Phyu5 June 2002 Group 2a

1.

(a) secure the can to the bench with blu-tack to prevent it from rolling. balance the metre rule on the can and determine the period t1 of small oscillations of the rule. ..................................................................................................................................... ..................................................................................................................................... repeat the above to find the period t2 of small oscillations of the half-metre rule. ..................................................................................................................................... ..................................................................................................................................... to what extent do your measurements confirm that the period of such oscillations is proportional to the length of the rule? ..................................................................................................................................... ..................................................................................................................................... (6)

(b)

(i)

use the balance provided to find the mass m of the can and its contents.

........................................................................................................................... use the data given on the can to determine the mass m of the can itself. (1 litre of water has a mass of 1 kg.) explain how you calculated m. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... using the information on the card, estimate the volume v of material in the can itself. ........................................................................................................................... ........................................................................................................................... (3)

(ii)

measure the diameter d of the central part of the can and the length l of the can. draw a diagram below to show how you measured d.

........................................................................................................................... ...........................................................................................................................

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calculate a value for the thickness t of the can given that, to a good approximation

V t = πD( L + D) ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (7) (total 16 marks)

2.

(a) the apparatus shown in the diagram below has already been set up for you with m = 100 g. A .c . p o w e r s u p p ly

M a g n e tic fie ld p e r p e n d ic u la r to w ire

× × × × × × × × ×

K n ife edge

C r o c o d ile c lip

l

M switch on the power supply. adjust the length l of the wire between the wooden blocks and the knife edge until you can see that the amplitude of vibration of the wire passing through the magnetic field is at its maximum value. record the length l1 at this point. ..................................................................................................................................... ..................................................................................................................................... explain carefully how you ensured that the value of l1 was as accurate as possible. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................

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estimate the percentage uncertainty in your value of l1. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... repeat the above procedure with m = 300 g to obtain a value for the new resonant length l2. ..................................................................................................................................... ..................................................................................................................................... switch off the power supply. (6)

(b)

when a wire is forced to vibrate at its natural frequency, the tension t in the wire and the length 1 of the wire are related by an equation of the form T l2 = k where k = a constant. use your results from part (a) to determine two values for k. comment on the extent to which your results support the relationship. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (5)

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(c)

measure the diameter d of the wire. hence determine a value for the density ρ of the material of the wire given that 22

k = ρ πd f

where f = the frequency of the a.c. supply, which is given on the card. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (5) (total 16 marks)

3.

you are to plan an investigation into the relationship between the intensity of the light passing through a pair of polaroid filters and the angle between their planes of polarisation. you are then to analyse a set of data from such an experiment. (a)

you have been provided with a pair of polaroid filters to observe what happens when one filter is rotated with respect to the other, but you are not required to take any measurements. the following additional apparatus would be available: • light source • ldr and ohmmeter together with a calibration curve enabling resistance measurements to be converted to light intensity in a unit called lux • light shield • protractor • stands and clamps draw a diagram of the experimental arrangement which you would use.

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describe, with the aid of diagrams, how you would measure the angle through which one filter had been turned with respect to the other.

..................................................................................................................................... ..................................................................................................................................... state a suitable starting angle between the planes of polarisation of the two filters. explain how you would determine when the planes are at this angle from your resistance readings. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (8)

(b)

the intensity i of light passing through the two polaroids is thought to be related to the n angle θ between their planes of polarisation by an equation of the form i = k(cos θ ) where k and n are constants. write this equation in a suitable format which can be used to plot a linear graph. .................................................................................................................................... .................................................................................................................................... (1)

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(c)

the following data was obtained in an investigation of the above equation.

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θ/°

i / lux

cos θ

10

481

0.985

20

450

0.940

30

398

0.866

40

330

0.766

50

256

0.643

60

172

0.500

70

98

0.342

80

40

0.174

6

use the empty columns provided for your processed data, and then plot a suitable graph to test the equation on the grid below.

(5)

(d)

use your graph to determine a value for n. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... (2) (total 16 marks)

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