Mechanics, Materials
and Waves
AQA GCE 2450 Physics A
AS Unit 2 Exam Questions
Physics A Unit2 Mechanics, Materials and Waves
Mechanics
1.
(a)
Distinguish between a scalar quantity and a vector quantity.
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(2)
(b)
A car travels one complete lap around a circular track at an average speed of
100 km h–1.
(i)
If the lap takes 3.0 minutes, show that the length of the track is 5.0 km.
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(ii)
What is the magnitude of displacement of the car after 1.5 minutes?
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(4)
(Total 6 marks)
2.
The diagram shows a straight, horizontal swimming bath spring board of length 4.00m and
of weight 300 N. It is freely hinged at A and rests on a roller B, where AB is 1.60m. A boy
of weight 400N stands at end C.
1.60m
4.0m
A
B
C
(a)
On the diagram show the directions of the forces acting on the board at A and B.
(2)
(b)
Calculate the magnitudes of the forces
(i)
at A ...................................................................................................................
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(ii)
at B ...................................................................................................................
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(4)
(Total 6 marks)
3.
A ball is dropped and rebounds vertically to less than the original height.
For this first bounce only, sketch graphs of
(a)
the velocity of the ball plotted against time,
velocity
time
(4)
(b)
the acceleration of the ball plotted against time.
acceleration
time
(1)
Q
P
(c)
50°
The ball is then thrown at an angle to the horizontal and follows the trajectory shown
in the diagram.
Mark on the diagram the directions of
(i)
the acceleration vector at P,
(ii)
the acceleration vector at Q,
(iii)
the momentum vector at P,
(iv)
the momentum vector at Q.
(4)
(Total 9 marks)
4.
A mass of 1500kg is attached to a cable and raised vertically by a crane. The graph shows
how its velocity varies with time.
3.0
velocity/ms–1
2.0
1.0
A
0
(a)
B C
1.0
D E
2.0
3.0
F
4.0 time/s 5.0
Determine
(i)
the initial uniform acceleration of the mass, ...................................................
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(ii)
the distance travelled by the mass while it is accelerating upwards.
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(3)
(b)
(i)
Calculate the tension in the cable in the intervals
AB, ...................................................................................................................
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...........................................................................................................................
CD. ...................................................................................................................
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(ii)
State in which interval of the motion the tension in the cable is least.
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(4)
(c)
Calculate the power supplied by the crane during the interval CD.
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(2)
(Total 9 marks)
5.
The graph shows how the vertical speed of a parachutist changes with time during the first
20 s of his jump. To avoid air turbulence caused by the aircraft, he waits a short time after
jumping before pulling the cord to release his parachute.
50
C
vertical
speed/ms –1 40
B
30
D
20
10
A
0
0
(a)
2
4
6
8
10
12
time/s
14
16
18
Regions A, B and C of the graph show the speed before the parachute has opened.
With reference to the forces acting on the parachutist, explain why the graph has this
shape in the region marked
(i)
A, ......................................................................................................................
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...........................................................................................................................
(ii)
B, .......................................................................................................................
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(iii) C. ......................................................................................................................
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20
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(6)
(b)
Calculate the maximum deceleration of the parachutist in the region of the graph
marked D, which shows how the speed changes just after the parachute has opened.
Show your method clearly,
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(2)
(c)
Use the graph to find the total vertical distance fallen by the parachutist in the first 10
s of the jump. Show your method clearly.
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(4)
(d)
During his descent, the parachutist drifts sideways in the wind and hits the ground
with a vertical speed of 5.0 m s–1 and a horizontal speed of 3.0 m s–1. Find
(i)
the resultant speed with which he hits the ground,
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(ii)
the angle his resultant velocity makes with the vertical.
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(2)
(Total 14 marks)
6.
(a)
The diagram shows an object at rest at the top of a straight slope which makes a fixed
angle with the horizontal.
P
Q
(i)
The object is released and slides down the slope from P to Q with negligible
friction. Assume that the potential energy is zero at Q. Sketch a graph showing
the potential energy at different distances measured along the slope, and label it
A. On the same set of axes, sketch a second graph showing the kinetic energy of
the object at different distances along the slope and label it B.
energy
0
P
Q
distance along slope
(ii)
Using the same axes as in part (i), sketch a third graph, labelled C, showing the
kinetic energy at different distances along the slope when there is a constant
frictional force between the object and the surface.
(iii)
Use your knowledge of the principle of conservation of energy to explain the
important features of the graphs you have drawn in part (i) and part (ii).
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(6)
(b)
In a theme park ride, a cage containing passengers falls freely a distance of 30 m from
A to B and travels in a circular arc of radius 20m from B to C. Assume that friction is
negligible between A and C. Brakes are applied at C after which the cage with its
passengers travels 60m along an upward sloping ramp and comes to rest at D. The
track, together with relevant distances, is shown in the diagram. CD makes an angle of
20° with the horizontal
passenger cage
A
30 m
B
20 m
radius
60 m
C
(i)
D
20°
Calculate the speed of the cage at C
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(ii)
Calculate the force required on a passenger of mass 80 kg for circular motion at
C and state the direction of this force.
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(iii)
If the mass of the cage and passengers is 620 kg, determine the gain in
gravitational potential energy in travelling from C to D.
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(iv)
Calculate the average resistive force exerted by the brakes between C and D
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(9) (Total 15 marks)
7.
The diagram shows a uniform bar, AB, which is 1.6 m long and freely pivoted to a wall at B.
The bar is maintained horizontal and in equilibrium by an angled string which passes over a
pulley and which carries a mass of 2.0 kg at its free end.
1.6 m
30°
A
B
2.0 kg
(a)
The pulley is positioned as shown in the diagram, with the string at 30° to the vertical.
(i)
Calculate the tension, T, in the string.
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(ii)
Show that the mass of the bar is approximately 3.5 kg.
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(4)
(b)
A mass, M, is attached to the bar at a point 0.40 m from A. The pulley is moved
horizontally to change the angle made by the string to the vertical, and to maintain the
rod
horizontal and in equilibrium.
Determine the largest value of the mass, M, for which this equilibrium can be
maintained.
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(4)
(Total 8 marks)
8.
An athlete is analysing his shot putting technique so as to improve his performance. He finds
that the optimum performance is achieved when the angle which his leg makes with the
ground is 57° immediately before releasing the shot. The maximum force he can exert on the
ground is 650 N at an angle of 57° to the ground.
57°
(a)
Draw and label arrows on the diagram above to represent
(i)
T, the force the foot exerts on the ground,
(ii)
N, the normal reaction of the ground on the foot,
(iii)
F, the frictional force of the ground on the foot.
(3)
(b)
Calculate the magnitude of
(i)
the frictional force F,
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(ii)
the normal reaction of the ground N.
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(2)
(Total 5 marks)
9.
A solid iron ball of mass 890 kg is used on a demolition site. It hangs from the jib of a crane
suspended by a steel rope. The distance from the point of suspension to the centre of mass of
the ball is 15 m.
(a)
Calculate the tension in the rope when the mass hangs vertically and stationary.
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(2)
(b)
The iron ball is pulled back by a horizontal chain so that the suspension rope makes an
angle of 30° with the vertical. Calculate the new tension in the suspension rope.
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(2)
(c)
The ball is now released from rest and hits a brick wall just as it passes through the
vertical position. It can be assumed that the ball is brought to rest by the impact with
the wall in 0.2s.
Calculate
(i) the vertical height through which the ball falls,
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(ii)
the speed of the ball just before impact,
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(iii)
the average force exerted by the ball on the wall.
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(5) (Total 9 marks)
10.
F
The diagram shows
stationary kite. The
the air exerts on the
the forces acting on a
force F is the force that
kite.
30º
tension, T, in string
weight
(a) Show on the diagram how force F can be resolved into horizontal and vertical components.
(2)
(b)
The magnitude of the tension, T, is 25 N.
Calculate
(i)
the horizontal component of the tension,
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(ii)
the vertical component of the tension.
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(2)
(c)
(i)
Calculate the magnitude of the vertical component of F when the weight of the
kite is 2.5 N.
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(ii)
State the magnitude of the horizontal component of F.
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(iii)
Hence calculate the magnitude of F.
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(4) (Total 8 marks)
11.
(a)
A cricketer throws a ball vertically upwards so that the ball leaves his hands at a speed
of 25 m s–1. If air resistance can be neglected, calculate
(i)
the maximum height reached by the ball,
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(ii)
the time taken to reach maximum height,
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(iii)
the speed of the ball when it is at 50% of the maximum height.
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(4)
(b)
When catching the ball, the cricketer moves his hands for a short distance in the
direction of travel of the ball as it makes contact with his hands. Explain why this
technique results in less force being exerted on the cricketer’s hands.
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(2) (Total 6 marks)
12.
A heavy sledge is pulled across snowfields. The diagram shows the direction of the force F
exerted on the sledge. Once the sledge is moving, the average horizontal force needed to
keep it moving at a steady speed over level ground is 300 N.
F
20º
(a)
Calculate the force F needed to produce a horizontal component of 300 N on the
sledge.
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.....................................................................................................................................
(1)
(b)
(i)
Explain why the work done in pulling the sledge cannot be calculated by
multiplying F by the distance the sledge is pulled.
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(ii)
Calculate the work done in pulling the sledge a distance of 8.0 km over level
ground.
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(iii)
Calculate the average power used to pull the sledge 8.0 km in 5.0 hours.
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(6)
(c)
The same average power is maintained when pulling the sledge uphill. Explain in
terms of energy transformations why it would take longer than 5.0 hours to cover
8.0 km uphill.
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(3) (Total 10 marks)
13.
(a)
The torque of a couple is given by
torque = Fs.
(i)
With the aid of a diagram explain what is meant by a couple. Label F and s on
your diagram.
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(ii)
State the unit for the torque of a couple.
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(4)
(b)
The see-saw shown in the diagram consists of a uniform beam freely pivoted at the
centre of the beam. Two children sit opposite each other so that the see-saw is in
equilibrium.
Explain why
(i)
the see-saw is in equilibrium,
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(ii)
the weight of the beam does not affect equilibrium.
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(3)
(c)
The diagram shows the see-saw with three children of weights 400N, 250N and 200N
sitting so that the see-saw is in equilibrium.
d
1.0 m
400 N
0.50 m
200 N
250 N
Calculate the distance, d.
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(2) (Total 9 marks)
14.
The diagram shows a car travelling at a constant velocity along a horizontal road.
(a)
(i)
Draw and label arrows on the diagram representing the forces acting on the car.
(ii)
Referring to Newton’s Laws of motion, explain why the car is travelling at
constant velocity.
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(5)
(b)
The car has an effective power output of 18 kW and is travelling at a constant velocity
of 10 m s–1. Show that the total resistive force acting is 1800 N.
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(1)
(c)
The total resistive force consists of two components. One of these is a constant
frictional force of 250 N and the other is the force of air resistance, which is
proportional to the square of the car’s speed.
Calculate
(i)
the force of air resistance when the car is travelling at 10 m s–1,
...........................................................................................................................
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(ii)
the force of air resistance when the car is travelling at 20 m s–1,
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(iii)
the effective output power of the car required to maintain a constant speed of
20 m s–1 in a horizontal road.
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(4) (Total 10 marks)
15.
A public house sign is fixed to a vertical wall as shown in the diagram.
40°
wall
wire
hinge
metal bar
sign
A uniform metal bar 0.75 m long is fixed to the wall by a hinged joint that allows free
movement in the vertical plane only. The wire is fixed to the wall directly above the hinge
and to the free end of the horizontal metal bar. The wire makes an angle of 40° with the wall.
A single support holds the sign and is mounted at the mid point of the metal bar so that the
weight of the sign acts through that point.
(a)
(i)
Draw on the diagram three arrows showing the forces acting on the metal bar,
given that the system is in equilibrium. Label the arrows A, B and C.
(ii)
State the origin of the forces.
A .......................................................................................................................
B .......................................................................................................................
C .......................................................................................................................
(b)
The combined mass of the metal bar and sign is 12 kg and the mass of the wire is
negligible. By taking moments about the hinged end of the bar, or otherwise, calculate
the tension in the wire.
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(4) (Total 9 marks)
16.
A student carried out an experiment to determine the terminal speed of various ball bearings
as they fell through a viscous liquid. She did this by timing their fall between two marks, P
and Q, which were 850 mm apart on a vertical glass tube.
ball
bearing
P
850 mm
Q
You may be awarded marks for the quality of written communication in your answer.
(a)
(i)
Describe the motion of a ball bearing after being released from rest at the
surface.
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(ii)
In terms of the forces acting, explain why a ball bearing reaches a terminal
speed under these conditions.
(5)
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(5)
(b)
The student’s results are shown in columns A and B. Complete column C.
column A
column B
column C
column D
column E
radius of ball bearing
r / mm
time of fall / s
(through 850 mm)
terminal speed
 / mm s–1
log10(r / mm)
log10( / mm s–
1
)
1.62
32.0
0.210
1.98
21.4
0.297
2.21
17.2
0.344
2.73
11.3
0.436
3.40
7.2
0.531
4.12
4.9
0.615
(2)
(c)
The relationship between  and r is known to be of the form
 = krn,
where n and k are constants.
(i)
Enter the corresponding values for log10( / mm s–1) in column E of the table in
part (b).
(ii)
Plot a graph of log10( / mm s–1) on the y-axis, against log10(r / mm) on the xaxis.
(Allow one sheet of graph paper)
(4)
(d)
Use your graph to determine
(i)
the constant n,
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(ii)
the constant k.
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(5)
(Total 16 marks)
17.
A fairground ride ends with the car moving up a ramp at a slope of 30° to the horizontal as
shown in the figure below.
ramp
30°
(a)
The car and its passengers have a total weight of 7.2 × 103 N. Show that the
component of the weight parallel to the ramp is 3.6 × 103 N.
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(b)
(1)
Calculate the deceleration of the car assuming the only force causing the car to
decelerate is that calculated in part (a).
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(c)
The car enters at the bottom of the ramp at 18 m s–1. Calculate the minimum length of
the ramp for the car to stop before it reaches the end. The length of the car should be
neglected.
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(2)
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(d)
(2)
Explain why the stopping distance is, in practice, shorter than the value calculated in
part (c).
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(2)
(Total 7 marks)
18.
(a)
Define the moment of a force.
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................................................................................................................................…
(2)
(b)
The diagram shows a uniform diving board of weight, W, that is fixed at A. The diving
board is supported by a cylinder at C, that exerts an upward force, P, on the board.
P
A
B
C
W
(i)
By considering moments about A, explain why the force P must be greater than
the weight of the board, W.
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(ii)
State and explain what would be the effect on the force P of a girl walking
along the board from A to B.
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(4)
(Total 6 marks)
19.
While investigating projectile motion, a student used stroboscopic photography to determine
the position of a steel ball at regular intervals as it fell under gravity. With the stroboscope
flashing 20 times per second, the ball was released from rest at the top of an inclined track,
and left the foot of the track at P, as shown in the diagram below.
straight ramp
P
curved path
y
x
ball at time t
after passing P
For each of the images on the photograph, the student calculated the horizontal distance, x,
and the vertical distance, y, covered by the ball at time t after passing P. Both distances were
measured from point P. He recorded his results for the distances x and y in the table.
(a)
image
x/cm
y/cm
t/s
1
11.6
9.3
0.05
2
22.0
21.0
0.10
3
32.4
35.0
0.15
4
44.2
51.8
0.20
5
54.8
71.0
0.25
6
66.0
92.2
0.30
(y/t)/cm s–1
Using two sets of measurements from the table, calculate the horizontal component of
velocity of the ball. Give a reason for your choice of measurements.
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(2)
(b)
The student worked out that the variables y and t in the experiment could be
represented by
y
= u + kt
t
where u and k are constants.
(i)
Complete the table above.
(ii)
Use the data in the table to plot a suitable graph to confirm the equation.
(Allow one sheet of graph paper)
(iii)
Use your graph to find the values of u and k.
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(9)
(c)
State the physical significance of
u ..............................................................................................................................
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k ..............................................................................................................................
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(2)
(d)
Calculate the magnitude of the velocity of the ball at point P.
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(2)
(Total 15 marks)
20.
(a)
What do you understand by the principle of conservation of energy?
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.....................................................................................................................................
(2)
(b)
(i)
Explain how the principle of conservation of energy applies to a man sliding
from rest down a vertical pole, if there is a constant resistive force opposing the
motion.
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...........................................................................................................................
...........................................................................................................................
(ii)
The man starts sliding at time t = 0 and reaches the ground at time t. Consider
each form of energy that varies with time and sketch graphs on the axes to show
these variations. Include a graph of the total energy involved and indicate the
effect of the resistive force. Name each energy graph drawn and point out
important features.
energy
time
(5)
(c)
A domestic kettle is marked 250V, 2.3 kW and the manufacturer claims that it will
heat a pint of cold water to boiling point in 94s.
specific heat capacity of water = 4.2 × 103 J kg–1 K–1
specific latent heat of vaporisation of water = 2.3 × 106 J kg–1 K–1
density of water = 1000 kg m–3
1 pint = 5.7 × 10–4 m3
(i)
Test this claim by calculation and state any simplifying assumptions that you
make.
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(ii)
If the kettle is left switched on after it boils, how long will it take to boil away
half a pint of water, measured from when it first boils?
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(5)
(Total 12 marks)
Waves
21.
The diagram shows two identical loudspeakers, A and B, placed 0.75 m apart. Each
loudspeaker emits sound of frequency 2000 Hz.
not to scale
A
E
0.75m
C
D
B
5.0m
Point C is on a line midway between the speakers and 5.0 m away from the line joining the
speakers. A listener at C hears a maximum intensity of sound. If the listener then moves from
C to E or D, the sound intensity heard decreases to a minimum. Further movement in the
same direction results in the repeated increase and decrease in the sound intensity.
speed of sound in air = 330 m s–1
(a)
Explain why the sound intensity
(i) is a maximum at C,
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...........................................................................................................................
...........................................................................................................................
(ii)
is a minimum at D or E.
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(4)
(b)
Calculate
(i) the wavelength of the sound,
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...........................................................................................................................
(ii)
the distance CE.
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(4)
(Total 8 marks)
22.
Stationary waves in air can be demonstrated using a long horizontal tube which contains fine
powder. With a loudspeaker connected to a signal generator positioned at one end of the
tube, stationary waves are formed by reflection of waves from the ends of the tube. The
diagram shows part of the tube in such an arrangement. The powder forms heaps at nodes.
Speed of sound waves in air = 340 m s–1
P
Q
0.27 m
(a)
Determine
(i)
the wavelength of the waves,
...........................................................................................................................
(ii)
the frequency of vibration of the loudspeaker.
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...........................................................................................................................
...........................................................................................................................
(2)
(b)
Distinguish between longitudinal waves and transverse waves and state which type of
wave is being generated in the tube.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(c)
P and Q are two points in the tube. Compare the motion of air particles at P with the
motion of air particles at Q with reference to
(i)
frequency,
...........................................................................................................................
...........................................................................................................................
(ii)
amplitude,
...........................................................................................................................
...........................................................................................................................
(iii)
phase.
...........................................................................................................................
...........................................................................................................................
(3) (Total 8 marks)
23.
(a)
Optical interference effects can be observed by the superposition of light waves from
coherent sources. Explain the meanings of the words in italics.
superposition ..............................................................................................................
....................................................................................................................................
coherent .....................................................................................................................
....................................................................................................................................
(2)
(b)
A laser, emitting light, is used to illuminate two parallel slits, giving coherent sources.
(i)
Interference takes place where light beams from the two slits overlap.
With the aid of a diagram, explain how this overlap is produced.
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
(ii)
State and explain what two changes you would expect in the fringe system if
each of the slits were made narrower, but their separation were kept the same.
change 1 ...........................................................................................................
..........................................................................................................................
..........................................................................................................................
change 2 ...........................................................................................................
..........................................................................................................................
..........................................................................................................................
(4)
(Total 6 marks)
24.
(a)
State what is meant by coherent sources of light.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
screen
slit
monochromatic
source
slits
S1
S
S2
Figure 1
Young’s fringes are produced on the screen from the monochromatic source by the
arrangement shown in Figure 1.
You may be awarded marks for the quality of written communication in your answers.
(i)
Explain why slit S should be narrow.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
Why do slits S1 and S2 act as coherent sources?
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(c)
The pattern on the screen may be represented as a graph of intensity against position
on the screen. The central fringe is shown on the graph in Figure 2. Complete this
graph to represent the rest of the pattern by drawing on Figure 2.
intensity
position on the screen
centre of pattern
Figure 2
(2)
(Total 8 marks)
25.
Explain the differences between an undamped progressive transverse wave and a stationary
transverse wave, in terms of (i) amplitude, (ii) phase and (iii) energy transfer.
(i)
amplitude
progressive wave ........................................................................................................
.....................................................................................................................................
stationary wave ...........................................................................................................
.....................................................................................................................................
(ii)
phase
progressive wave ........................................................................................................
.....................................................................................................................................
stationary wave ...........................................................................................................
.....................................................................................................................................
(iii)
energy transfer
progressive wave ........................................................................................................
.....................................................................................................................................
stationary wave ...........................................................................................................
.....................................................................................................................................
(Total 5 marks)
26.
screen
narrow slit
laser
Figure 1
Red light from a laser is passed through a single narrow slit, as shown in Figure 1. A pattern
of bright and dark regions can be observed on the screen which is placed several metres
beyond the slit.
(a)
The pattern on the screen may be represented as a graph of intensity against distance
along the screen. The graph has been started in outline in Figure 2. The central bright
region is already shown. Complete this graph to represent the rest of the pattern by
drawing on Figure 2.
intensity
distance along screen
centre of pattern
Figure 2
(4)
(b)
State the effect on the pattern if each of the following changes is made separately.
(i)
The width of the narrow slit is reduced.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
With the original slit width, the intense red source is replaced with an intense
source of green light.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(Total 7 marks)
27.
The diagram below shows a section of a diffraction grating. Monochromatic light of
wavelength  is incident normally on its surface. Light waves diffracted through angle 
form the second order image after passing through a converging lens (not shown). A, B and
C are adjacent slits on the grating.
d
d
C
B
E

