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**PH02
Summer 97 ^{
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mark scheme
}**

1
The isotope of ^{238 }_{92 }U is at the head of a chain
of radioactive decays. The first few decays in the series are shown below.

(a) Use data from the data book to identify the decay process X and the decay products Y and Z.

(3)

(b) (i) Calculate the mass difference between U-238 and Th-234.

(ii) Show that the energy released in this decay is about 4 MeV.

(4)=(7)

3

A trolley of mass 0.40 kg is attached to two fixed points by springs as shown. When it is displaced horizontally 0.20 m from its equilibrium position and released, it moves with simple harmonic motion with a period of 4.0 s.

(a) Ignoring any frictional effects, calculate

(i) the maximum speed of the trolley,

(ii) the maximum kinetic energy of the trolley,

(iii) the effective stiffness constant, k, of the spring system.

(5)

(b) In practice, frictional forces gradually reduce the kinetic energy of the trolley. If the trolley loses one-tenth of its kinetic energy in every complete oscillation, calculate the kinetic energy of the trolley at the equilibrium position when it has made four complete oscillations. Assume that the kinetic energy when it first passes the equilibrium position is the value which you have calculated in (a) (ii).

(2)=(7)

4 (a)
Explain the meanings of the following terms:

free vibration

forced vibration

resonance

(3)

(b)

A, B and C are three pendulums, each with a light paper cone for a bob. X is another pendulum with a heavy metal bob. Pendulum X is displaced perpendicular to the plane containing the bobs at rest and then released.

Compare the motions of pendulums A, B and C to that of X, with reference to period and amplitude.

Pendulum A:

Pendulum B:

Pendulum C

(3)=(6)

5 (a)
Explain what is
meant by

(i) unpolarised light

(ii) plane polarised light

(2)

(b)

A light source appears bright when viewed through two pieces of
polaroid, as shown. Describe what is seen when B is slowly rotated through 180^{o}
in its own plane.

(2)

(c) (i) Tick which of the following categories of waves can be polarised.

(ii) State your criterion for deciding which to tick.

.(2)=(6)

6 (a) Describe, with the aid of a diagram, how you would set up the apparatus to produce and observe optical interference fringes using a double slit and any other essential apparatus.

(3)

(b) A student set up a two-slit interference experiment in the laboratory to determine the wavelength of the yellow light from a sodium lamp. A travelling microscope was used to make measurements on the fringes produced and the readings obtained are shown below. The slit separation was 0.40 mm and the distance from the double slit to the plane in which the fringes were viewed was 1.80 m.

Use these values to calculate the wavelength of the yellow light.

(4)

(c) For the apparatus used in (b), describe and explain the effect on the appearance of the fringes of

(i) reducing the separation of the double slits but keeping the width of each slit constant,

(ii) making each of the double slits wider but keeping the slit separation constant.

(4)

(d) You have been asked to demonstrate two-source interference with sound waves. Describe, with the aid of a diagram which shows the approximate distances involved, how you would do this.

. . (4)=(15)

3
Describe an experiment you would perform, using **the
same apparatus **in each case, to illustrate the meaning of each of the
following terms. In each case explain what you would observe.

(i) free vibrations

(ii) forced vibrations

(iii) resonance

. . (6)=(6)

5
(a)
Explain why the apertures (or lines) of a diffraction grating for
visible light should be

(i) narrow
compared to the wavelength of visible light,

(ii) close together,

(iii) equally spaced.

(3)

(b)
Sodium light of wavelength 589 nm falls normally on a diffraction
grating which has 600 lines per mm. Calculate the angle between the directions
in which the first order and second order maxima, on the same side of the
straight through position,
are observed.

(5)=(8)

**PH02 June 1996
**

1
Red light of wavelength 7.00 x 10^{-7} rn, incident normally on
a diffraction grating, gave a first order maximum at an angle of 75^{o}.

(a) Calculate the
spacing of the diffraction grating.

(b) Calculate the angle at
which the first order maximum for violet light of wavelength 4.50 x 10^{-7 }m
would be observed.

(c) At what angle or angles
would a detector receive radiation which is of wavelength 7.5 x 10^{-7}
m transmitted by the grating? Explain your answer.

