Unit 2 Physics Past Paper
Questions
EM Radiation & Quantum Phenomena Questions Page 2-16
Mechanics Questions Page 17-67
Elastic Properties of Solids Questions Page 68-95
Oscillations & Waves Questions Page 96-145
Ashbourne Independent School
EM Radiation & Quantum Phenomena Questions
Q1.
The diagram shows a ray of light passing from air into a glass prism at an angle of
incidence θi. The light emerges from face BC as shown.
refractive index of the glass = 1.55
(a)
(i)
Mark the critical angle along the path of the ray with the symbol θc.
(ii)
Calculate the critical angle, θc.
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(3)
(b)
For the ray shown calculate the angle of incidence, θi.
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(2)
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(c)
Without further calculations draw the path of another ray of light incident at the same
point on the prism but with a smaller angle of incidence. The path should show the
ray emerging from the prism into the air.
(3)
(Total 8 marks)
Q2.
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
(a)
Calculate the speed of light
(i)
in the glass,
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(ii)
in the liquid droplet.
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(3)
(b)
Calculate the refractive index of the liquid.
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(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)
Q3.
Figure 1 shows a cross-section through a rectangular light-emitting diode (LED).
When current passes through the LED, light is emitted from the semiconductor material at
P and passes through the transparent material and into the air at Q.
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Figure 1
(a)
(i)
The refractive index of the transparent material of the LED is 1.5. Calculate
the critical angle of this material when the LED is in air.
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(ii)
Figure 1 shows a light ray PQ incident on the surface at Q. Calculate the
angle of incidence of this light ray at Q if the angle of refraction is 40°.
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(iii)
Figure 1 also shows a second light ray PR incident at R at an angle of
incidence of 45°. Use Figure 1 to explain why this light ray cannot escape into
the air.
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(7)
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(b)
The LED in part (a) is used to send pulses of light down two straight optical fibres of
the same refractive index as the transparent material of the LED. The fibres are
placed end-on with the LED, as shown in Figure 2. Optical fibre 1 is positioned at Q
and the other at S directly opposite P.
Figure 2
(i)
Continue the path of the light ray PQ into and along the optical fibre.
(ii)
Compare the times taken for pulses of light to travel along the same length of
each fibre.
Give a reason for your answer.
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(3)
(Total 10 marks)
Q4.
The diagram shows a ray of monochromatic light, in the plane of the paper, incident
on the end face of an optical fibre.
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(a)
(i)
Draw on the diagram the complete path followed by the incident ray, showing
it entering into the fibre and emerging from the fibre at the far end.
(ii)
State any changes that occur in the speed of the ray as it follows this path
from the source.
Calculations are not required.
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(4)
(b)
(i)
Calculate the critical angle for the optical fibre at the air boundary.
refractive index of the optical fibre glass = 1.57
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(ii)
The optical fibre is now surrounded by cladding of refractive index 1.47.
Calculate the critical angle at the core-cladding boundary.
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(iii)
State one advantage of cladding an optical fibre.
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(6)
(Total 10 marks)
Q5.
The diagram shows a cross-sectional view of the base of a glass tank containing
water. A point monochromatic light source is in contact with the base and ray, R1, from the
source has been drawn up to the point where it emerges along the surface of the water.
(a)
(i)
Which angle, A to F, is a critical angle?
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(ii)
Explain how the path of R1 demonstrates that the refractive index of glass is
greater than the refractive index of water.
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(2)
(b)
Using the following information
A = 47.1°
B = 42.9°
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C = E = 41.2°
D = F = 48.8°
calculate
(i)
the refractive index of water,
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(ii)
the ratio,
.
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(5)
(c)
Ray R2 emerges from the source a few degrees away from ray R1 as shown.
Draw on the diagram above the continuation of ray R2.
Where possible show the ray being refracted.
(2)
(Total 9 marks)
Q6.
The diagram, which is not to scale, shows the cross-section of a 45° right angled
glass prism supported by a film of liquid on a glass table. A ray of monochromatic light is
incident on the prism at an angle of incidence θ and emerges along the glass - liquid
boundary as shown.
refractive index of glass = 1.5
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(a)
Calculate the speed of light in the glass.
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(2)
(b)
Determine
(i)
the angle of incidence, θ,
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(ii)
the refractive index of the liquid.
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(5)
(c)
The liquid is now changed to one with a lower refractive index. Draw a possible path
for the ray beyond the point A and into the air.
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Ashbourne Independent School
(2)
(Total 9 marks)
Q7.
The diagram shows a cube of glass. A ray of light, incident at the centre of a face of
the cube, at an angle of incidence θ, goes on to meet another face at an angle of
incidence of 50°, as shown in the figure bellow
critical angle at the glass-air boundary = 45°
(a)
Draw on the diagram the continuation of the path of the ray, showing it passing
through the glass and out into the air.
(3)
(b)
Show that the refractive index of the glass is 1.41
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(2)
(c)
Calculate the angle of incidence, θ.
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(3)
(Total 8 marks)
Q8.
The figure below shows a ray of light passing from air into glass at the top face of
glass block 1 and emerging along the bottom face of glass block 2.
refractive index of the glass in block 1 = 1.45
(a)
Calculate
(i)
the incident angle θ1,
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(ii)
the refractive index of the glass in block 2,
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(iii)
the angle θ3 by considering the refraction at point A.
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(7)
(b)
In which of the two blocks of glass will the speed of light be greater?
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Explain your reasoning.
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(2)
(c)
Using a ruler, draw the path of a ray partially reflected at A on the figure above.
Continue the ray to show it emerging into the air. No calculations are expected.
(2)
(Total 11 marks)
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Ashbourne Independent School
Q9.
A ray of light passes from air into a glass prism as shown in Figure 1.
Figure 1
(a)
Confirm, by calculation, that the refractive index of the glass from which the prism
was made is 1.49.
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(1)
(b)
On Figure 1, draw the continuation of the path of the ray of light until it emerges
back into the air. Write on Figure 1 the values of the angles between the ray and
any normals you have drawn.
the critical angle from glass to air is less than 45°
(2)
(c)
A second prism, prism 2, made from transparent material of refractive index 1.37 is
placed firmly against the original prism, prism 1, to form a cube as shown in Figure
2.
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Figure 2
(i)
The ray strikes the boundary between the prisms. Calculate the angle of
refraction of the ray in prism 2.
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(ii)
Calculate the speed of light in prism 2.
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(iii)
Draw a path the ray could follow to emerge from prism 2 into the air.
(7)
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(Total 10 marks)
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Ashbourne Independent School
Mechanics Questions
Q1.
In an experiment to measure the power output of a motor, the motor is used to lift a
metal block vertically at constant speed.
You may be awarded marks for the quality of written communication in your answers.
(a)
Describe an experiment to check whether the speed of the rising mass is constant.
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(2)
(b)
Explain how the output power of the motor is calculated, stating what measurements
need to be made.
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(2)
(Total 4 marks)
Q2.
(a) A man jumps from a plane that is travelling horizontally at a speed of 70 m s–1. If
air resistance can be ignored, determine
(i)
his horizontal velocity 2.0 s after jumping,
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(ii)
his vertical velocity 2.0 s after jumping,
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(iii)
the magnitude and direction of his resultant velocity 2.0 s after jumping.
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(5)
(b)
After 2.0 s the man opens his parachute. Air resistance is no longer negligible.
Explain in terms of Newton’s laws of motion, why
(i)
his velocity initially decreases,
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(ii)
a terminal velocity is reached.
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(4)
(Total 9 marks)
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Q3.
A waiter holds a tray horizontally in one hand between fingers and thumb as shown in
the diagram.
P, Q and W are the three forces acting on the tray.
(a)
(i)
State two relationships between the forces that must be satisfied if the tray is
to remain horizontal and in equilibrium.
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(ii)
If the mass of the tray is 0.12 kg, calculate the magnitude of the force W.
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(iii)
Calculate the magnitudes of forces P and Q.
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(6)
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Ashbourne Independent School
(b)
The waiter places a glass on the tray. State and explain where the glass should be
positioned on the tray if the force, P, is to have the same value as in part (a).
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(2)
(Total 8 marks)
Q4.
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.
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.
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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
v / mm s–1
log10(r / mm)
log10(v / 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 v and r is known to be of the form
v = kr ,
n
where n and k are constants.
(i)
Enter the corresponding values for log10(v / mm s–1) in column E of the table in
part (b).
(ii)
Plot a graph of log10(v / mm s–1) on the y-axis, against log10(r / mm) on the xaxis.
