J rx'"c-
wn3
-3 -
l,Lrr:,tI l.
(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
f^{*,
,
-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
I
I
tl
it It
ll mark J Total 10 marks
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t
- 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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l1
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