D
A
(a)
(i)
State the phase difference between the waves at A and D.
...........................................................................................................................
(ii)
State the path length between C and E in terms of .
...........................................................................................................................
(iii)
Use your results to show that, for the second order image,
2 = d sin ,
where d is the distance between adjacent slits.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(b)
A diffraction grating has 4.5 × 105 lines m–1. It is being used to investigate the line
spectrum of hydrogen, which contains a visible blue-green line of wavelength 486 nm.
Determine the highest order diffracted image that could be produced for this spectral
line by this grating.
................................................................................................................................…
................................................................................................................................…
................................................................................................................................…
................................................................................................................................…
................................................................................................................................…
................................................................................................................................…
(2)
(Total 5 marks)
28.
(a)
A helium-neon laser produces monochromatic light of wavelength 632.8 nm which
falls normally on a diffraction grating. A first order maximum is produced at an angle
of 18.5° measured from the normal to the grating.
Calculate
(i)
the number of lines per metre on the grating,
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
(ii)
the highest order which is observable.
..........................................................................................................................
..........................................................................................................................
..........................................................................................................................
(6)
(b)
When the grating is used with a different monochromatic source, the first order
maximum is observed at an angle of 17.2°
Calculate the wavelength of this second source.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 8 marks)
29.
Two prisms made from different glass are placed in perfect contact to form a rectangular
block surrounded by air as shown. Medium 1 has a smaller refractive index than medium 2.
medium 2
air
n da
bou
ry
medium 1
incident ray
air
70º
(a)
A ray of light in air is incident normally on medium 1 as shown. At the boundary
between medium 1 and medium 2 some light is transmitted and the remainder
reflected.
(i)
Sketch, without calculation, the path followed by the refracted ray as it enters
medium 2 and then emerges into the air.
(ii)
Sketch, without calculation, the path followed by the reflected ray showing it
emerging from medium 1 into the air.
(4)
(b)
The refractive index of medium 1 is 1.40 and that of medium 2 is 1.60.
(i)
Give the angle of incidence at the boundary between medium 1 and medium 2.
...........................................................................................................................
(ii)
Calculate the angle of refraction at this boundary.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(c)
Calculate the critical angle for a ray passing from medium 2 into the air.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(Total 10 marks)
30.
(a)
A double slit interference experiment is set up in a laboratory using a source of yellow
monochromatic light of wavelength 5.86 × 10–7 m. The separation of the two vertical
parallel slits is 0.36 mm and the distance from the slits to the plane where the fringes
are observed is 1.80 m.
(i)
Describe the appearance of the fringes.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(ii)
Calculate the fringe separation, and also the angle between the middle of the
central fringe and the middle of the second bright fringe.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(iii)
Explain why more fringes will be seen if each of the slits is made narrower,
assuming that no other changes are made.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(b)
(8)
Light of wavelength 5.86 × 10–7 Tim falls at right angles on a diffraction grating
which has 400 lines per mm.
(i)
Calculate the angle between the straight through image and the first order
image.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(ii)
Determine the highest order image which can be seen with this arrangement.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(5)
(c)
Give two reasons why the diffraction grating arrangement is more suitable for the
accurate measurement of the wavelength of light than the two-slit interference
arrangement.
..................................................................................................................................
..................................................................................................................................
..................................................................................................................................
(2)
(Total 15 marks)
31.
The graph shows the variation of displacement of the particles with distance along a
stationary transverse wave at time t = 0 when the displacement of the particles is greatest.
The period of the vibrations causing the wave is 0.040 s.
displacement
/mm
20
Z
W
0
20
60
40
20
(a)
(b)
100
80
120
distance/mm
V
Using the same axes,
(i)
draw the appearance of the wave at t = 0.010 s, labelling this graph B,
(ii)
draw the appearance of the wave at t = 0.020 s, labelling this graph C,
(iii)
show an antinode labelled A and a node labelled N.
(i)
Describe the motion of the particle at V, giving its frequency and amplitude.
(3)
.........................................................................................................................
.........................................................................................................................
(ii)
State the amplitude of the particle at W and its phase relations with the particle
at V and the particle at Z.
.........................................................................................................................
.........................................................................................................................
.........................................................................................................................
(6) (Total 9 marks)
32.
metal plate
detector
movement
microwave
transmitter
A microwave transmitter directs waves towards a metal plate. When a microwave detector is
moved along a line normal to the transmitter and the plate, it passes through a sequence of
equally spaced maxima and minima of intensity.
(a)
Explain how these maxima and minima are formed.
You may be awarded marks for the quality of written communication in your answer.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(b)
The detector is placed at a position where the intensity is a minimum. When it is
moved a distance of 144 mm it passes through nine maxima and reaches the ninth
minimum from the starting point.
Calculate
(i)
the wavelength of the microwaves,
...........................................................................................................................
...........................................................................................................................
(4)
(ii)
the frequency of the microwave transmitter.
...........................................................................................................................
...........................................................................................................................
(3)
(Total 7 marks)
33.
The diagram shows a cross-section of one wall and part of the base of an empty fish tank,
viewed from the side. It is made from glass of refractive index 1.5. A ray of light travelling
in air is incident on the base at an angle of 35 as shown.
wall
inside the tank
glass tank

