page 11 of 18

6 Fig. 6 shows the variation with time t of P, the pressure difference with respect to atmospheric pressure, at a point in a progressive sound wave in air. The speed of the wave in air is 340 m s-1.

Fig. 6

(a) (i) Explain whether this wave can be polarized.

…………………………………………………………………………………………………… …………………………………………………………………………………………………… …………………………………………………………………………………………………… ……………………………………………………………………………………………………

[2]

(ii) Mark on Fig. 6 all the instances in time when the air particles (at that point) are displaced furthest from their equilibrium position with X.

[1]

(b) The variation of P as shown in Fig. 6 can be described by the equation

max sin( )P P t

(i) State the value of Pmax.

Pmax = ………………….. Pa [1]

P/Pa


Page 12 of 18

(ii) Determine the phase angle, 𝜑.

𝜑 = ………………….. rad

[1]

(iii) Determine the angular frequency, 𝜔.

angular frequency = ………………….. rad s-1

[1]

(iv) Hence determine the wavelength.

wavelength = ………………….. m

[1]

(c) This sound wave is emitted by a point source. Explain why the intensity of the sound wave is inversely proportional to the square of the distance from the point source.

…………………………………………………………………………………………………………. …………………………………………………………………………………………………………. …………………………………………………………………………………………………………. …………………………………………………………………………………………………………. …………………………………………………………………………………………………………. ………………………………………………………………………………………………………….

[3]


Page 13 of 18

7 (a) Explain what is meant by the principle of superposition as applied to waves. [2]

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

(b) Fig 7.1 below shows an experiment with sound waves.

Fig. 7.1

The loudspeaker connected to a signal generator is mounted, pointing downwards, above a

horizontal bench. The sound is detected by a microphone connected to an oscilloscope. The

height of the trace on the oscilloscope is proportional to the amplitude of the sound waves at

the microphone.

When the vertical distance x between the microphone and the bench is varied, the amplitude

of the sound waves is found to vary as shown in Fig. 7.2

Fig. 7.2


Page 14 of 18

(i) Explain why the amplitude of the sound detected has a number of maxima and

minima.

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

……………………………………………………………………………………………………….[3]

(ii) The frequency of the sound waves is 3.20 kHz. Use this, together with information

from Fig. 7.2, to determine the speed of sound in air for this experiment.

speed = …………………… m s-1 [2]

(iii) The contrast between the maxima and the minima becomes less pronounced as the

microphone is raised further from the surface of the bench. Suggest an explanation for

this observation.

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

…………………………………………………………………………………………………………..

……………………………………………………………………………………………………....[2]


Page 15 of 18

8 (a) State the principle of conservation of momentum. [2] ………………………………………………………………………………………………………………...…… ………………………………………………………………………………………………………………...…… ………………………………………………………………………………………………………………...…… (b) A trolley of mass 6.0 kg travelling at a speed of 5.0 m s-1 collides head-on and locks together with

another trolley of mass 8.0 kg which is travelling in the opposite direction at a speed of 3.0 m s-1 (Fig. 8.1). The collision lasts for 0.30 s.

Fig. 8.1

(i) Show that the final speed of the trolleys after the collision is 0.43 m s-1. [1] (ii) Calculate the work done on the 6.0 kg trolley during the collision.

work done = ……………….. J [2] (iii) Calculate the impulse acting on the 8.0 kg trolley during the collision.

impulse = ……………….. N s [2]

6.0 kg

8.0 kg

5.0 m s-1 3.0 m s-1


Page 16 of 18

(c) The trolleys are modified by attaching a spring to one of the trolleys (Fig. 8.2) so that the collision is now elastic. The spring has a spring constant of 950 N m-1. The experiment is then repeated with the same initial velocities.

Fig. 8.2

(i) Which trolley should come to rest first during the collision? Explain. [2] …………………………………………………………………………………………………................…… …………………………………………………………………………………………………................…… …………………………………………………………………………………………………................…… …………………………………………………………………………………………………................…… (ii) At one instant during the collision, the 6.0 kg trolley was travelling at a speed of 2.0 m s-1

towards the left. 1. Show that the speed of the 8.0 kg trolley is 2.25 m s-1 at this instant. [1] 2. Hence, calculate the compression of the spring at this instant.

compression = ……………….. m [3]

6.0 kg

8.0 kg

5.0 m s-1 3.0 m s-1

spring


Page 17 of 18

(d) The experiment is repeated using another set of two trolleys of different masses and different initial speeds (Fig. 8.3). The variations with time of the velocities of both trolleys are shown in Fig. 8.4a.

Figure 8.3

Fig. 8.4a

i) Bearing in mind that the collision is elastic, complete the graph in Fig. 8.4a to show the variation

with time of the velocity of trolley B. [1]

MA

MB

uA uB

Velocity

Time

uA

uB

collision

Trolley A Trolley B


Page 18 of 18

ii) Sketch in Fig. 8.4b the variation with time of 1. force experienced by trolley A (label FA) and 2. force experienced by trolley B (label FB). [2]

Fig. 8.4b

iii) Sketch in Fig. 8.4c the variation with time of 1. the total kinetic energy of the two trolleys (label KE) and 2. the elastic potential energy stored in the spring (label EPE). [2]

Fig. 8.4c

End of Paper

Force

Time

collision

Energy

Time

collision

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PHYSICS PAPER 2 9646/02 - A Level Tuition