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(a)

whichunderlies thecheckingof the balanceof equations using tr#ffiprinciple

[1 mark (b)

StateONE limitation of usingbasequantitiesto check the balanceof equations.

[1 mark ] (c)

A body moving through air at a high speed,v, experiencesa force, 4 given by F = kAPv2, where A is the surface area of the body, p is the density of air and k is a unitlessconstant. lf A r 0.10 + 0.005 m2, p = 1000 t 0.1 kg m-3 and v = 30.0 + I m s-1,find the fractionalerror in the force. F.

[3 rnarks] (d)

The speed,v, of oceanwavesis relatedto the wavelength,l, and the accelerationdue to gravity, g. Tlvo relationshipsare proposed,v = ag)" or v = br6", where a and b are constantswith no units. Determinewhich of theseequationsis possible.

[3 marksl

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002471/CAPE2003

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-4-

(e)

Assuming that your result in (d) is correct, determine the full equation if an ocean wave has a speed of 16 m s-l and a wavelength of 160 m,

[2 marks] Total 10 marks

2.

(a)

Define the term gr av i tv ' .

'acceleration'

and explain what is meant by the

'acceleration due to

[2 marks] t

(b)

A ball is thrown horizontally from a height, h, and with a speed, u. lt hits the ground at a horizontal distance, d, from where it is thrown in a time, r. Throughout this question assume that air resistance is negligible. (i)

Use the equations of motion to derive the relationship between h and d, given that the acceleration due to gravity is g.

[3 marks]

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aa247liCAPE2003


-5-

(i i)

Explainhow Newton'slaws of motion applyto a)

the horizontalrnotion of the ball

[2 marks] b)

the vertical motion of the ball.

[1 mark ] (iii )

Without performing the calculation, explain how you would find thefinal velociry of the ball.

[2 marks] Total 10 marks

3.

(a)

(i)

A small cork floats in water, exactly half submerged, on Earth. If the container, water and cork were all transferred to a place where the acceleration due to gravity is less than that on Earth, would the submerged proportion of the cork be greater.stay the same or become less?

[1 mark ] (ii)

Give TWO reasonsfor vour answer.

[2 marks]

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00247I/CAPE2003


-6-

(b)

Consider the Figures 1 and 2 which show two identical, rectangular wooden blocks floating respectively in water and in a liquid L. (Densiry of water = 1000 kg m-:;

Y t,

L

Liquid L

li

t; D lt

Figure 1 (i)

Figure 2

Find the a)

weight of the block

[4 marksl b)

densityof liquid L.

[2 marks]

(ii)

Explain why frictional forces between the blocks and the water should NOT be considered in your calculations. 0

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it It

ll mark J Total 10 marks

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- 7-

(a)

StatetheTWO conditionsnecessaryfor simpieharmonicmotion (S.H.M.) to occur.

[2 marks] (b)

(i)

A body is undergoingS.H.M. of amplitude4 x 10-2 m and with a maximum speedof 0.20 m s-1. Calculatetheperiodof the oscillationgiven thatthevelocity, v, of a body undergoingS.H.M. is v - 6t[ fr - *, where trl is the angular velocity, A is the maximum displacementand x its displacementfrom the equilibriumposition"

[2 marks] (ii)

Calculatethe maximum accelerationduringthe motion.

[2 marks] (iii)

In the space below, sketch and label on the sdme axes, graphs of kinetic energy against displacement and potential energy against displacement for one complete oscillation of the body.

{ [3 marks] (iv)

Write an equation to represent the relationship between kinetic energy and potential energy during S.H-M. [1 mark ] Total 10 marks GO ON TO THE NEXT PAGE

a02471/cAPE2003


-8-

f,.

(a)

Explain what is meant by the 'refractive index' and 'critical angle' of a material. Refractive index:

[1 mark ] Critical angle:

[1 rnark ] (b)

(i)

A sound wave has a speedof 330 m rl in air and 1.5 x 103m s-l in water. Determine the refractive index for soundwaves passingfrom air into water.

[3 marks] (ii)

Calculatethe critical anglefor soundwavesat a boundarybetweenair andwater. I

[2 marks] (c)

In the space below, draw a labelled ray diagram to represent two sound waves striking a boundary between air and water, with one wave at an angle less than the critical angle and one wave which is totally internally reflected.

[3 marks] Total 10 marks

oo247llcAPE2A03

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- 9-

(a)

State the meaning of the term 'diffraction

[l mark ] (b)

Briefly describehow the diffractionof (i) soundand (ii) light may be observed. Sound:

[1 mark I Light:

[2 marks] (c )

A diffraction grating has 300 lines per millimetre. How many orders of diffraction are possiblefor red light of wavelength6.4 x 10-7m?

[4 marks] (d)

Without performing any calculation, if blue light were to be used insteadof red light, would you expect a larger or smaller number of orders of diffraction to be possible? Explain your answer.

[2 marksJ Total l0 marks

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002471/CAPE 2003


-10-

7.

(a)

'specific Define the terms heat capacity' and 'heat capacity'. Specific heat capacity:

tl mark l Heat capacity:

[1 mark ] (b)

(i)

A massof 0.45 kg of water is heatedby an immersion heaterin a containerof heat capacity90 J K-1. The water is heatedfor 9 minutes and the temperature " "C. risesfrom 25 C to 79 Find the power of the heater.You may considerheat lossesnegligible.

[6 marks] (ii)

Use the kinetic theory of matter to outline what happensto the thermal energy suppliedby the immersionheaterin (b) (i) above.

[2 marks] Total 10 marks

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8.

(a)

Explainwhatis meantby

'Young 'tensile modulus'. stress','tensilestrain'and

Tensilestress:

[1 mark ] Tensilestrain:

[1 mark ] Youngmodulus:

[1 mark ]

(b)

What stresswould be required to increasethe length of a metal wire, X, by 0.L5Vo2 (Youngmodulusfor metal of wire, X = 1.2 x 10ll N m-2)

[3 marksJ (c)

(i)

If the cross-sectional area of the wire is 2.0 ffiD2, calculate the tension needed for this extension

[2 marks] (ii)

Calculate the work done during the extension of the wire if the wire is 1 metre long.

[2 marks] Total 10 marks

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t29.

(a)

Describe the mechanisms of the conduction of thermal energy in (i)

a metal bar

[2 marksf (ii)

a piece of wood.

[1 mark ] (b)

Compare the approaches at determining thermal conductiviry for good and bad thermal conductors.

[5 marks] (c)

To demonstrate different conductivities of materials, bars of similar dimensions are heated. What other characteristics of the bars, or the materials from which they are made, may affect these results?

[2 marks] Total 10 rnarks END OF TEST

002471/CAPE 2003


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