base
35°
(a)
Calculate the angle .
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
(i)
Calculate the critical angle for the glass-air interface.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
Hence, draw on the diagram the continuation of the path of the ray through the
glass wall and out into the air. Mark in the values of all angles of incidence,
refraction and reflection.
(6)
(Total 8 marks)
34.
Red light of wavelength 7.00 × 10–7 m, incident normally on a diffraction grating, gave a
first order maximum at an angle of 75°.
(a)
Calculate the spacing of the diffraction grating.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(1)
(b)
Calculate the angle at which the first order maximum for violet light of wavelength
4.50 × 10–7 m would be observed.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(1)
(c)
At what angle or angles would a detector receive radiation which is of wavelength
7.50 × 10–7 m transmitted by the grating? Explain your answer.
....................................................................................................................................
....................................................................................................................................
....................................................................................................................................
(2)
(Total 4 marks)
35.
(a) State Snell’s law of refraction of light and explain the conditions under which the law
applies.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(b)
The diagram shows a glass pentaprism as used in the viewfinder of some cameras.
Light enters face AB and leaves face BC. The faces AE, ED and DC are silvered and
the refractive index of the glass is 1.52.
E
D
A
112.5°
112.5°
B
C
(i)
On the diagram draw the path of the incident ray from face AB to CD.
(ii)
State why you have drawn the ray in this direction.
...........................................................................................................................
...........................................................................................................................
(2)
(c)
Explain, with the aid of a calculation, why the face CD needs to be silvered if the ray
shown is not to be refracted at face CD.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(d)
On the diagram, continue the ray until it leaves the prism.
(1)
(Total 9 marks)
36.
(a)
white screen
not to scale
grating
laser
n=5
0.860 m
n=4
0.687 m
n=3
0.499 m
n=2
0.316 m
n=1
0.173 m
central
maximum
2.0 m
figure 1
In a laboratory experiment, monochromatic light of wavelength 633 nm from a laser is
incident normal to a diffraction grating. The diffracted waves are received on a white
screen which is parallel to the plane of the grating and 2.0 m from it. Figure 1 shows
the positions of the diffraction maxima with distances measured from the central
maximum.
By means of a graphical method, use all these measurements to determine a mean
value for the number of rulings per unit length of the grating.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(Allow one sheet of graph paper)
(6)
(b)
Describe and explain the effect, if any, on the appearance of the diffraction pattern of
(i)
using a grating which has more rulings per unit length,
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
using a laser source which has a shorter wavelength,
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii)
increasing the distance between the grating and the screen.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(6)
(c)
Figure 2, below, shows the diffracted waves
from four narrow slits of a diffraction grating
similar to the one described in part (a).
The slit separation AB = BC = CD = DE = d
Q
A
and EQ is a line drawn at a tangent to several
wavefronts and which makes an angle  with
the grating.
figure 2
(i)
Explain why the waves advancing perpendicular to EQ will reinforce if
superposed.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
Show that this will happen when sin  =