(Allow one sheet of graph paper)
(4)
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(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)
Q5.
Tidal power could make a significant contribution to UK energy requirements. This
question is about a tidal power station which traps sea water behind a tidal barrier at high
tide and then releases the water through turbines 10.0 m below the high tide mark.
(i)
Calculate the mass of sea water covering an area of 120 km2 and depth 10.0 m.
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density of sea water = 1100 kg m–3
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(ii)
Calculate the maximum loss of potential energy of the sea water in part (i) when it is
released through the turbines.
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(iii)
The potential energy of the sea water released through the turbines, calculated in
part (ii), is lost over a period of 6.0 hours. Estimate the average power output of the
power station over this time period. Assume the power station efficiency is 40%.
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(Total 7 marks)
Q6.
The diagram shows a 250 kg iron ball being used on a demolition site. The ball is
suspended from a cable at point A, and is pulled into the position shown by a rope that is
kept horizontal. The tension in the rope is 1200 N.
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(a)
In the position shown the ball is in equilibrium.
(i)
What balances the force of the rope on the ball?
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(ii)
What balances the weight of the ball?
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(2)
(b)
Determine
(i)
the magnitude of the vertical component of the tension in the cable,
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(ii)
the magnitude of the horizontal component of the tension in the cable,
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(iii)
the magnitude of the tension in the cable,
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(iv)
the angle the cable makes to the vertical.
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(6)
(Total 8 marks)
Q7.
An apple and a leaf fall from a tree at the same instant. Both apple and leaf start at
the same height above the ground but the apple hits the ground first.
You may be awarded marks for the quality of written communication in your answer.
Use Newton’s laws of motion to explain why
(i)
the leaf accelerates at first then reaches a terminal velocity,
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(ii)
the apple hits the ground first.
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(Total 5 marks)
Q8.
The diagram represents an experiment that can be used to investigate stopping
distances for a moving trolley.
The trolley is placed on the raised section of the track. When released it moves down the
track and then travels along the horizontal section before colliding with the block. The
trolley and block join and move together after the collision. The distance they move is
measured.
(a)
State the main energy changes taking place
(i)
as the trolley descends,
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(ii)
after the collision, as the trolley and block move together.
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(2)
(b)
Describe how the speed of the trolley, just before it collides with the block may be
measured experimentally.
You may be awarded marks for the quality of written communication in your answer.
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(3)
(c)
State and explain how the speed of the trolley, prior to impact could be varied.
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(2)
(Total 7 marks)
Q9.
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.
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.
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image
x/cm
y/cm
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
(a)
t/s
(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
= u + kt
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 pf 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)
Q10.
(a)
State the principle of moments.
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(3)
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Ashbourne Independent School
(b)
(i)
Draw a labelled diagram of the apparatus you would use to verify the principle
of moments.
(ii)
Describe the procedure that would be used and state what measurements are
taken.
You may be awarded marks for the quality of written communication in your
answer.
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(iii)
Explain how the results would be used to verify the principle of moments.
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(7)
(Total 10 marks)
Q11.
A constant resultant horizontal force of 1.8 × 103 N acts on a car of mass 900 kg,
initially at rest on a level road.
(a)
Calculate
(i)
the acceleration of the car,
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(ii)
the speed of the car after 8.0 s,
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(iii)
the momentum of the car after 8.0 s,
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(iv)
the distance travelled by the car in the first 8.0 s of its motion,
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(v)
the work done by the resultant horizontal force during the first 8.0 s.
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(9)
(b)
On the axes below sketch the graphs for speed, v, and distance travelled, s, against
time, t, for the first 8.0 s of the car’s motion.
(2)
(c)
In practice the resultant force on the car changes with time. Air resistance is one
factor that affects the resultant force acting on the vehicle.
You may be awarded marks for the quality of written communication in your answer.
(i)
Suggest, with a reason, how the resultant force on the car changes as its
speed increases.
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(ii)
Explain, using Newton’s laws of motion, why the vehicle has a maximum
speed.
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(5)
(Total 16 marks)
Q12.
(a)
(i)
State what is meant by a scalar quantity.
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(ii)
State two examples of scalar quantities.
example 1: .........................................................................................
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example 2: ..........................................................................................
(3)
(b)
An object is acted upon by two forces at right angles to each other. One of the
forces has a magnitude of 5.0 N and the resultant force produced on the object is
9.5 N.
Determine
(i)
the magnitude of the other force,
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(ii)
the angle between the resultant force and the 5.0 N force.
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(4)
(Total 7 marks)
Q13.
A skydiver of mass 70 kg, jumps from a stationary balloon and reaches a speed of
45 m s–1 after falling a distance of 150 m.
(a)
Calculate the skydiver’s
(i)
loss of gravitational potential energy,
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(ii)
gain in kinetic energy.
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(4)
(b)
The difference between the loss of gravitational potential energy and the gain in
kinetic energy is equal to the work done against air resistance. Use this fact to
calculate
(i)
the work done against air resistance,
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(ii)
the average force due to air resistance acting on the skydiver.
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(3)
(Total 7 marks)
Q14.
(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.
(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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Ashbourne Independent School
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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)
Q15.
The aeroplane shown in the diagram below is travelling horizontally at 95 m s–1.
It has to drop a crate of emergency supplies.
The air resistance acting on the crate may be neglected.
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(a)
(i)
The crate is released from the aircraft at point P and lands at point Q. Sketch
the path followed by the crate between P and Q as seen from the ground.
(ii)
Explain why the horizontal component of the crate’s velocity remains constant
while it is moving through the air.
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(3)
(b)
(i)
To avoid damage to the crate, the maximum vertical component of the crate’s
velocity on landing should be 32 m s–1. Show that the maximum height from
which the crate can be dropped is approximately 52 m.
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(ii)
Calculate the time taken for the crate to reach the ground if the crate is
dropped from a height of 52 m.
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(iii)
If R is a point on the ground directly below P, calculate the horizontal
distance QR.
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(6)
(c)
In practice air resistance is not negligible. State and explain the effect this has on
the maximum height from which the crate can be dropped.
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(2)
(Total 11 marks)
Q16.
(a)
Define the moment of a force about a point.
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(2)
(b)
The diagram shows a trailer attached to the towbar of a stationary car. The weight of
the trailer is 1800 N and is shown acting through its centre of gravity.
F is the force exerted by the towbar on the trailer. FR is the total normal reaction
force experienced by the trailer. When stationary all forces acting on the trailer are
vertical.
(i)
Explain what is meant by centre of gravity.
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(ii)
Calculate the force, F, exerted by the towbar on the trailer.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(3)
(iii)
Calculate FR.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(2)
(c)
The car starts to move forwards. State and explain what happens to the magnitude
and direction of force, F.
You may be awarded marks for the quality of written communication in your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(Total 10 marks)
Q17.
The graph represents the motion of two cars, A and B, as they move along a
straight, horizontal road.
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Ashbourne Independent School
(a)
Describe the motion of each car as shown on the graph.
(i)
car A: ..........................................................................……………..….
.............................................................................................................
(ii)
car B: ...........................................................................………………..
.............................................................................................................
(3)
(b)
Calculate the distance travelled by each car during the first 5.0 s.
(i)
car A: ....................................….....................................................................
.............................................................................................................
.............................................................................................................
(ii)
car B: ........….......................................................................................
.............................................................................................................
.............................................................................................................
(4)
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Ashbourne Independent School
(c)
At time t = 0, the two cars are level. Explain why car A is at its maximum distance
ahead of B at t = 2.5 s
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(Total 10 marks)
Q18.
A packing case is being lifted vertically at a constant speed by a cable attached to a
crane.
The packing case has a mass of 640 kg.
(a)
With reference to one of Newton’s laws of motion, explain why the tension, T, in the
cable must be equal to the weight of the packing case.
You may be awarded marks for the quality of written communication in your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(b)
The packing case is lifted through a vertical height of 8.0 m in 4.5 s.
Calculate
(i)
the work done on the packing case,
.............................................................................................................
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Ashbourne Independent School
.............................................................................................................
(ii)
the power output of the crane in this situation.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(3)
(Total 6 marks)
Q19.
(a)
State the difference between vector and scalar quantities.
......................................................................................................................
......................................................................................................................
(1)
(b)
State one example of a vector quantity (other than force) and one example of a
scalar quantity.
vector quantity .............................................................................................
scalar quantity ..............................................................................................
(2)
(c)
A 12.0 N force and a 8.0 N force act on a body of mass 6.5 kg at the same time.