(2)=(4)

4. (b) Graph C below shows the variation of displacement with distance along a stationary transverse wave at time

t = 0 when the displacement of the particles is the greatest. The period of the vibrations causing the wave is 0.10 s.

(i) Draw, on the same axes, the appearance of the wave at t = 0.025 s, labelling this graph D, and the appearance of the wave at t = 0.050 s, labelling this graph E.

(ii) Compare the frequency, amplitude and phase of the particles whose positions at t = 0 are shown by V, W and Z.

(iii) State the two conditions necessary for the production of a stationary wave.

(8)

**PH02 Feb 1996
**

1.

The graph shows the displacement of particles in a transverse progressive wave against the distance from the source at a particular instant with points labelled A, B, C, D and E.

(a) Write down the letters of

(i) all the points at which the speed of the particle is a maximum,

(ii) all the points at which the magnitude of the acceleration of the particle is a maximum,

(iii) two points which are in phase,

(iv) two points which are 90^{o}
out of phase.

. .

(b) State

(i) the amplitude of the wave,

(ii) the wavelength of the wave.

(6)

**PH02 JUNE 1995
**

view mark scheme

1 Use data from the data booklet in this question.

^{
238 }_{92}U decays by the emission of an alpha particle.

(a) Give an equation for this process.

(2)

(b) Calculate the energy in MeV released in the reaction.

(3)=(5)

2 (a) A simple pendulum of length 50 cm. oscillates with simple harmonic motion with an amplitude of 2.0 cm.

Calculate

(i) the period of these oscillations,

(ii) the maximum velocity of the bob. State where this maximum velocity occurs.

(4)

(b) By referring to a simple pendulum, or otherwise, explain what is meant by

(i) free oscillations,

(ii) forced oscillations.

(2)

(c) (i) Explain what is mean by resonance. Illustrate your answer by referring to a demonstration.

(ii) What is meant by damping? State how the amount of damping influences resonance.

(7)=(13)

3

Graph A shows the variation of displacement with distance along the path of a progressive transverse wave of constant amplitude at time t = 0. The wave is travelling in the direction of the arrow. Graph B shows the same wave at time t = 50 ms.

(a) Determine

(i) the wavelength,

(ii) the speed of the wave,

(iii) the frequency of the vibrations producing the wave.

(3)

(b) (i) Describe the motion of the particle whose position at t = 0 is shown by X on the graph.

(ii) Sketch a graph showing displacement against time for this particle, starting from time t = 0, with scales on both axes.

Label a point P on your graph at which the speed of the particle is a maximum.

(4)=(7)

4 A laser emitting light of wavelength 6.0 x 10‑7 m is used to illuminate two parallel slits, giving two coherent sources. Interference fringes are to be produced on a screen 2.0 m from the slits. The separation of the fringes required is 5.0 mm.

(i) Calculate the distance between the centres of the two slits.

(ii) Interference takes place where light beams from the two slits overlap. With the aid of a diagram, explain how this overlap is produced.

(iii) State and explain what two changes you would expect in the fringe system if each of the slits was made narrower, but their separation was kept the same.

(6)=(6)

**PH02 March 1995
**

view mark scheme

1. (a)
**With reference **to sound waves
in air and a wave on a string, distinguish between
longitudinal waves and transverse waves.
2

(b) Describe an experiment you could perform in a laboratory to show that light is a transverse wave. State what you would expect to observe, and explain your observations.

5=7

2 A
parallel beam of light from an illuminated vertical slit consists of one red
wavelength and one blue wavelength. It is incident normally on a diffraction
grating having 3.00 x 10^{ 5} lines m^{‑1} placed on a
horizontal surface.

(a) The wavelength of the blue light is 450 nm

Calculate the angle between the straight through position and the first order maximum for this wavelength.

(b) The diffracted light is observed as the angle from the straight through position is increased and the following lines are seen in sequence: blue, red, blue. Then a blue line and a red line are seen to coincide.

(i) Which order red line is the one which coincides?

(ii) Calculate the wavelength of the red light.

(iii) Calculate the angle at which the red and blue lines coincide.

5

(c) Diffracted light is observed at greater angles than in (b). At what other angle, any, can a red line and a blue line be seen to coincide?

2=9