.
d
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(Total 15 marks)
37.
The diagram for this question is drawn to scale and 1 mm on the diagram represents an
actual distance of 5 mm.
Y
R
S1
Q
P
S2
Y'
S1 and S2 are identical coherent transmitters emitting, in phase, microwaves with a
wavelength of 25 mm. They are positioned 250mm apart on a horizontal surface and a
detector can be placed anywhere along the line YY which is in the same plane as the
transmitters and parallel to the line containing S1 and S2.
(a)
Explain what is meant by coherent.
.....................................................................................................................................
.....................................................................................................................................
(2)
(b)
By making measurements on the diagram and using the scale, determine the number
of wavelengths in the path
(i)
S1R,
...........................................................................................................................
...........................................................................................................................
(ii)
S2R.
...........................................................................................................................
...........................................................................................................................
(iii)
Use your answers to (i) and (ii) to determine whether or not you expect the
signal received by a detector placed at R to be a maximum. Explain your
answer.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(5)
(c)
Describe how you would expect the signal strength to vary as the detector is moved
from R to P via Q.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(d)
Calculate the frequency of the microwaves.
.....................................................................................................................................
.....................................................................................................................................
(1)
(Total 10 marks)
38.
A small intense light source is 1.5 m below the surface of the water in a large swimming
pool, as shown in the diagram.
X
Y
30°
Z
60°
light source
(i)
Complete the paths of rays from the light source which strike the water surface at X, Y
and Z.
(ii)
Calculate the diameter of the disc through which light emerges from the surface of the
water.
speed of light in water = 2.25 × 108 m s–1
speed of light in air = 3.00 × 108 m s–1
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(Total 7 marks)
Materials
39.
(a)
The Young modulus is defined as the ratio of tensile stress to tensile strain.
Explain what is meant by each of the terms in italics.
tensile stress ...............................................................................................................
.....................................................................................................................................
.....................................................................................................................................
tensile strain ...............................................................................................................
.....................................................................................................................................
(3)
(b)
A long wire is suspended vertically and a load of 10 N is attached to its lower end. The
extension of the wire is measured accurately. In order to obtain a value for the Young
modulus of the material of the wire, two more quantities must be measured. State what
these are and in each case indicate how an accurate measurement might be made.
quantity 1 ....................................................................................................................
method of measurement .............................................................................................
.....................................................................................................................................
quantity 2 ....................................................................................................................
method of measurement .............................................................................................
.....................................................................................................................................
(c)
(4)
Sketch below a graph showing how stress and strain are related for a ductile substance
and label important features.
stress
strain
(2)
(Total 9 marks)
40.
The diagram below shows a liquid droplet placed on a cube of glass. A ray of light from air,
incident normally on to the droplet, continues in a straight line and is refracted at the liquid
to glass boundary as shown.
refractive index of the glass = 1.45
air
29.2°
liquid
glass
26.6°
(a)
Calculate the speed of light
(i)
in the glass,
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
in the liquid droplet.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(b)
Calculate the refractive index of the liquid.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(c)
On the diagram above, complete the path of the ray showing it emerge from the glass
cube into the air.
No further calculations are required.
(2)
(Total 7 marks)
41.
The diagram shows tensile stress-strain curves for three different materials X, Y and Z.
stress
X
Y
Z
strain
For each material named below, state which curve is typical of the material, giving the
reasoning behind your choice.
(a)
copper ..................................
reasoning ....................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(b)
glass ....................................
reasoning ....................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(c)
hard steel ..............................
reasoning ....................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(Total 6 marks)
42.
(a)
Describe an experiment to determine the Young modulus for a material in the form of
a wire. Draw a labelled diagram and explain how you would make the necessary
measurements. Show how you would use your measurements to calculate the result.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(8)
(b)
rigid support
F
aluminium
copper
A copper wire and an aluminium wire, each of diameter 0.72 mm, are joined end to
end as shown in the diagram with the aluminium wire fixed at right angles to a rigid
support. A steadily increasing force, F, is applied. Use data from the Data Sheet to
(i)
explain which wire will yield,
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
determine the value of F at which yield should occur.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(Total 12 marks)
43.
As part of a quality check, a manufacturer of fishing line subjects a sample to a tensile test.
The sample of line is 2.0 m long and is of constant circular cross-section of diameter
0.50mm. Hooke’s law is obeyed up to the point when the line has been extended by 52mm at
a tensile stress of 1.8 × 108 Pa.
The maximum load the line can support before breaking is 45 N at an extension of 88 mm.
(a)
Calculate
(i)
the value of the Young modulus,
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
the breaking stress (assuming the cross-sectional area remains constant),
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii)
the breaking strain.
...........................................................................................................................
(5)
(b)
Sketch a graph on the axes below to show how you expect the tensile stress to vary
with strain. Mark the value of stress and corresponding strain at
(i)
the limit of Hooke’s law,
(ii)
the breaking point.
stress
strain
(4) (Total 9 marks)
44.
(a)
(i)
Describe the behaviour of a wire that obeys Hooke’s law.
...........................................................................................................................
...........................................................................................................................
(ii)
Explain what is meant by the elastic limit of the wire.
...........................................................................................................................
...........................................................................................................................
(iii)
Define the Young modulus of a material and state the unit in which it is
measured.
...........................................................................................................................
...........................................................................................................................
(b)
A student is required to carry out an experiment and draw a suitable graph in order to
obtain a value for the Young modulus of a material in the form of a wire.
A long, uniform wire is suspended vertically and a weight, sufficient to make the wire
taut, is fixed to the free end. The student increases the load gradually by adding known
weights. As each weight is added, the extension of the wire is measured accurately.
(i)
What other quantities must be measured before the value of the Young modulus
can be obtained?
(5)
...........................................................................................................................
...........................................................................................................................
(ii)
Explain how the student may obtain a value of the Young modulus.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii) How would a value for the elastic energy stored in the wire be found from the
results?
...........................................................................................................................
...........................................................................................................................
(6) (Total 11 marks)
45.
A student carries out an experiment to investigate how the extension of a steel wire varies
with an increasing tensile force. The results of the experiment are shown plotted on the
graph. The initial length of the wire is 0.50m and its diameter is 0.80 mm. The wire breaks at
an extension of 1.46 mm.
force/N
110
100
90
80
70
60
50
40
30
20
10
0
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
extension/mm
Use information from the graph to determine
the Young modulus for the material,
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
an estimate of the yield stress for the material.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
(Total 6 marks)
46.
An aerial system consists of a horizontal copper wire of length 38 m supported between two
masts, as shown in the figure below. The wire transmits electromagnetic waves when an
alternating potential is applied to it at one end.
38 m of copper wire
14.0 m
12.0
P
mast
(a)
Q
mast
The wavelength of the radiation transmitted from the wire is twice the length of the
copper wire. Calculate the frequency of the transmitted radiation.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(1)
(b)
The ends of the copper wire are fixed to masts of height 12.0 m. The masts are held in
a vertical position by cables, labelled P and Q, as shown in the figure above.
(i)
P has a length of 14.0 m and the tension in it is 110 N. Calculate the tension in
the copper wire.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii)
The copper wire has a diameter of 4.0 mm. Calculate the stress in the copper
wire.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii)
Discuss whether the wire is in danger of breaking if it is stretched further due to
movement of the top of the masts in strong winds.
breaking stress of copper = 3.0 × 108 Pa
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(7)
(Total 8 marks)
Unit 2 Mechanics, Materials and Waves
Answers
1.
(a)
(b)
scalars have magnitude (or size) (1)
vectors have magnitude and direction (1)
(i)
s = t (1)
s = 100 ×
(ii)
2
3
=5 km (1)
60
1.59 (1) km (or other correct unit) (1)
4
[6]
FB (1)
2.
(a)
2
FA (1)
(b)
(i)
taking moments (about A) (1)
(400 × 4.0) + (300 × 2) = FB × 1.6 (1)
2200
= FB so FB = 1375(N) (1)
1.6
(ii)
FA = 1375 – 700 = 675 (1) N (1) allow e.c.f. from FB
(no marks if weight of board not used)
max 4
[6]
3.
accept mirror image for (a) and (b)
(a)
(b)
velocity
1
acceleration
time
straight line sloping up (1)
sudden change to negative velocity (1)
time
constant value shown (1)
smaller negative velocity (1)
same gradient as positive line (1)
(c)
(i)
vertically down at P (1)
(ii)
vertically down at Q (1)
(iii)
along tangent at P (1)
(iv)
along tangent at Q (1)
4
4
[9]
4.
(a)
(b)
2 .1
= 3.0 ms–2 (1)
0 .7
(i)
gradient =
(ii)
distance is area under graph (to t = 0.1 s)
1
or
× 0.7 × 2.1  2.1  2.5  0.3 (1) = 1.4(2) m (1)
2
2