For this body, calculate
(i)
the maximum resultant acceleration that it could experience,
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(ii)
the minimum resultant acceleration that it could experience.
.............................................................................................................
.............................................................................................................
(4)
(Total 7 marks)
Q20.
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.
(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.
......................................................................................................................
......................................................................................................................
(1)
(b)
Calculate the deceleration of the car assuming the only force causing the car to
decelerate is that calculated in part (a).
......................................................................................................................
......................................................................................................................
(2)
(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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Ashbourne Independent School
......................................................................................................................
......................................................................................................................
(2)
(d)
Explain why the stopping distance is, in practice, shorter than the value calculated in
part (c).
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 7 marks)
Q21.
(a) Explain why a raindrop falling vertically through still air reaches a constant
velocity. You may be awarded marks for the quality of written communication in your
answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(4)
(b)
A raindrop falls at a constant vertical velocity of 1.8 m s–1 in still air. The mass of the
raindrop is 7.2 × 10–9 kg.
Calculate
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Ashbourne Independent School
(i)
the kinetic energy of the raindrop,
.............................................................................................................
.............................................................................................................
(ii)
the work done on the raindrop as it falls through a vertical distance of 4.5 m.
.............................................................................................................
.............................................................................................................
(4)
(c)
The raindrop in part (b) now falls through air in which a horizontal wind is blowing. If
the velocity of the wind is 1.4 m s–1, use a scale diagram or calculation to determine
the magnitude and direction of the resultant velocity of the raindrop.
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(Total 11 marks)
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Ashbourne Independent School
Q22.
The figure below shows a uniform steel girder being held horizontally by a crane.
Two cables are attached to the ends of the girder and the tension in each of these cables
is T.
(a)
If the tension, T, in each cable is 850 N, calculate
(i)
the horizontal component of the tension in each cable,
.............................................................................................................
.............................................................................................................
(ii)
the vertical component of the tension in each cable,
.............................................................................................................
.............................................................................................................
(iii)
the weight of the girder.
.............................................................................................................
.............................................................................................................
(4)
(b)
On the figure draw an arrow to show the line of action of the weight of the girder.
(1)
(Total 5 marks)
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Ashbourne Independent School
Q23.
The figure below shows a stationary metal block hanging from the middle of a
stretched wire which is suspended from a horizontal beam. The tension in each half of the
wire is 15 N.
(a)
Calculate for the wire at A,
(i)
the resultant horizontal component of the tension forces,
.............................................................................................................
.............................................................................................................
(ii)
the resultant vertical component of the tension forces.
.............................................................................................................
.............................................................................................................
(3)
(b)
(i)
State the weight of the metal block.
.............................................................................................................
(ii)
Explain how you arrived at your answer, with reference to an appropriate law
of motion.
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Ashbourne Independent School
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(3)
(Total 6 marks)
Q24.
The figure below shows a supermarket trolley.
The weight of the trolley and its contents is 160 N.
(a)
Explain what is meant by centre of gravity.
......................................................................................................................
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Ashbourne Independent School
......................................................................................................................
(2)
(b)
P and Q are the resultant forces that the ground exerts on the rear wheels and front
wheels respectively. Calculate the magnitude of
(i)
force P,
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
force Q.
.............................................................................................................
.............................................................................................................
(3)
(c)
Calculate the minimum force that needs to be applied vertically at A to lift the front
wheels off the ground.
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(d)
State and explain, without calculation, how the minimum force that needs to be
applied vertically at A to lift the rear wheels off the ground compares to the force you
calculated in part (c).
You may be awarded marks for the quality of written communication in your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(Total 10 marks)
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Ashbourne Independent School
Q25.
The figure below shows apparatus that can be used to investigate energy changes.
The trolley and the mass are joined by an inextensible string. In an experiment to
investigate energy changes, the trolley is initially held at rest, and is then released so that
the mass falls vertically to the ground.
You may be awarded marks for the quality of written communication in your answer.
(a)
(i)
State the energy changes of the falling mass.
.............................................................................................................
.............................................................................................................
(ii)
Describe the energy changes that take place in this system.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(b)
State what measurements would need to be made to investigate the conservation of
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Ashbourne Independent School
energy.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(c)
Describe how the measurements in part (b) would be used to investigate the
conservation of energy.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(4)
(Total 10 marks)
Q26.
A car accelerates from rest to a speed of 26 m s–1. The table shows how the speed of
the car varies over the first 30 seconds of motion.
time/ s
0
5.0
10.0
15.0
20.0
25.0
30.0
speed/ m s–1
0
16.5
22.5
24.5
25.5
26.0
26.0
(a)
Draw a graph of speed against time on the grid provided.
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Ashbourne Independent School
(3)
(b)
Calculate the average acceleration of the car over the first 25 s.
......................................................................................................................
......................................................................................................................
(2)
(c)
Use your graph to estimate the distance travelled by the car in the first 25 s.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(d)
Using the axes below, sketch a graph to show how the resultant force acting on the
car varies over the first 30 s of motion.
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Ashbourne Independent School
(2)
(e)
Explain the shape of the graph you have sketched in part (d), with reference to the
graph you plotted in part (a).
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 11 marks)
Q27.
A supertanker of mass 4.0 × 108 kg, cruising at an initial speed of 4.5 m s–1, takes one
hour to come to rest.
(a)
Assuming that the force slowing the tanker down is constant, calculate
(i)
the deceleration of the tanker,
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(ii)
the distance travelled by the tanker while slowing to a stop.
.............................................................................................................
.............................................................................................................
(4)
(b)
Sketch, using the axes below, a distance-time graph representing the motion of the
tanker until it stops.
(2)
(c)
Explain the shape of the graph you have sketched in part (b).
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 8 marks)
Q28.
The figure below shows an apparatus used to locate the centre of gravity of a nonuniform metal rod.
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Ashbourne Independent School
The rod is supported horizontally by two wires, P and Q and is in equilibrium.
(a)
State two conditions that must be satisfied for the rod to be in equilibrium.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(b)
Wire Q is attached to a newtonmeter so that the force the wire exerts on the rod can
be measured. The reading on the newtonmeter is 2.0 N and the weight of the rod is
5.0 N.
Calculate
(i)
the force that wire P exerts on the rod,
.............................................................................................................
(ii)
the distance d.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(3)
(Total 5 marks)
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Ashbourne Independent School
Q29.
The figure below shows a skateboarder descending a ramp.
The skateboarder starts from rest at the top of the ramp at A and leaves the ramp at B
horizontally with a velocity v.
(a)
State the energy changes that take place as the skateboarder moves from A to B.
......................................................................................................................
......................................................................................................................
(2)
(b)
In going from A to B the skateboarder’s centre of gravity descends a vertical height
of 1.5 m. Calculate the horizontal velocity, v, stating an assumption that you make.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
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Ashbourne Independent School
(c)
Explain why the acceleration decreases as the skateboarder moves from A to B.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(d)
After leaving the ramp at B the skateboarder lands on the ground at C 0.42 s later.
Calculate for the skateboarder
(i)
the horizontal distance travelled between B and C,
.............................................................................................................
.............................................................................................................
(ii)
the vertical component of the velocity immediately before impact at C,
.............................................................................................................
.............................................................................................................
.............................................................................................................
(iii)
the magnitude of the resultant velocity immediately before impact at C.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(5)
(Total 12 marks)
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Ashbourne Independent School
Q30.
A car accelerates from rest to a speed of 26 m s–1. The table shows how the speed of
the car varies over the first 30 seconds of motion.
time/s
0
5.0
10.0
15.0
20.0
25.0
30.0
speed/m s–1
0
16.5
22.5
24.5
25.5
26.0
26.0
(a)
Draw a graph of speed against time on the grid below.
(5)
(b)
Calculate the average acceleration of the car over the first 25 s.
(2)
(c)
Use your graph to estimate the distance travelled by the car in the first 25 s.
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Ashbourne Independent School
(2)
(d)
Using the axes below, sketch a graph to show how the resultant force acting on the
car varies over the first 30 s of motion.
(3)
(e)
Explain the shape of the graph you have sketched in part (d), with reference to the
graph you plotted in part (a).
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 14 marks)
Q31.
The diagram below shows a swimmer standing at the end of a diving board above a
swimming pool.
The mass of the swimmer is 72 kg and the horizontal distance between point A and his
centre of mass is 2.4 m.
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Ashbourne Independent School
(a)
Calculate the moment of the swimmer’s weight about point A.
Gravitational field strength of the Earth, g = 9.8 N kg–1.
Moment .......................
