2

3
 4

1. (a) State what is meant by a scalar quantity and by a vector quantity.

scalar:...........................................................................................................................

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

vector:..........................................................................................................................

................................................................................................................................. [2]

(b) Complete Fig. 1.1 to indicate whether each of the quantities is a vector or a scalar.

Fig. 1.1
[2]

(c) An aircraft is travelling in wind. Fig. 1.2 shows the velocities for the aircraft in still air
and for the wind.

Fig. 1.2

The velocity of the aircraft in still air is 95ms–1 to the west.

The velocity of the wind is 28ms–1 from 65° south of east.

(i) On Fig. 1.2, draw an arrow, labelled R, in the direction of the resultant
velocity of the aircraft. [1]
 5

(ii) Determine the magnitude of the resultant velocity of the aircraft.

magnitude of velocity = ................................................. ms–1 [2]

[Total: 7]

2. (a) State Hooke’s law.

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

.................................................................................................................................[1]

(b) The variation with compression x of the force F acting on a spring is shown in Fig.
2.1.

Fig. 2.1

The spring is fixed to the closed end of a horizontal tube. A block is pushed into the
tube so that the spring is compressed, as shown in Fig. 2.2.

Fig. 2.2 (not to scale)

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The compression of the spring is 4.0 cm. The mass of the block is 0.025 kg.

(i) Calculate the spring constant of the spring.

spring constant = ................................................ N m–1 [2]

(ii) Show that the work done to compress the spring by 4.0 cm is 0.48 J.

[2]

(iii) The block is now released and accelerates along the tube as the spring
returns to its original length.
The block leaves the end of the tube with a speed of 6.0 m s–1.

1. Calculate the kinetic energy of the block as it leaves the end of the tube.

kinetic energy = ....................................................... J [2]

 7

2. Assume that the spring has negligible kinetic energy as the block
leaves the tube.

Determine the average resistive force acting against the block as it

moves along the tube.

resistive force = ...................................................... N [3]

(iv) Determine the efficiency of the transfer of elastic potential energy from the
spring to the kinetic energy of the block.

efficiency = .......................................................... [2]

[Total: 12]
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3. (a) State the difference between a stationary wave and a progressive wave in terms of

(i) the energy transfer along the wave,

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

......................................................................................................................[1]

(ii) the phase of two adjacent vibrating particles.

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

.....................................................................................................................[1]

(b) A tube is open at both ends. A loudspeaker, emitting sound of a single frequency, is
placed near one end of the tube, as shown in Fig. 3.1.

Fig. 3.1

The speed of the sound in the tube is 340ms–1.

The length of the tube is 0.60m.

A stationary wave is formed with an antinode A at each end of the tube and two
antinodes inside the tube.

(i) State what is meant by an antinode of the stationary wave.

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

.....................................................................................................................[1]

(ii) State the distance between a node and an adjacent antinode.

distance = ...................................................... m [1]

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(iii) Determine, for the sound in the tube,

1. the wavelength,

wavelength = ...................................................... m [1]

2. the frequency.

frequency = .................................................... Hz [2]

(iv) Determine the minimum frequency of the sound from the loudspeaker that
produces a stationary wave in the tube.

minimum frequency = .................................................... Hz [2]

[Total: 9]
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4. (a) State the two conditions for an object to be in equilibrium.

1. .................................................................................................................................

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

2. .................................................................................................................................

...............................................................................................................................[2]

(b) A uniform beam AC is attached to a vertical wall at end A. The beam is held
horizontal by a rigid bar BD, as shown in Fig. 4.1.

Fig. 4.1 (not to scale)

The beam is of length 0.40 m and weight W. An empty bucket of weight 12 N is

suspended by a light metal wire from end C.

The bar exerts a force on the beam of 33 N at 52° to the horizontal. The beam is in
equilibrium.

(i) Calculate the vertical component of the force exerted by the bar on the
beam.

component of the force = ...................................................... N [1]

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(ii) By taking moments about A, calculate the weight W of the beam.

W = ...................................................... N [3]

(c) The metal of the wire in (b) has a Young modulus of 2.0 × 1011 Pa. Initially the
bucket is empty.

When the bucket is filled with paint of weight 78 N, the strain of the wire increases
by 7.5 × 10–4. The wire obeys Hooke’s law.

Calculate, for the wire,

(i) the increase in stress due to the addition of the paint,

increase in stress = .................................................... Pa [2]

(ii) its diameter.

diameter = ...................................................... m [3]

[Total: 11]
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5. (a) Define the volt.

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

..................................................................................................................................[1]

(b) A battery of electromotive force (e.m.f.) 7.0 V and negligible internal resistance is
connected in series with three components, as shown in Fig. 5.1.

Fig. 5.1

Resistor X has a resistance of 5.2 Ω. The resistance of the filament wire of lamp Y
is 6.0 Ω. The potential difference across resistor Z is 1.4 V.

(i) Calculate the current in the circuit.

current = ....................................................... A [2]

(ii) Determine the resistance of resistor Z.

resistance = ...................................................... Ω [1]

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(iii) Calculate the percentage efficiency with which the battery supplies power to
the lamp.

efficiency = ...................................................... % [3]

(iv) The filament wire of the lamp is made of metal of resistivity 3.7 × 10 –7 Ωm at
its operating temperature in the circuit.

Determine, for the filament wire, the value of α where

α = ...................................................... m [2]

[Total: 9]

6. (a) Light waves emerging from the slits of a diffraction grating are coherent and
produce an interference pattern.

Explain what is meant by:

(i) coherence

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

.....................................................................................................................[1]

(ii) interference.

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

.....................................................................................................................[1]
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(b) A narrow beam of light from a laser is incident normally on a diffraction grating, as
shown in Fig. 6.1.

Fig. 6.1 (not to scale)

Spots of light are seen on a screen positioned parallel to the grating. The angle
corresponding to each of the second order maxima is 51°. The number of lines per
unit length on the diffraction grating is 6.7 × 105 m–1.

(i) Determine the wavelength of the light.

wavelength = ..................................................... m [2]

(ii) State and explain the change, if any, to the distance between the second
order maximum spots on the screen when the light from the laser is
replaced by light of a shorter wavelength.

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

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

.....................................................................................................................[1]

[Total: 5]