(i)
3
T – mg = ma [or T = 1500(9.8+3.0)] (1)
= 1.9 × 104 N (1)
T = mg = l.5 × 104 N (1)
(ii)
(c)
EF (1)
4
power = F or l.5 × 104 × 2.5 (1)
= 3.7[3.8] × 104 W (1)
2
[9]
5.
(a)
(i)
region A: uniform acceleration
(or (free-fall) acceleration = g( = 9.8(i) m s–2))
force acting on parachutist is entirely his weight
(or other forces are very small) (1)
(ii)
region B: speed is still increasing
acceleration is decreasing (2)
(any two)
because frictional (drag) forces become significant
(at higher speeds)
(iii)
region C: uniform speed (50 m s–1)
because resultant force on parachutist is zero (2) (any two)
weight balanced exactly by resistive force upwards
6
QWC
(b)
(c)
(d)
deceleration is gradient of the graph (at t = 13s) (1)
(e.g. 20/1 or 40/2) = 20 m s–2 (1)
2
distance = area under graph (1)
suitable method used to determine area (e.g. counting squares) (1)
with a suitable scaling factor (e.g. area of each square = 5 m2) (1)
distance=335m (±15m) (1)
4
(i)
speed = (5.02 + 3.02) = 5.8 m s–1 (1)
(ii)
tan  =
3
5
gives  = 31°(1)
2
[14]
6.
(a)
(i) and (ii)
energy
A (1)
B same height as A and above C
C(1)
Q distance along slope
(iii) A + B = constant (1)
loss in potential energy = gain in kinetic energy for A and B
[or potential energy at P = kinetic energy at Q for A and B] (1)
reason for C being below B e.g. transfer to heat
[or work done against friction] (1)
(b)
(i)
clear reference to energy c(= 2 gh ) =
–1
= 31(.3)m s (1)
(ii)
(iii)
2


80  (31.3) 2
F   m c  =
(1)