(3)
(b)
The swimmer dives off the diving board and his centre of mass falls through 3.2 m
before he reaches the water. Calculate the swimmer’s vertical speed as he enters
the water. Neglect air resistance.
Gravitational field strength of the Earth, g = 9.8 N kg–1
Speed ...........................
(3)
(c)
The water brings the diver to rest when his centre of mass is 1.6 m below the
surface of the water. Calculate the average total upward force acting on the diver
which brings his vertical velocity to zero.
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Ashbourne Independent School
(3)
(Total 9 marks)
Q32.
The diagram below shows the path of a ball thrown horizontally from the top of a
tower of height 24 m which is surrounded by level ground.
(a)
Using two labelled arrows, show on the diagram above the direction of the velocity,
v, and the acceleration, a, of the ball when it is at point P.
(2)
(b)
(i)
Calculate the time taken from when the ball is thrown to when it first hits the
ground. Assume air resistance is negligible.
Answer ................................ s
(2)
(ii)
The ball hits the ground 27 m from the base of the tower. Calculate the speed
at which the ball is thrown.
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Ashbourne Independent School
Answer ......................... m s–1
(2)
(Total 6 marks)
Q33.
(a)
(i)
State the difference between a scalar quantity and a vector quantity.
.............................................................................................................
.............................................................................................................
(1)
(ii)
State two examples of a scalar quantity and two examples of a vector
quantity.
scalar quantities ..................................................................................
vector quantities …..............................................................................
(3)
(b)
The diagram below shows a ship fitted with a sail attached to a cable. The force of
the wind on the sail assists the driving force of the ship’s propellors.
The cable exerts a steady force of 2.8 kN on the ship at an angle of 35° above a
horizontal line.
(i)
Calculate the horizontal and vertical components of this force.
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Ashbourne Independent School
horizontal component of force ............. kN
vertical component of force ................. kN
(2)
(ii)
The ship is moving at a constant velocity of 8.3 m s–1 and the horizontal
component of the force of the cable on the ship acts in the direction in which
the ship is moving.
Calculate the power provided by the wind to this ship, stating an appropriate
unit.
Answer ..................................
(3)
(c)
The cable has a diameter of 0.014 m. Calculate the tensile stress in the cable when
it exerts a force of 2.8 kN on the ship, stating an appropriate unit.
Assume the weight of the cable is negligible.
Answer ................................
(5)
(Total 14 marks)
Q34.
A car is travelling on a level road at a speed of 15.0 m s–1 towards a set of traffic
lights when the lights turn red. The driver applies the brakes 0.5 s after seeing the lights
turn red and stops the car at the traffic lights. The table below shows how the speed of the
car changes from when the traffic lights turn red.
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Ashbourne Independent School
time/s
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
speed/m s–1
15.0
15.0
12.5
10.0
7.5
5.0
2.5
0.0
(a)
Draw a graph of speed on the y-axis against time on the x-axis on the grid provided.
(5)
(b)
(i)
State and explain what feature of the graph shows that the car’s deceleration
was uniform.
.............................................................................................................
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
.............................................................................................................
(2)
(ii)
Use your graph to calculate the distance the car travelled after the lights
turned red to when it stopped.
Answer .................. m
(4)
(Total 11 marks)
Q35.
A car is travelling on a level road at a speed of 15.0 m s–1 towards a set of traffic
lights when the lights turn red. The driver applies the brakes 0.5 s after seeing the lights
turn red and stops the car at the traffic lights. The table below shows how the speed of the
car changes from when the traffic lights turn red.
time/s
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
speed/m s–1
15.0
15.0
12.5
10.0
7.5
5.0
2.5
0.0
(a)
Draw a graph of speed on the y-axis against time on the x-axis on the grid provided.
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Ashbourne Independent School
(5)
(b)
(i)
State and explain what feature of the graph shows that the car’s deceleration
was uniform.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(2)
(ii)
Use your graph to calculate the distance the car travelled after the lights
turned red to when it stopped.
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Ashbourne Independent School
Answer .................. m
(4)
(Total 11 marks)
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Ashbourne Independent School
Elastic Properties of Solids Questions
Q1.
A uniform wooden beam of mass 35.0 kg and length 5.52 m is supported by two
identical vertical steel cables A and B attached at either end, as shown in Figure 1.
Figure 1
(a)
Calculate
(i)
the weight of the beam,
.............................................................................................................
(ii)
the tension in each cable.
.............................................................................................................
.............................................................................................................
(2)
(b)
Each unstretched cable has a diameter of 8.26 mm and a length 2.50 m. Calculate
the extension of each cable when supporting the beam.
The Young modulus for steel = 2.10 × 1011 Pa
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(4)
(c)
An object of mass 20.0 kg is hung from the beam 1.00 m from cable A, as shown in
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Ashbourne Independent School
Figure 2.
Figure 2
(i)
Show that the new tension in cable A is 332 N.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
Calculate the new tension in cable B.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(6)
(Total 12 marks)
Q2.
A material in the form of a wire, 3.0 m long and cross-sectional area = 2.8 × 10–7 m2 is
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Ashbourne Independent School
suspended from a support so that it hangs vertically. Different masses may be suspended
from its lower end. The table shows the extension of the wire when it is subjected to an
increasing load and then a decreasing load.
load/N
0
24
52
70
82
88
94
101
71
50
16
0
extension/mm
0
2.2
4.6
6.4
7.4
8.2
9.6
13.0
10.2
8.0
4.8
3.2
(a)
Plot a graph of load (on y axis) against extension (on x axis) both for increasing and
decreasing loads.
(Allow one sheet of graph paper)
(4)
(b)
Explain what the shape of the graph tells us about the behaviour of the material in
the wire. You may be awarded marks for the quality of written communication in
your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(4)
(c)
Using the graph, determine a value of the Young modulus for the material of the
wire.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(d)
State how the graph can be used to estimate the energy stored during the loading
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Ashbourne Independent School
process.
......................................................................................................................
......................................................................................................................
(1)
(Total 12 marks)
Q3.
(a)
Define the density of a material.
......................................................................................................................
......................................................................................................................
(1)
(b)
Brass, an alloy of copper and zinc, consists of 70% by volume of copper and 30%
by volume of zinc.
density of copper
density of zinc
(i)
= 8.9 × 103 kg m–3
= 7.1 × 103 kg m–3
Determine the mass of copper and the mass of zinc required to make a rod of
brass of volume 0.80 × 10–3 m3.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
Calculate the density of brass.
.............................................................................................................
.............................................................................................................
(4)
(Total 5 marks)
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Ashbourne Independent School
Q4.
(a) When a tensile stress is applied to a wire, a tensile strain is produced in the
wire. State the meaning of
tensile stress, ...............................................................................................
......................................................................................................................
tensile strain. ................................................................................................
......................................................................................................................
(2)
(b)
A long thin line metallic wire is suspended from a fixed support and hangs vertically.
Weights are added to increase the load on the free end of the wire until the wire
breaks. The graph below shows how the tensile strain in the wire increases as the
tensile stress increases.
With reference to the graph, describe the behaviour of the wire as the load on the
free end is increased. To assist with your answer refer to the point A, and regions B
and C.
You may be awarded marks for the quality of written communication in your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(5)
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Ashbourne Independent School
(Total 7 marks)
Q5.
The diagram below shows how the impact force on the heel of a runner’s foot varies
with time during an impact when the runner is wearing cushioned sports shoes.
(a)
Estimate the maximum stress on the cartilage pad in the knee joint as a result of this
force acting on the cartilage pad over a contact area of 550 mm2.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(4)
(b)
On the diagram above, sketch the graph of force against time you would expect to
see if a sports shoe with less cushioning had been used.
(3)
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Ashbourne Independent School
(Total 7 marks)
Q6.
(a)
State Hooke’s law for a material in the form of a wire.
......................................................................................................................
......................................................................................................................
(2)
(b)
A rigid bar AB of negligible mass, is suspended horizontally from two long,
vertical wires as shown in the diagram. One wire is made of steel and the other of
brass. The wires are fixed at their upper end to a rigid horizontal surface. Each
wire is 2.5 m long but they have different cross-sectional areas.
When a mass of 16 kg is suspended from the centre of AB, the bar remains
horizontal.
the Young modulus for steel = 2.0 × 1011 Pa
the Young modulus for brass = 1.0 × 1011 Pa
(i)
What is the tension in each wire?
.............................................................................................................
(ii)
If the cross-sectional area of the steel wire is 2.8 × 10–7 m2, calculate the
extension of the steel wire.
.............................................................................................................
