Cape 2003 Unit 1 Paper 1

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l . (a) tr#ffiprinciple whichunderlieshechecking f thebalance f equationssing f^{*

[1 mark(b) StateONE limitation of usingbasequantitieso check he balanceof equations.

[1 mark ](c) A body moving throughair at a high speed,v, experiencesa force, 4 given byF = kAPv2, whereA is the surface areaof the body, p is the density of air and k isa unitlessconstant. lf A r 0.10 + 0.005 m2, p = 1000 t 0.1 kg m-3 andv = 30.0 + I m s-1, ind the ractionalerror n the force.F.

[3 rnarks]The speed, , of oceanwaves s related o the wavelength,l, and heacceleration ue ogravity, g. Tlvo relationshipsare proposed,v = ag) or v = br6 , where a andbareconstantswith no units. Determinewhich of theseequations s possible.

[3 marksl

(d)

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

[2 marks]Total 10 marks

2. (a) Define the term 'acceleration' and explain what is meant by the 'acceleration due togravi tv ' .

[2 marks]t

(b) A ball is thrown horizontally from a height, h, and with a speed, u. lt hits the ground ata horizontal distance, d, from where it is thrown in a time, r. Throughout this questionassume 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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(i )

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Explainhow Newton's awsof motion apply oa) thehorizontal notionof theball

[2 marks]b) the vertical motion of the ball.

Without performing the calculation, explainof the ball.

[1 mark ]how youwould find the inal velociry

(a ).

( i i i

( 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 togravity is less than that on Earth, would the submerged proportion of the corkbe greater. tay the same or become less?

[1 mark ](ii) Give TWO reasonsor vour answer.

[2 marks]

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(b )

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Consider the Figures 1 and 2 which show twofloating respectively in water and in a liquid L.

identical, rectangular wooden blocks(Densiry of water = 1000 kg m-:;

(i )

Liquid L

Figure 1Find the

Figure 2

a) weight of the block

[4 marksldensityof liquid L.

[2 marks]Explain why frictional forces between the blocks and the water should NOT beconsidered n your calculations.

l l mark JTotal 10 marks

Yt ,Ll it ;Dlt

0IItlitItt

b)

(ii)

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(a) State heTWO conditionsnecessaryor simpieharmonicmotion (S.H.M.) to occur.

[2 marks]A body is undergoingS.H.M. of amplitude4 x 10-2m and with a maximumspeed f 0.20m s-1. Calculateheperiodof theoscillationgiven hat hevelocity,v, of a body undergoingS.H.M. is v - 6t[ fr - *, where trl is the angularvelocity, A is the maximum displacement nd x its displacement rom theequilibriumposition

[2 marks](ii) Calculate he maximum acceleration uring he 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 completeoscillation of the body.

[3 marks](iv) Write an equation to represent he relationship between kinetic energy andpotentialenergyduring S.H-M.

[1 mark ]Total 10 marks

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(i)b)

{

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(a),.

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

( i)b)

[1 mark ]Critical angle:

[1 rnark ]A soundwave has a speedof 330 m rl in air and 1.5 x 103m s-l in water.Determine the refractive index for soundwaves passing rom air into water.

[3 marks](ii) Calculate he critical angle or soundwavesat aboundarybetween ir andwater.

I

[2 marks]In the spacebelow, draw a labelled ray diagram to represent two sound waves striking aboundary between air and water, with one wave at an angle less than the critical angleand one wave which is totally internally reflected.


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(c)

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(a )

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State he meaningof the term 'diffraction

[l mark ]Briefly describe ow thediffractionof (i) soundand(ii) light may be observed.Sound:

[1 mark ILight:

(b)

(c) A diffraction gratinghas300 ines permillimetre.possible or red ightof wavelength .4 x 10-7m?

[2 marks]How many ordersof diffraction are

[4 marks]Without performing any calculation, f blue light were to be used insteadof red light,would you expect a larger or smallernumber of orders of diffraction to be possible?Explain your answer.

[2 marksJTotal l0 marks

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(d)

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7. (a) Define the terms 'specif ic heat capacity' and heat capacity'.Specific heat capacity:

tl mark lHeat capacity:

[1 mark ](b) (i) A massof 0.45kg of water s heated y an mmersionheater n a containerofheatcapacity90 J K-1. The water s heated or 9 minutesand the temperaturerises rom 25 C to 79 C. Find hepowerof the heater.You may considerheatlosses egligible.

[6 marks](ii) Use the kinetic theoryof matter o outline what happens o the thermalenergysuppliedby the mmersionheatern (b) (i) above.


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l 1

(a). Explainwhat s meantby 'tensilestress',tensilestrain'and Youngmodulus'.Tensile tress:

[1 mark ]Tensile train:

(b)

[1 mark ]Youngmodulus:

[1 mark ]

What stresswould be required o increase he length of a metal wire, X, by 0.L5Vo2(Youngmodulus or metalof wire, X = 1.2 x 10ll N m-2)

[3 marksJ(i) If the cross-sectionalarea 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.


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(c )

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t 2 -9. (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 thermalconductors.

[5 marks](c) To demonstrate different conductivities of materials, bars of similar dimensions areheated. What other characteristics of the bars, or the materials from which they aremade, may affect these results?

[2 marks]Total 10 rnarks

END OF TEST

002471/CAPE2003

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Cape 2003 Unit 1 Paper 1