20
r


= 3.9(2) × 103 N
towards centre of circle (1)
gain in gravitational potential energy
2  9.8  50 (1)
6
( = mgh sin ) = 620 × 9.8 × 60 × sin 20° (1)
= 1.25 × 105 J
(iv)
620 × 9.8 × 50 = (F × 60) (1) +1.25 ×105 (1)
F = 3000N (1)
alternative (iv)
calculation of acceleration = (–)8.0 m s–2 (1)
use of F + mg sin  = ma (1)
F = 3000N (1)
max 9
[15]
7.
(a)
(b)
(i)
T = 2.0 × 9.8 = 19.6N (1)
(ii)
moments about B
19.6cos30° × 1.6 (1) = mg × 0.8 (1)
33.9
mass =
(1) (= 3.46 kg)
9.8
maximum support when wire vertical (1)
moments about B
2.0 × 9.8 × 1.6 = (M × 9.8 × 1 .2) (1) + 33.9 × 0.8 (1)
M = 0.36 kg (1)
[n.b. 0.33 kg if 3.5 used]
4
4
[8]
8.
(a)
N (1)
F (1)
T (1)
lines of action of the three forces pass through single point (1)
max 3
(b)
(i)
F = 350N (1)
(ii)
N = 550N (1)
if “sine” used in (i) and “cos” in (ii) allow one mark
allow calculation from drawing scale diagram
if (i) and (ii) not awarded marks, then award
one mark for correct vector diagram
2
[5]
9.
(a)
T = mg = 890 × 10 = 8900 (1) N (1)
(accept alternative correct value using g = 9.81 N kg–1)
30°
2
T
(b)
F
mg
resolve vertically T cos 30° =mg (1)
mg
T=
= 10280(1.03 × 104 )N (1)
cos 30
(c)
(i)
(ii)
(iii)
2
vertical height fallen = l(1 – cos ) = 15(1 – 0.866) = 2.0(1) m (1)
(allow e.c.f if h calculated wrongly)
1
m2 = mgh or reference energy (1)  =
2
(max 1/3 if equations of motion used)
2  10  2.01 = 6.34 m s–1 (1)
890  6.34
F   (m )  =
= 2.8 × 104 N (1)
0
.
2
t 

(allow e.c.f of  and m as before)
5
[9]
10.
(a)
F

T
W
2
components at right angles (1)
vertical component in line with the weight (1)
vertical components to start from the )
(b)
(c)
(i)
(horizontal component) = 25 sin  = 12 (or 13) N (12.5) (1)
( 0.5N if scale drawing)
(ii)
(vertical component) = 25 cos  = 22 N (21.7) (1)
(± 0.5 N if scale drawing)
(i)
vertical component of F = 21.7 + 2.5 = 24 N (24.2)
2
[or 25 (24.5)] (1)
(allow C.E. from (b))
(ii)
horizontal component of F.= 12 (or 13) N (1) (12.5)
(allow C.E. from (b))
(iii)
F = (12.52 + 24.22) (1) (allow C.E. from parts (i) and (ii))
= 27 N (27.2) [or 28 (28.2) ] (1) (26 N to 29 N if scale drawing)
[if  measured on diagram and F cos used, (1) (1)
(same tolerance)]
4
[8]
11.
(a)
(b)
(i)
(use of v2 = u2 + 2as gives) 0 = 252 - 2 × 9.81 × s (1)
19.6 s = 625 and s = 32 m (1)
(ii)
t=
(iii)
(use of v2 = u2 + 2as gives) v2 = 252 – 2 × 9.81 × 16 (1)
(allow C.E. from (a)(i))
and v = 18 m s–1 (1)
max 4
25
= 2.5 s (1)
9.81
time to stop the ball is greater (1)
 rate of change of momentum is less (1)
[or work done on ball is the same but greater distance (1)  less force (1) ]
2
[6]
12.
(a)
F cos 20 = 300 gives F = 319 N(1)
(b)
(i)
work done = force × distance moved in direction of force (1)
F is not in the direction of motion (1)
(ii)
work done = force × distance = 300 × 8000 = 2.4 × 106 J
(iii)
power =
(c)
work done
(1)
time taken
2.4
=
 10 6 (1) (allow e.c.f. for work done in (ii))
5.0  (60  60)
= 133 W (1)
(allow e.c.f. for incorrect time conversion)
1
6
on the level, work is done only against friction (1)
uphill, more work must be done to increase in potential energy (1)
sensible conclusion drawn
(e.g. increased work at constant power requires longer time) (1)
3
[10]
13.
(a)
(i)
F
s
two forces opposing
(1)
forces parallel (1)
s correct (1)
F
(b)
(c)
(ii)
N m (1)
4
(i)
anticlockwise moments = clockwise moments (1)
(ii)
weight of beam acts at centre (1)
this is through the pivot (1)
3
(equating moments gives) 400 × 1.0 = 200 × 0.50 + 250 × d (1)
400 – 100 = 250 × d and d = 1.2 m (1)
2
[9]
14.
(a)
(i)
F1 weight / mg (1)
F2 reaction or normal contact force (1)
F3 driving force (1)
F4 friction or air resistance (1)
(ii)
zero acceleration (1)
zero resultant force (1)
max 5
QWC
(b)
(P = Fv gives) 18 × 103 = F × 10 (1)
(and F = 1.8 × 103 N)
(c)
(i)
1800 – 250 = 1.6 × 103 N (1)
(ii)
force = 4 × 1.55 × 103 = 6.2 × 103 N (1)
(allow e.c.f. from(i))
(iii)
total force = 6200 + 250(N) (1)
(1.55 × 103 N)
(= 6.45 × 103(N))
1
(P = Fv gives) P = 6.45 × 103 × 20 = 1.3 × 105 W (1)
(allow e.c.f. for value of total force)
(1.29 × 105 W)
4
[10]
15.
(a)
(i)
C
(1)
B
(1)
A (1)
n.b. B must make an appreciable angle with wall and bar
(ii)
A
B
C
weight of sign and bar (accept gravity) (1)
reaction of wall (1)
tension in wire (1)
max 5
40°
(b)
0.375m
118N
use of mg (1)
clockwise moments 118 × 0.375 (1)
= anticlockwise moments (Tcos40° (1)) × 0.750 (1)
T = 77 N (1)
max 4
[9]
16.
(a)
(i)
initial acceleration/increase of speed (1)
reaches a constant speed/velocity (1)
acceleration decreases to become zero (at this speed) (1)
(ii)
drag/frictional forces increases with speed (1)
drag equal to weight (– upthrust) (1)
no resultant force at terminal speed
[or balanced forces or forces cancel] (1)
max 5
(b)
(c)
column C
26.6
39.7
49.4
75.2
118
173.5
(i)
(ii)
(d)
(i)
(ii)
column E
1.42
1.60
1.69
1.88
2.07
2.24
four values correct (1)
all values correct and to 3 or 4 s.f. (1)
2
all values correct and to 3 or 4 s.f. (1)
axes labelled and suitable scales chosen (1)
at least 5 points plotted correctly (1)
acceptable line (1)
4
gradient =  (e.g) 2.40 – 1.00  = 2.0 (1)
0.7