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(iii)
Calculate the cross-sectional area of the brass wire.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(iv)
Calculate the energy stored in the steel wire.
.............................................................................................................
.............................................................................................................
(7)
(c)
The brass wire is replaced by a steel wire of the same dimensions as the brass wire.
The same mass is suspended from the midpoint of AB.
(i)
Which end of the bar is lower?
.............................................................................................................
(ii)
Calculate the vertical distance between the ends of the bar.
.............................................................................................................
.............................................................................................................
(2)
(Total 11 marks)
Q7.
(a) When determining the Young modulus for the material of a wire, a tensile stress
is applied to the wire and the tensile strain is measured.
(i)
State the meaning of
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Ashbourne Independent School
tensile stress .......................................................................................
.............................................................................................................
tensile strain ........................................................................................
.............................................................................................................
(ii)
Define the Young modulus ..................................................................
.............................................................................................................
(3)
(b)
The diagram below shows two wires, one made of steel and the other of brass,
firmly clamped together at their ends. The wires have the same unstretched length
and the same cross-sectional area.
One of the clamped ends is fixed to a horizontal support and a mass M is
suspended from the other end, so that the wires hang vertically.
(i)
Since the wires are clamped together the extension of each wire will be the
same.
If ES is the Young modulus for steel and EB the Young modulus for brass, show
that
where FS and FB are the respective forces in the steel and brass wire.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
The mass M produces a total force of 15 N. Show that the magnitude of the
force
FS = 10 N.
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Ashbourne Independent School
the Young modulus for steel = 2.0 × 1011 Pa
the Young modulus for brass = 1.0 × 1011 Pa
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(iii)
The cross-sectional area of each wire is 1.4 × 10–6 m2 and the unstretched
length is 1.5 m. Determine the extension produced in either wire.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(6)
(Total 9 marks)
(a) State Hooke’s law for a material in the form of a wire and state the conditions
under which this law applies.
Q8.
......................................................................................................................
......................................................................................................................
(2)
(b)
A length of steel wire and a length of brass wire are joined together. This
combination is suspended from a fixed support and a force of 80 N is applied at the
bottom end, as shown in the figure below.
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Ashbourne Independent School
Each wire has a cross-sectional area of 2.4 × 10–6 m2.
length of the steel wire = 0.80 m
length of the brass wire = 1.40 m
the Young modulus for steel = 2.0 × 1011 Pa
the Young modulus for brass = 1.0 × 1011 Pa
(i)
Calculate the total extension produced when the force of 80 N is applied.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
Show that the mass of the combination wire = 4.4 × 10–2 kg.
density of steel = 7.9 × 103 kg m–3
density of brass = 8.5 × 103 kg m–3
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(7)
(c)
A single brass wire has the same mass and the same cross-sectional area as the
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Ashbourne Independent School
combination wire described in part (b). Calculate its length.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 11 marks)
Q9.
(a) When a tensile stress is applied to a wire, a tensile strain is produced in the
wire.
State the meaning of
tensile stress, …...........................................................................................
......................................................................................................................
tensile strain. ................................................................................................
......................................................................................................................
(2)
(b)
A long, thin metal wire is suspended from a fixed support and hangs vertically.
Masses are suspended from its lower end.
As the load on the lower end is increased from zero to a certain value, and then
decreased again to zero, the variation of the resulting tensile strain with the applied
tensile stress is shown in the graph.
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Ashbourne Independent School
(i)
Describe the behaviour of the wire during this process. Refer to the points
A, B, C and D in your answer.
You may be awarded marks for the quality of written communication in your
answer.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(ii)
State, with a reason, whether the material of the wire is ductile or brittle.
.............................................................................................................
.............................................................................................................
(iii)
What does AD represent?
.............................................................................................................
(iv)
State how the Young modulus for the material may be obtained from the
graph.
.............................................................................................................
(v)
State how the energy per unit volume stored in the wire during the loading
process may be estimated from the graph.
.............................................................................................................
(9)
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Ashbourne Independent School
(c)
The wire described in part (b) has an unstretched length of 3.0 m and crosssectional area 2.8 × 10–7 m2. At a certain stage between the points A and B on the
graph, the wire supports a load of 75 N. Calculate the extension produced in the
wire by this load.
the Young modulus for the material of the wire = 2.1 × 1011 Pa
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 13 marks)
Q10.
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.
(a)
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
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Ashbourne Independent School
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)
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Ashbourne Independent School
Q11.
(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.
.............................................................................................................
.............................................................................................................
(5)
(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?
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(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)
Q12.
(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.
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Ashbourne Independent School
.............................................................................................................
.............................................................................................................
(5)
(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?
.............................................................................................................
.............................................................................................................
(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)
Q13.
(a)
State Hooke’s law.
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Ashbourne Independent School
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(b)
A student is asked to measure the mass of a rock sample using a steel spring,
standard masses and a metre rule. She measured the unstretched length of the
spring and then set up the arrangement shown in the diagram below.
(i)
Describe how you would use this arrangement to measure the mass of the
rock sample. State the measurements you would make and explain how you
would use the measurements to find the mass of the rock sample.
The quality of your written communication will be assessed in this question.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(6)
(ii)
State and explain one modification you could make to the arrangement in the
diagram above to make it more stable.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(2)
(Total 10 marks)
Q14.
(a) Describe how to obtain, accurately by experiment, the data to determine the
Young modulus of a metal wire.
A space is provided for a labelled diagram.
The quality of your written answer will be assessed in this question.
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Ashbourne Independent School
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(6)
(b)
The diagram below is a plot of some results from an experiment in which a metal
wire was stretched.
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Ashbourne Independent School
(i)
Draw a best-fit line using the data points.
(1)
(ii)
Use your line to find the Young modulus of the metal, stating an appropriate
unit.
answer = ......................................
(4)
(c)
After reaching a strain of 7.7 × 10–3, the wire is to be unloaded. On the diagram
above, sketch the line you would expect to obtain for this.
(1)
(Total 12 marks)
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Ashbourne Independent School
Q15.
The table below shows the results of an experiment where a force was applied to a
sample of metal.
(a)
On the axes below, plot a graph of stress against strain using the data in the table.
Strain
/ 10–3
0
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
Stress
/108 Pa
0
0.90
2.15
3.15
3.35
3.20
3.30
3.50
3.60
3.60
3.50
(3)
(b)
Use your graph to find the Young modulus of the metal.
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Ashbourne Independent School
answer = ...................................... Pa
(2)
(c)
A 3.0 m length of steel rod is going to be used in the construction of a bridge. The
tension in the rod will be 10 kN and the rod must extend by no more than 1.0mm.
Calculate the minimum cross-sectional area required for the rod.
Young modulus of steel = 1.90 × 1011 Pa
answer = ...................................... m2
(3)
(Total 8 marks)
Q16.
The figure below shows a stress-strain graph for a copper wire.
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Ashbourne Independent School
(a)
Define tensile strain.
........................................................................................................................
........................................................................................................................
(1)
(b)
State the breaking stress of this copper wire.
answer = ................................ Pa
(1)
(c)
Mark on the figure above a point on the line where you consider plastic deformation
may start.
Label this point A.
(1)
(d)
Use the graph to calculate the Young modulus of copper. State an appropriate unit
for your answer.
answer = .....................................
(3)
(e)
The area under the line in a stress-strain graph represents the work done per unit
volume to stretch the wire.
(i)
Use the graph to find the work done per unit volume in stretching the wire to a
strain of 3.0 × 10–3.
answer = .....................................J m–3
(2)
(ii)
Calculate the work done to stretch a 0.015 kg sample of this wire to a strain
of3.0 × 10–3.
The density of copper = 8960 kg m–3.
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Ashbourne Independent School
answer = .....................................J
(2)
(f)
A certain material has a Young modulus greater than copper and undergoes brittle
fracture at a stress of 176 MPa.
On the figure above draw a line showing the possible variation of stress with strain
for this material.
(2)
(Total 12 marks)
Q17.
(a) Describe an experiment to accurately determine the spring constant k of a
spring that is thought to reach its limit of proportionality when the load is about 20 N.
Include details of the necessary measurements and calculations and describe how
you would reduce uncertainty in your measurements. A space is provided for a
labelled diagram should you wish to include one.
The quality of your written communication will be assessed in this question.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
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Ashbourne Independent School
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(6)
(b)
Two identical springs, each having a spring constant of 85 Nm–1, are shown
arranged in parallel and series in the figure below.
A load of 15 N is attached to each arrangement.