= n gradient (= 2) (1)
intercept on y-axis = log k (1)
intercept = 1.0 (1)
k (= 101.0) = 10 (1)
units of k: for n = 2, mm–1 s–1 (1)
max 5
[16]
17.
(a)
component (parallel to ramp) = 7.2 × 103 × sin 30 (1) (= 3.6 × 103 N)
(b)
mass =
(c)
(d)
7.2  10 3
= 734 (kg) (1)
9.81
3600
a=
= 4.9(1) m s–2 (1)
734
(use of v2 = u2 + 2as gives) 0 = 182 – (2 × 4.9 × s) (1)
s = 33(.1) m (1)
(allow C.E. for value of a from (b))
frictional forces are acting (1)
increasing resultant force [or opposing motion] (1)
hence higher deceleration [or car stops quicker] (1)
energy is lost as thermal energy/heat (1)
1
2
2
Max 2
[7]
18.
(a)
(b)
product of the force and the perpendicular distance (1)
reference to a point/pivot (1)
(i)
since W is at a greater distance from A (1)
then W must be less than P if moments are to be equal (1)
(ii)
P must increase (1)
since moment of girl’s weight increases as she moves from A to B (1)
correct statement about how P changes
(e.g. P minimum at A, maximum at B, or P increases in a
linear fashion) (1)
2
max 4
[6]
19.
(a)
(b)
(c)
(d)
suitable calculation using a pair of values of x and corresponding t
to give an average of 2.2 m s–1 ( 0.05 m s–1) (1)
valid reason given (1)
(e.g. larger values are more reliable/accurate
or use of differences eliminates zero errors)
(i)
column D (y/t (cm s–1)
186
210
233
259
284
307
2
all values correct to 3 s.f. (1)
(ii)
graph:
chosen graph gives a straight line (e.g. y/t against t) (1)
axes labelled correctly (1)
suitable scale chosen (1)
minimum of four points correctly plotted (1)
best straight line (1)
(iii)
u (= y - intercept) = 162 cm s–1 ( 4 cm s–1) (1)
gradient = 495 (cm s–2) ( 25 cm s–2) (1)
k = gradient (= 495 cm s–2) (1)
(i)
u : initial vertical component of velocity (1)
(ii)
k : = ½ g (1)
v2 = u2 + 2.22 (1)
gives v = (1.622 + 2.22)1/2 = 2.7 m s–1 ( 0.1 m s –1) (1)
9
2
2
[15]
20.
(a)
(b)
energy of closed system is constant
(or energy is neither created or destroyed) (1)
energy is only converted from one form to another (1)
(i)
2
loss in p.e. = gain in k.e. + work done against resistance (1)
work appears as heat (1)
total energy constant (1)
energy
p.e.
shapes (1)
p.e. = k.e. + work, always (1)
(ii)
k.e.
0
(c)
5
work
t
time
(i)
use of power × time and mcT (1)
correct substitution to find T
(or to calculate t or to check both sides of equation using sensible T)
e.g. 2300 × 94, 0.57 × 4200 × 90 ( 2.2 × 10 J) (1)
assume no heat loss (1)
justification of claim (figures alone are acceptable) (1)
(ii)
energy to boil away 1/2 pint = 0.5 × 0.570 × 2.3 × 106
( = 6.55 × 105 J) (1)
6.55  10 5
time taken =
=285 s (1)
2300
max 5
[12]
21.
(a)
(i)
superposition (1)
between waves in phase (1)
gives constructive interference (1)
(ii)
at D or E waves out of phase (1)
so destructive interference (1)
max 4
(b)
(i)
=
330 = 0.165m (1)
2  10 3
separation between maxima =
 0.165  5  = 1.10(m) (1)


0.75 

D
s
(1)
distance CE (=
1
2
× separation)= 0.55 m (1)
4
[8]
22.
(a)
(b)
(i)
   0.270  2  = 0.18m (1)
3


(ii)
340
f   c  =
= 1.89 × 103 Hz (1)
   0.18
transverse
direction of vibration perpendicular to propagation
[or can be polarised] (1)
longitudinal
direction of vibration parallel to propagation
[or cannot be polarised] (1)
longitudinal (1)
(c)
2
3
(i)
frequency same (1)
(ii)
ap  aq
(iii)
phase difference =  (1)
3
[8]
23.
(a)
superposition
two or more vibrations(or waves) give a single vibration (or wave) (1)
coherent
same wavelength (or frequency) and constant phase relationship (1) 2
(b)
(i)
fringes in
overlap
diagram showing overlap (1)
waves diffracted at slits, stated or shown (1)
(ii)
diffraction pattern wider (or more overlap or more diffraction) (1)
more fringes (1)
fringes less bright because less light through narrow slit (1)
max 4
[6]
24.
(a)
(b)
same wavelength or frequency (1)
(same phase or) constant phase difference (1)
(i)
narrow slit gives wide diffraction (1)
2
(to ensure that) both S1 and S2 are illuminated (1)
(ii)
slit S acts as a point source (1)
S1 and S2 are illuminated from same source giving
monochromatic/same λ (1)
paths to S1 and S2 are of constant length giving constant phase
difference (1)
[or SS1 = SS2 so waves are in phase]
Max 4
QWC 1
(c)
graph to show:
maxima of similar intensity to central maximum (1)
[or some decrease in intensity outwards from centre]
all fringes same width as central fringe (1)
2
[8]
25.
amplitude:
each point along wave (1)
has same amplitude for progressive wave
but varies for stationary wave (1)
phase:
progressive wave, adjacent points vibrate with
different phase (1)
stationary wave, between nodes all particles vibrate
in phase
[or there are only two phases] (1)
energy transfer:
progressive wave, energy is transferred through space (1)
stationary wave, energy is not transferred through
space (1)
max 5
[5]
26.
(a)
(b)
graph to show:
maxima of successively smaller intensity (1)
subsidiary maxima/minima equally spaced (1)
(at least two each side of central axis)
width of subsidiary sections half width of central section (1)
symmetrical pattern each side of central axis (1)
(i)
broader maxima or pattern (1) [or fringes wider apart]
dimmer pattern (1)
(ii)
maxima are closer (1) [or narrower fringes]
green and dark regions (1)
max 3
27.
(a)
(i)
0, 2 or 4 [or 0, 360° or 720°] (1)
4
[7]
(ii)
4 (1)
(iii)
sin  = CE (1)
AC
[or sin  = BD ]
AB
CE = 4 and AC = 2d (1) (hence result)
[or BD = 2 and AB = d]
max 3
(b)
28.
(a)
(limiting case is when  = 90° or sin  = 1)
2.22  10 6 (1)
d
sin



(1) (= 4.6)
n 

 

486  10 9
highest order is 4th (1)
(i)
2
[5]
(since d sin  = n) d sin l8.5° = 632.8 × 10–9 (1)
d = 1.99 × 10–6 (1)
number of lines per metre =
(ii)
1
= 5.01 × 105 (1)
d
n = 1.99 × 10–6 sin 90° (1)
n=–
1.99
= 3.1(5) (1)
0.6328
hence highest order is third (1)
(b)
new =
632.8 10 –9  sin 17.2 
= 590nm(1)
sin 18.5

or 1.994 10
6
–6

 sin 17.2  (1)
2
[8]
29.
(a)
Ray diagram to show:
(b)
(i)
refraction towards normal at boundary (1)
emerging ray refracted away from normal (1)
(ii)
reflection at boundary with i  r
emerging ray refracted away from normal (1)
(i)
20° (1)
(ii)
1n2
=
4
n2 sin 1

(1)
n1 sin 2
1.60 sin 20 

(1)
1.40
sin 
2 = 17 (.4)° (1)
(c)
(sin c = 1/n gives)
4
sin c = 1/1.60 (1)
= c = 38.7° (1)
2
[10]
30.
(a)
(i)
vertical or parallel (1)
equally spaced (1)
black and yellow [or dark and light] bands (1)
(ii)
(iii)
D  5.86  10 –7  1.8
w  
(1)
 =
 s 
0.36  10 –3
= 2.9 × 10–3 m (1)
2  2.9  10 –3
tan  =
(1) gives  = 0.18° (1)
1.8
narrower slits give more diffraction (1)
more overlap (so more fringes) (1)
fringes same width (1)
max 8
(b)
(c)
1
(1)
400  10 3
1
× sin  = 5.86 × 10–7 (1)
3
400  10
 = 13.6° (1)
(i)
d=
(ii)
 = 90° and correctly used (1)
1
n=
= 4.3  4th order (1)
3
400  10  5.86  10 – 7
5
brighter images (1)
large angles (1)
sharper (or narrower) lines (1)
max 2
[15]
31.
(a)
(b)
(i)
B line along distance axis (1)
(ii)
C negative sine wave starting at O (1)
(iii)
A, N (1)
(i)
s.h.m. [or particle stationary] (1)
amplitude = 20 mm (1)
1
f=
= 25 Hz or s–1 (1)
T
(ii)
10 mm (1)
W,V phase difference  [or antiphase or 180°] (1)
W,Z in phase (1)
3
6
[9]
32.
(a)
interference or superposition (1)
reflection from metal plate (1)
two waves of the same frequency/wavelength (1)
travelling in opposite directions (or forward/reflected waves) (1)
maxima where waves are in phase or interfere constructively (1)
minima where waves are out of phase/antiphase or interfere destructively (1)
nodes and antinodes or stationary waves identified (1)
max 4
QWC 2
(b)
(i)
(distance between minima =  ) (1)
2
   144 gives   = 32.0 mm (1)
9
2

(ii)
c = f and c = 3 × 108 (m s–1) (1)
8
f = 3  10 – 3 = 9.38 × 109 Hz (1)
32  10
(allow C.E. for value of  from (i))
3
[7]
33.
(a)
(b)
sin 1
sin 35 o
gives) 1.5 =
(1)
sin  2
sin 
 = 22° (1) (22.48°)
(1n2 =
(i)
(sinc = 1/n gives) sinc =
c = 42° (1) (41.8°)
(ii)
2
1
(1)
1.5
ray diagram to show:
one total internal reflection (1)
with one angle of reflection marked as 68° (1)
correct refraction of ray on exit from top surface with 35° marked (1)
angle of incidence of 22° marked at point of exit (1)
6
[8]
34.
(a)
–7
d =  n  = (1  7.00  10 ) = 7.2 × 10–7 m (accept 7.3) (1)
sin 75
 sin  
(b)
 = sin–1 
(c)
 4.5  10 –7
–7
 1  7.2  10