(i)
Calculate the extension for the parallel arrangement when the load is midway
between the lower ends of the springs.
answer = ................................. m
(2)
(ii)
Calculate the extension for the series arrangement.
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Ashbourne Independent School
answer = ................................. m
(2)
(iii)
Calculate the energy stored in the parallel arrangement.
answer = ................................. J
(2)
(iv)
Without further calculation, discuss whether the energy stored in the series
arrangement is less, or greater, or the same as in the parallel arrangement.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
(3)
(Total 15 marks)
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Ashbourne Independent School
Oscillations & Waves Questions
Q1.
A vertical screen is placed several metres beyond a vertical double slit arrangement
illuminated by a laser. The diagram below shows a full-size tracing of the pattern of spots
obtained on this screen. The black patches represent red light whilst the spaces between
them are dark.
(a)
Using the wave theory, explain how the pattern of bright and dark patches is formed.
You may be awarded marks for the quality of written communication provided in
your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(b)
The slit separation was 0.90 mm and the distance between the slits and the screen
was 4.2 m.
(i)
Calculate the spacing of the bright fringes by taking measurements on the
diagram of the tracing.
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(ii)
Hence determine the wavelength of the laser light used.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(Total 7 marks)
Q2.
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.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
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Ashbourne Independent School
(4)
(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,
.............................................................................................................
.............................................................................................................
(ii)
the frequency of the microwave transmitter.
.............................................................................................................
.............................................................................................................
(3)
(Total 7 marks)
Q3.
(a) The diagram below shows an arrangement used to investigate the properties of
microwaves.
When the transmitter T was rotated through 90° about the straight line XY, the
receiver signal decreased to zero. Explain why this happened and state the property
of microwaves responsible for this effect.
You may be awarded marks for the quality of written communication in your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
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Ashbourne Independent School
......................................................................................................................
(3)
(b)
A microwave oven produces microwaves of wavelength 0.12 m in air.
(i)
Calculate the frequency of these microwaves.
.............................................................................................................
.............................................................................................................
(ii)
In a certain oven, explain why food heated in a fixed position in this oven
would be uncooked at certain points if stationary waves were allowed to form.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(3)
(Total 6 marks)
Q4.
(a)
State the conditions that are necessary for the formation of a stationary wave.
You may be awarded marks for the quality of written communication provided in
your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
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Ashbourne Independent School
(b)
The diagram represents a stationary wave on a stretched string. The continuous line
shows the position of the string at a particular instant when the displacement is a
maximum. P and S are the fixed ends of the string. Q and R are the positions of the
nodes. The speed of waves on the string is 200 m s–1.
(i)
State the wavelength of the waves on the string.
.............................................................................................................
(ii)
Calculate the frequency of vibration.
.............................................................................................................
.............................................................................................................
(iii)
Draw on the diagram the position of the string 3.0 ms later than the position
shown. Explain below how you arrive at your answer.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(5)
(Total 7 marks)
Q5.
(a)
(i)
State the characteristic features of
longitudinal waves,
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Ashbourne Independent School
.............................................................................................................
.............................................................................................................
(ii)
transverse waves.
.............................................................................................................
.............................................................................................................
(3)
(b)
Daylight passes horizontally through a fixed polarising filter P. An observer views
the light emerging through a second polarising filter Q, which may be rotated in a
vertical plane about point X as shown in Figure 1.
Figure 1
Describe what the observer would see as Q is rotated slowly through 360°.
You may be awarded marks for the quality of written communication provided in
your answer.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 5 marks)
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Ashbourne Independent School
Q6.
(a)
State what is meant by coherent sources of light.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(b)
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.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
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Ashbourne Independent School
(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.
Figure 2
(2)
(Total 8 marks)
Q7.
Figure 1 shows a stretched string driven by a vibrator. The right-hand end of a string
is fixed to a wall. A stationary wave is produced on the string; the string vibrates in two
loops.
Figure 1
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Ashbourne Independent School
(a)
State the physical conditions that are necessary for a stationary wave to form on the
string.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(b)
State how you know that the wave on the string is transverse.
......................................................................................................................
(1)
(c)
Compare the amplitude and phase of the oscillations of points A and B on the string.
Amplitude ....................................................................................................
Phase ..........................................................................................................
(2)
(d)
The length of the string is 1.2 m and the speed of the transverse wave on the string
is 6.2 m s–1. Calculate the vibration frequency of the vibrator.
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Ashbourne Independent School
Vibration frequency ............................
(4)
(e)
The frequency of the vibrator is tripled.
(i)
Sketch the new shape of the stationary wave on Figure 2.
Figure 2
(ii)
Show on your diagram three points, P, Q and R that oscillate in phase.
(2)
(Total 12 marks)
Q8.
(a) State and explain two physical properties of the light produced by a laser which
makes it different from the light produced by a filament lamp.
Property 1 ....................................................................................................
......................................................................................................................
......................................................................................................................
Property 2 ....................................................................................................
......................................................................................................................
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Ashbourne Independent School
......................................................................................................................
(4)
(b)
The diagram below shows a cross-section through an optical fibre used for
transmitting information. A laser beam, carrying digital data, is incident on the end of
the core of the fibre at an angle of incidence i.
The core is made from glass of refractive index 1.5.
(i)
Complete the graph below to show how the refractive index changes with
radial distance along the line ABCD in the diagram, above.
(ii)
Calculate the value of the angle of incidence, i, shown in the diagram.
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Ashbourne Independent School
Angle of incidence, i ........................
(iii)
Explain how the glass cladding around the optical fibre’s core improves the
security of data being transmitted through it and give a reason why this is
important.
.............................................................................................................
.............................................................................................................
.............................................................................................................
(8)
(Total 12 marks)
Q9.
(a)
State two requirements for two light sources to be coherent.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(b)
Figure 1
Young’s fringes are produced on the screen from the monochromatic source by the
arrangement shown in Figure 1.
Explain how this arrangement produces interference fringes on the screen. In your
answer, explain why slit S should be narrow and why slits S1 and S2 act as coherent
sources.
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Ashbourne Independent School
The quality of your written answer will be assessed in this question.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(6)
(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.
Figure 2
(2)
(Total 10 marks)
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Ashbourne Independent School
Q10.
A narrow beam of monochromatic red light is directed at a double slit arrangement.
Parallel red and dark fringes are seen on the screen shown in the diagram above.
(a)
(i)
Light passing through each slit spreads out. What is the name for this effect?
.............................................................................................................
(1)
(ii)
Explain the formation of the fringes seen on the screen.
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(iii)
The slit spacing was 0.56 mm. The distance across 4 fringe spacings was 3.6
mm when the screen was at a distance of 0.80 m from the slits. Calculate the
wavelength of the red light.
Answer ..................... m
(4)
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Ashbourne Independent School
(b)
Describe how the appearance of the fringes would differ if white light had been used
instead of red light.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(Total 12 marks)
Q11.
The diagram below shows a rectangular glass fish tank containing water. Three light
rays,
P, Q and R from the same point on a small object O at the bottom of the tank are shown.
(a)
(i)
Light ray Q is refracted along the water-air surface. The angle of incidence of
light ray Q at the water surface is 49.0°. Calculate the refractive index of the
water. Give your answer to an appropriate number of significant figures.
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Ashbourne Independent School
Answer ...............................
(1)
(ii)
Draw on the diagram above the path of light ray P from the water-air surface.
(3)
(b)
In the diagram above, the angle of incidence of light ray R at the water-air surface is
60.0°.
(i)
Explain why this light ray is totally internally reflected at the water surface.
.............................................................................................................
.............................................................................................................
(2)
(ii)
Draw the path of light ray R from the water surface and explain whether or not
R enters the glass at the right-hand side of the tank.
the refractive index of the glass = 1.50
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
.............................................................................................................
(4)
(Total 10 marks)
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Ashbourne Independent School
Q12.
Figure 1 represents a stationary wave formed on a steel string fixed at P and Q
when it is plucked at its centre.
Figure 1
(a)
Explain why a stationary wave is formed on the string.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(3)
(b)
(i)
The stationary wave in Figure 1 has a frequency of 150 Hz. The string PQ has
a length of 1.2 m.
Calculate the wave speed of the waves forming the stationary wave.
Answer ........................... m s–1
(2)
(ii)
On Figure 2, draw the stationary wave that would be formed on the string at
the same tension if it was made to vibrate at a frequency of 450 Hz.
Figure 2
(2)
(Total 7 marks)
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Q13.
A narrow beam of monochromatic light of wavelength 590 nm is directed normally at
a diffraction grating, as shown in the diagram below.