 = 39° (accept 38°) (1)


1
1
–7

= 7.5  10 > 1 (or sin  > 1) (1)
d
7.2  10 – 7
0° (or straight through position) because no first order line (1)
2
[4]
35.
(a)
for monochromatic light (1)
travelling from one medium to another (1)
sin (angle of incidence)
= constant 3
sin (angle of refraction)
E
D
A
(b)
(c)
(d)
B
C
(i)
correct ray (1)
(ii)
no deviation because i = 0° [or because ray is normal to AB] (1)
2
1
c = 41° (1)
i= 22.5° (1)
1.52
i < c , refracted angle = 35.6°
so no total internal reflection [or rays would emerge] (1)
3
correct ray (1)
1
sinc =
[9]
36.
(a)
1
2
3
4
5
x/m
0.173
0.316
0.499
0.687
0.860
sin 
0.086
0.156
0.242
0.325
0.395
If angles only calculated 1/2
at least 4 points plotted correctly (1)
best straight line (1)
gradient calculated from suitable triangle, 50% of each axis (1)
correct value from readings (1)
appropriate use of d sin  = n (1)
hence N (rulings per metre) = 1.25 × 105 m–1 (1.1 to 1.4 ok) (1)
max 2/6 if no graph and more than one data set used correctly,
1/6 only one set
if tan calc but plotted as sin, mark as scheme
tan or distance plotted, 0/6
max 6
(b)
(c)
(i)
maxima wider spaced [or pattern brighter] (1)
sin  or  increases with N [or light more concentrated] (1)
(ii)
maxima spacing less (1)
sin  or  decreases with  [or statement] (1)
(iii)
maxima wider spaced [or pattern less bright] (1)
same  but larger D [or light more spread out] (1)
(i)
waves in phase from (1)
any sensible ref to coherence (1)
whole number of wavelengths path difference (1)
(ii)
use of geometry to show that sin  =
6

(1)
d
max 3
[15]
37.
(a)
(b)
constant phase relationship (1) (1)
[or same frequency (wavelength) (1) and same phase difference (1)]
2
S1R = 15cm on diagram (1) =75cm  30 waves (1)
S2R = 16cm on diagram (1) = 80cm  32 waves (1)
2 whole waves difference so in phase at R (1) maximum (1)
max 5
(c)
(d)
(falls then rises to) maximum at Q (1)
(then falls and rises to) maximum at P (1)
 c
3.0  10 8
f   =
= 1.2 × 1010 Hz (or 12 GHz) (1)
–3


 25  10
2
1
[10]
38.
(i)
(ii)
ray straight through at X (1)
ray refracted at >30° at Y (1)
ray totally internally reflected at Z (1)
sin  water
c water
2.25  10 8
=
[or =
]
sin  air
c air
3.00  10 8
at critical angle sinair = 1 (1)
sinwater = 0.75, water = 48.6° (1)
radius = 1.5tan48.6° (1) =1.7m,  diameter = 3.4m (1)
[Max 7]
39.
(tensile) force
(1)
cross – sectional area
extension
tensile strain =
(1)
original length
mention of tensile and original (1) 3
(a)
tensilestress =
(b)
diameter of wire (1)
in several places [or repeated] (1)
using a micrometer (1)
(original) length of wire (1)
using a metre rule (or tape measure) (1)
max 4
stress
(1) (plastic region)
(c)
2
(1)(linear region)
strain
[9]
40.
(a)
(i)
(use of n =
c1
gives)
c2
8 

cglass = ×   3.00  10 
1.45 

= 2.07 × 108 m s–1 (1)
(ii)
use of
sin 1 c1

(1)
sin  2 c 2
8
cliquid = 2.07  10  sin 29.2 = 2.26 × 108 m s–1 (1)
sin 26.6
(allow C.E. for values of cglass from (i))
(b)
use of 1n2 =
c1
n
and 1n2 = 2
c2
n1
to give nliquid = 1.45  2.07 810 = 1.33 (1)
2.26  10
8
8


c1
 3  10 8  1.33
or n1  c
2.26  10
liquid


(allow C.E. for value of cliquid)
3
[or use 1n2 =
(c)
sin  1
n
and 1n2 = 2 = to give correct answer]
sin  2
n1
diagram to show :
total internal reflection on the vertical surface (1)
refraction at bottom surface with angle in air greater
than that in the liquid (29.2°) (1)
2
2
[7]
stress
X
Y
41.
Z
strain
(a)
Y (1)
significant plastic deformation (or Young modulus less than X) (1)
(b)
Z (1)
no plastic deformation (or smallest value of Young modulus) (1)
(c)
X (1)
small amount of plastic deformation (or Young modulus greater than Y) (1)
[6]
42.
(a)
diagram showing two supported wires and vernier
[or long wire and appropriate scale] (1)
one justification of design (1)
measurements:
identified length with ruler (1)
diameter with micrometer (1)
in several places [or in different directions] (1)
add load [mass] and read vernier (1)
repeat for range of loads (1)
within limit of proportionality [allow elastic limit] (1)
calculation of at least one value from readings (1)
graph or calc and average (1)
if apparatus unsuitable, mark to scheme to max 6/8
max 8
(b)
aluminium yields, has smaller yield strength identified from
data sheet (1)
use of F(=sA) (1)
= 50 × 106 ×  × (0.36 × 10–3)2 (1)
= 20.3N (1)
4
[12]
43.
(a)
(i)
strain = 0.026 (1)
E = 6.92 × 109 Pa (1)
(ii)
A = 1.96 × 10–7 (m2) (1)
stress = 230 × 108 Pa (1)
(iii)
stress/
108 Pa
breaking strain = 0.044 (1)
(i)
2.5
5
(ii)
2.0
1.5
1.0
(b)
0.5
0
0
0.01 0.02 0.03 0.04 0.05 strain
shape overall (1)
(i)
straight line (1)
0 to (0.026, 1.8) (1)
(ii)
curve (1)
to (0.044, 2.3) (1)
Max 4
[9]
44.
(a)
(b)
(i)
the extension produced (by a force) in a wire is directly
proportional to the force applied (1)
applies up to the limit of proportionality (1)
(ii)
elastic limit:
(iii)
the Young modulus: ratio of tensile stress to tensile strain (1)
unit: Pa or Nm–2 (1)
the maximum amount that a material can be
stretched (by a force) and still return to its original
length (when the force is removed) (1)
[or correct use of permanent deformation]
(i)
length of wire (1)
diameter (of wire) (1)
(ii)
graph of force vs extension (1)
reference to gradient (1)
5
gradient = E
A
(1)
l
[or graph of stress vs strain, with both defined
reference to gradient
gradient = E]
area under the line of F vs e (1)
[or energy per unit volume = area under graph of stress vs strain]
6
[11]
45.
uses slope of straight line region (1)
slope = 1.54 × 105 (Nm–1) (1)
l
E = slope ×
(1)
A
A = 5.03 × 10–7 (m2) (1)
E = 1.5 × 1011 Pa (1)
Fy = 87 (N) (1)
yield stress = 1.7 × 108 Pa (1)
46.
(a)
 c 3.0  10 8 
  3.9(4) MHz (1)
f  
76 

(b)
[6]
(=2 × 38) = 76(m)
(i)
12 

angle between cable and horizontal =  sin –1   59  (1)
14 

T= 110cos59° = 57N • (56.7N) (1)
(allow C.E. for value of angle)
(ii)
cross-sectional area (= (2.0 × 10–3)2)
=1.3 × 10–5(m2) (1)
(1.26 × 10–5(m2))
57
 tension
stress =  
(1)

–5
 area  1.3  10
= 4.4 × 106Pa (1)
(4.38 × 106Pa)
(use of 56.7 and 1.26 gives 4.5 × 106 Pa)
(allow C.E. for values of T and area)
(iii)
breaking stress is  65 × stress
copper is ductile
copper wire could extend much more before breaking
because of plastic deformation
extension to breaking point unlikely
1
any three (1)(1)(1)
7
[8]