(a)
The grating spacing of the diffraction grating is 1.67 × 10–6 m.
(i)
Calculate the angle of diffraction of the second order diffracted beam.
answer .................................... degrees
(4)
(ii)
Show that no beams higher than the second order can be observed at this
wavelength.
(3)
(b)
The light source is replaced by a monochromatic light source of unknown
wavelength.
A narrow beam of light from this light source is directed normally at the grating.
Measurement of the angle of diffraction of the second order beam gives a value of
42.1°.
Calculate the wavelength of this light source.
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Ashbourne Independent School
answer ....................................... m
(2)
(Total 9 marks)
Q14.
An optical fibre used for communications has a core of refractive index 1.55 which is
surrounded by cladding of refractive index 1.45.
(a)
The diagram above shows a light ray P inside the core of the fibre. The light ray
strikes the core-cladding boundary at Q at an angle of incidence of 60.0°.
(i)
Calculate the critical angle of the core-cladding boundary.
answer ........................... degrees
(3)
(ii)
State why the light ray enters the cladding at Q.
.............................................................................................................
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.............................................................................................................
(1)
(iii)
Calculate the angle of refraction, θ, at Q.
answer .............................. degrees
(3)
(b)
Explain why optical fibres used for communications need to have cladding.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 9 marks)
Q15.
(a) The diagram below represents a progressive wave travelling from left to right
on a stretched string.
(i)
Calculate the wavelength of the wave.
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Ashbourne Independent School
answer ................................... m
(1)
(ii)
The frequency of the wave is 22 Hz. Calculate the speed of the wave.
answer............................m s–1
(2)
(iii)
State the phase difference between points X and Y on the string, giving an
appropriate unit.
answer ..............................
(2)
(b)
Describe how the displacement of point Y on the string varies in the next half-period.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 7 marks)
Q16.
Just over two hundred years ago Thomas Young demonstrated the interference of
light by illuminating two closely spaced narrow slits with light from a single light source.
(a)
What did this suggest to Young about the nature of light?
......................................................................................................................
......................................................................................................................
(1)
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(b)
The demonstration can be carried out more conveniently with a laser. A laser
produces coherent, monochromatic light.
(i)
State what is meant by monochromatic.
.............................................................................................................
.............................................................................................................
(ii)
State what is meant by coherent.
.............................................................................................................
.............................................................................................................
(2)
(iii)
State one safety precaution that should be taken while using a laser.
.............................................................................................................
.............................................................................................................
(1)
(c)
The diagram below shows the maxima of a two slit interference pattern produced on
a screen when a laser was used as a monochromatic light source.
The slit spacing = 0.30 mm.
The distance from the slits to the screen = 10.0 m.
Use the diagram above to calculate the wavelength of the light that produced the
pattern.
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answer = ...................................... m
(3)
(d)
The laser is replaced by another laser emitting visible light with a shorter
wavelength.
State and explain how this will affect the spacing of the maxima on the screen.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 9 marks)
Q17.
Figure 1 shows a side view of a string on a guitar. The string cannot move at either
of the two bridges when it is vibrating. When vibrating in its fundamental mode the
frequency of the sound produced is 108 Hz.
(a)
(i)
On Figure 1, sketch the stationary wave produced when the string is vibrating
in its fundamental mode.
Figure 1
(1)
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Ashbourne Independent School
(ii)
Calculate the wavelength of the fundamental mode of vibration.
answer = ........................................... m
(2)
(iii)
Calculate the speed of a progressive wave on this string.
answer = ...................................... m s–1
(2)
(b)
While tuning the guitar, the guitarist produces an overtone that has a node 0.16 m
from bridge A.
(i)
On Figure 2, sketch the stationary wave produced and label all nodes that are
present.
Figure 2
(2)
(ii)
Calculate the frequency of the overtone.
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Ashbourne Independent School
answer = ...................................... Hz
(1)
(c)
The guitarist needs to raise the fundamental frequency of vibration of this string.
State one way in which this can be achieved.
......................................................................................................................
......................................................................................................................
(1)
(Total 9 marks)
Q18.
The diagram below shows a cross-section through a step index optical fibre.
(a)
(i)
Name the parts A and B of the fibre.
A
B
(1)
(ii)
On the diagram above, draw the path of the ray of light through the fibre.
Assume the light ray undergoes total internal reflection at the boundary
between A and B.
(2)
(b)
Calculate the critical angle for the boundary between A and B.
Give your answer to an appropriate number of significant figures.
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The refractive index of part A = 1.46
The refractive index of part B = 1.48
answer = ...................................... degrees
(2)
(c)
State and explain one reason why part B of the optical fibre is made as narrow as
possible.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(d)
State one application of optical fibres and explain how this has benefited society.
Application
......................................................................................................................
......................................................................................................................
Benefit
......................................................................................................................
......................................................................................................................
(2)
(Total 9 marks)
Q19.
A glass cube is held in contact with a liquid and a light ray is directed at a vertical
face of the cube. The angle of incidence at the vertical face is then decreased to 42° as
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Ashbourne Independent School
shown in the figure below. At this point the angle of refraction is 27° and the ray is totally
internally reflected at P for the first time.
(a)
Complete the figure above to show the path of the ray beyond P until it returns to
air.
(3)
(b)
Show that the refractive index of the glass is about 1. 5.
(2)
(c)
Calculate the critical angle for the glass-liquid boundary.
answer = ........................ degrees
(1)
(d)
Calculate the refractive index of the liquid.
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Ashbourne Independent School
answer = .....................................
(2)
(Total 8 marks)
Q20.
For a plane transmission diffraction grating, the diffraction grating equation for the
first order beam is:
λ = d sin θ
(a)
The figure below shows two of the slits in the grating. Label the figure below with the
distances d and λ.
(2)
(b)
State and explain what happens to the value of angle θ for the first order beam if the
wavelength of the monochromatic light decreases.
......................................................................................................................
......................................................................................................................
......................................................................................................................
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......................................................................................................................
(2)
(c)
A diffraction grating was used with a spectrometer to obtain the line spectrum of star
X shown in the figure below. Shown are some line spectra for six elements that have
been obtained in the laboratory.
Place ticks in the boxes next to the three elements that are present in the
atmosphere of star X.
(2)
(d)
The diffraction grating used to obtain the spectrum of star X had 300 slits per mm.
(i)
Calculate the distance between the centres of two adjacent slits on this
grating.
answer = ................................. m
(1)
(ii)
Calculate the first order angle of diffraction of line P in the figure above.
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Ashbourne Independent School
answer = ........................ degrees
(2)
(Total 9 marks)
Q21.
(a)
Define the amplitude of a wave.
......................................................................................................................
......................................................................................................................
(1)
(b)
(i)
Other than electromagnetic radiation, give one example of a wave that is
transverse.
.............................................................................................................
(1)
(ii)
State one difference between a transverse wave and a longitudinal wave.
.............................................................................................................
.............................................................................................................
(1)
(c)
The figure below shows two identical polarising filters, A and B, and an unpolarised
light source. The arrows indicate the plane in which the electric field of the wave
oscillates.
(i)
If polarised light is reaching the observer, draw the direction of the
transmission axis on filter B in the figure below.
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Ashbourne Independent School
(1)
(ii)
The polarising filter B is rotated clockwise through 360º about line XY from the
position shown in the figure above. On the axes below, sketch how the light
intensity reaching the observer varies as this is done.
(2)
(d)
State one application, other than in education, of a polarising filter and give a
reason for its use.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 8 marks)
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Ashbourne Independent School
Q22.
The figure below shows a layer of oil that is floating on water in a glass container. A
ray of light in the oil is incident at an angle of 44° on the water surface and refracts.
The refractive indices of the materials are as follows.
refractive index of oil
= 1.47
refractive index of water
= 1.33
refractive index of the glass = 1.47
(a)
Show that the angle of refraction θ in the figure above is about 50°.
(2)
(b)
The oil and the glass have the same refractive index. On the figure above, draw the
path of the light ray after it strikes the boundary between the water and the glass
and enters the glass. Show the value of the angle of refraction in the glass.
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Ashbourne Independent School
(2)
(c)
Explain why the total internal reflection will not occur when the ray travels from water
to glass.
......................................................................................................................
......................................................................................................................
......................................................................................................................
(1)
(d)
Calculate the critical angle for the boundary between the glass and air.
answer = ......................... degrees
(2)
(e)
On the figure above, complete the path of the ray after it strikes the boundary
between the glass and air.
(2)
(Total 9 marks)
Q23.
The figure below shows a stationary wave on a string. The string is tied onto a thin
metal bar at A and fixed at B. A vibration generator causes the bar to oscillate at a chosen
frequency.
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Ashbourne Independent School
Explain how a stationary wave is formed. Then describe the key features of the stationary
wave shown in the figure above.
The quality of your written answer will be assessed in this question.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
(Total 6 marks)
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Q24.
A single slit diffraction pattern is produced on a screen using a laser. The intensity of
the central maximum is plotted on the axes in the figure below.
(a)
On the figure above, sketch how the intensity varies across the screen to the right of
the central maximum.
(2)
(b)
A laser is a source of monochromatic, coherent light. State what is meant by
monochromatic light ....................................................................................
......................................................................................................................
coherent light ...............................................................................................
......................................................................................................................
(2)
(c)
Describe how the pattern would change if light of a longer wavelength was used.
......................................................................................................................
......................................................................................................................
(1)
(d)
State two ways in which the appearance of the fringes would change if the slit was
made narrower.
......................................................................................................................
......................................................................................................................
(2)
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Ashbourne Independent School
(e)
The laser is replaced with a lamp that produces a narrow beam of white light.
Sketch and label the appearance of the fringes as you would see them on a screen.
(3)
(Total 10 marks)
Q25.
A scientist is going to use a double-slit arrangement to carry out measurements in
order to determine the wavelength of light from a laser.
(a)
The scientist has a double slit of known separation. Describe the measurements
that need to be taken and explain how they are used to find the wavelength of the
light. Discuss any necessary safety precautions and how you would arrange the
apparatus to improve accuracy.
The quality of your written communication will be assessed in this question.
......................................................................................................................
......................................................................................................................
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......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(6)
(b)
In 1802 Thomas Young used candle light to observe the interference pattern from
two narrow slits acting as coherent light sources.
Explain what is meant by coherent light sources.
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(c)
Sketch and label on the diagram below the arrangement that Young would have
used to obtain his interference pattern.
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Ashbourne Independent School
(2)
(d)
State two differences in the appearance of the pattern obtained with a laser and that
produced by a white light source such as a candle.
Difference 1 ..................................................................................................
......................................................................................................................
Difference 2 ..................................................................................................
.......................................................................................................................
(2)
(e)
Explain how the wave theory of light accounts for the areas on the screen where the
intensity is a minimum.
.......................................................................................................................
.......................................................................................................................
.......................................................................................................................
.......................................................................................................................
(2)
(Total 14 marks)
Q26.
(a)
The speed of light is given by
c=fλ
State how each of these quantities will change, if at all, when light travels from air to
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Ashbourne Independent School
glass.
c .......................................................
f ........................................................
λ .......................................................
(3)
Figure 1 shows a side view of a step index optical fibre.
Figure 1
(b)
Ray A enters the end of the fibre and then undergoes total internal reflection.
On Figure 1 complete the path of this ray along the fibre.
(2)
(c)
(i)
The speed of light in the core is 2.04 × 108 ms–1. Show that the refractive index
of the core is 1.47.
(2)
(ii)
Show that the critical angle at the boundary between the core and the cladding
is
about 80°.
refractive index of the cladding = 1.45
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Ashbourne Independent School
(2)
(d)
Ray B enters the end of the fibre and refracts along the core-cladding boundary.
Calculate the angle of incidence, θ, of this ray at the point of entry to the fibre.
answer = ...................................... degrees
(3)
(e)
Figure 2 shows a pulse of monochromatic light (labelled X) that is transmitted a
significant distance along the fibre. The shape of the pulse after travelling along the
fibre is labelled Y. Explain why the pulse at Y has a lower amplitude and is longer
than it is at X.
Figure 2
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
(2)
(Total 14 marks)
Q27.
The figure below shows a continuous progressive wave on a rope. There is a knot in
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Ashbourne Independent School
the rope.
(a)
Define the amplitude of a wave.
........................................................................................................................
........................................................................................................................
(2)
(b)
The wave travels to the right.
Describe how the vertical displacement of the knot varies over the next complete
cycle.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(c)
A continuous wave of the same amplitude and frequency moves along the rope from
the right and passes through the first wave. The knot becomes motionless.
Explain how this could happen.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(3)
(Total 8 marks)
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Ashbourne Independent School
Q28.
The figure below shows a glass prism. Light is directed into the prism at an angle of
56°.
The path of the ray of light is shown as is it enters the prism.
(a)
(i)
Calculate the refractive index of the glass.
answer = ......................................
(2)
(ii)
Calculate the critical angle for the glass-air boundary.
answer = ......................... degrees
(2)
(b)
On the figure above, continue the path of the ray of light until it emerges from the
prism.
(2)
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Ashbourne Independent School
(Total 6 marks)
Q29.
(a) In an experiment, a narrow beam of white light from a filament lamp is directed
at normal incidence at a diffraction grating. Complete the diagram in the figure below
to show the light beams transmitted by the grating, showing the zero-order beam
and the first-order beams.
(3)
(b)
Light from a star is passed through the grating.
Explain how the appearance of the first-order beam can be used to deduce one
piece of information about the gases that make up the outer layers of the star.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(c)
In an experiment, a laser is used with a diffraction grating of known number of lines
per mm to measure the wavelength of the laser light.
(i)
Draw a labelled diagram of a suitable arrangement to carry out this
experiment.
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Ashbourne Independent School
(2)
(ii)
Describe the necessary procedure in order to obtain an accurate and reliable
value for the wavelength of the laser light.
Your answer should include details of all the measurements and necessary
calculations.
The quality of your written communication will be assessed in your answer.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
(6)
(Total 13 marks)
Q30.
The figure below shows two ways in which a wave can travel along a slinky spring.
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Ashbourne Independent School
(a)
State and explain which wave is longitudinal.
........................................................................................................................
........................................................................................................................
(2)
(b)
On the figure above,
(i)
clearly indicate and label the wavelength of wave B
(1)
(ii)
use arrows to show the direction in which the points P and Q are about to
move as each wave moves to the right.
(2)
(c)
Electromagnetic waves are similar in nature to wave A.
Explain why it is important to correctly align the aerial of a TV in order to receive the
strongest signal.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(Total 7 marks)
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Ashbourne Independent School
Q31.
When a note is played on a violin, the sound it produces consists of the fundamental
and many overtones.
Figure 1 shows the shape of the string for a stationary wave that corresponds to one of
these overtones. The positions of maximum and zero displacement for one overtone are
shown. Points A and B are fixed. Points X, Y and Z are points on the string.
Figure 1
(a)
(i)
Describe the motion of point X.
...............................................................................................................
...............................................................................................................
...............................................................................................................
...............................................................................................................
(2)
(ii)
State the phase relationship between
X and Y .................................................................................................
X and Z .................................................................................................
(2)
(b)
The frequency of this overtone is 780 Hz.
(i)
Show that the speed of a progressive wave on this string is about 125 ms–1.
(2)
(ii)
Calculate the time taken for the string at point Z to move from maximum
displacement back to zero displacement.
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Ashbourne Independent School
answer = ................................... s
(3)
(c)
The violinist presses on the string at C to shorten the part of the string that vibrates.
Figure 2 shows the string between C and B vibrating in its fundamental mode. The
length of the whole string is 320 mm and the distance between C and B is 240 mm.
Figure 2
(i)
State the name given to the point on the wave midway between C and B.
...............................................................................................................
(1)
(ii)
Calculate the wavelength of this stationary wave.
answer = ................................... m
(2)
(iii)
Calculate the frequency of this fundamental mode. The speed of the
progressive wave remains at 125 ms–1.
answer = .................................Hz
(1)
(Total 13 marks)
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Ashbourne Independent School
Q32.
Figure 1 shows a cross-section through an optical fibre used for communications.
Figure 1
(a)
(i)
Name the part of the fibre labelled X.
...............................................................................................................
(1)
(ii)
Calculate the critical angle for the boundary between the core and X.
answer = .........................degrees
(2)
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Ashbourne Independent School
(b)
(i)
The ray leaves the core at Y. At this point the fibre has been bent through an
angle of 30° as shown in Figure 1.
Calculate the value of the angle i.
answer = .........................degrees
(1)
(ii)
Calculate the angle r.
answer = .........................degrees
(2)
(c)
The core of another fibre is made with a smaller diameter than the first, as shown in
Figure 2. The curvature is the same and the path of a ray of light is shown.
Figure 2
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Ashbourne Independent School
(c)
State and explain one advantage associated with a smaller diameter core.
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
(2)
(Total 8 marks)
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