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St Ivo School 1
St Ivo Science
Physics Unit 2
Past Paper SECTION 2
Materials Questions
St Ivo School 2
1. As part of a quality check, a manufacturer of fishing line subjects a sample to a tensile
test. The sample of line is 2.0 m long and is of constant circular cross-section of diameter
0.50mm. Hooke’s law is obeyed up to the point when the line has been extended by 52mm at a
tensile stress of 1.8 × 108 Pa.
The maximum load the line can support before breaking is 45 N at an extension of 88 mm.
(a) Calculate
(i) the value of the Young modulus,
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...........................................................................................................................
...........................................................................................................................
(ii) the breaking stress (assuming the cross-sectional area remains constant),
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii) the breaking strain.
........................................................................................................................... (5)
(b) Sketch a graph on the axes below to show how you expect the tensile stress to vary with
strain. Mark the value of stress and corresponding strain at
(i) the limit of Hooke’s law,
(ii) the breaking point.
stress
strain (4)
(Total 9 marks)
2. The cross-section of an overhead power cable is shown below. The cable consists of a hard steel
St Ivo School 3
core surrounded by fifteen straight, thick copper wires.
copper wirediameter 6.5 mm
steel corediameter 25 mm
100m lengths of cable are suspended between adjacent pylons as part of an electricity
distribution system.
Calculate the mass of a 100m length of the cable.
density of copper = 8.93 × 103 kg m
–3
density of steel = 7.80 × 103 kg m
–3
mass of hard steel core .........................................................................................................
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mass of copper wires .............................................................................................................
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mass of cable ......................................................................................................................... (Total 4 marks)
3. The diagram shows tensile stress-strain curves for three different materials X, Y and Z.
stress
strain
Z
Y
X
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For each material named below, state which curve is typical of the material, giving the
reasoning behind your choice.
(a) copper ..................................
reasoning ....................................................................................................................
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.....................................................................................................................................
(b) glass ....................................
reasoning ....................................................................................................................
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(c) hard steel ..............................
reasoning ....................................................................................................................
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.....................................................................................................................................
..................................................................................................................................... (Total 6 marks)
4. (a) Describe an experiment to determine the Young modulus for a material in the form of a
wire. Draw a labelled diagram and explain how you would make the necessary
measurements. Show how you would use your measurements to calculate the result.
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.....................................................................................................................................
..................................................................................................................................... (8)
(b)
rigid support
aluminium copper
F
A copper wire and an aluminium wire, each of diameter 0.72 mm, are joined end to end
as shown in the diagram with the aluminium wire fixed at right angles to a rigid support.
A steadily increasing force, F, is applied. Use data from the Data Sheet to
(i) explain which wire will yield,
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(ii) determine the value of F at which yield should occur.
...........................................................................................................................
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...........................................................................................................................
........................................................................................................................... (4)
(Total 12 marks)
5. A mass of 1500kg is attached to a cable and raised vertically by a crane. The graph shows how
its velocity varies with time.
3.0
2.0
1.0
01.0 2.0 3.0 4.0 5.0
velocity/ms–1
time/s
B C D E FA
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(a) Determine
(i) the initial uniform acceleration of the mass, ...................................................
...........................................................................................................................
...........................................................................................................................
(ii) the distance travelled by the mass while it is accelerating upwards.
...........................................................................................................................
...........................................................................................................................
........................................................................................................................... (3)
(b) (i) Calculate the tension in the cable in the intervals
AB, ...................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
CD. ...................................................................................................................
...........................................................................................................................
(ii) State in which interval of the motion the tension in the cable is least.
........................................................................................................................... (4)
(c) Calculate the power supplied by the crane during the interval CD.
.....................................................................................................................................
..................................................................................................................................... (2)
(Total 9 marks)
6. One end of a steel wire of length 1.2 m and 2.0 mm diameter is attached to a rigid beam.
A 25 g mass is attached to the free end of the steel wire and placed against the underside of the
beam as shown.
fixing point 25 g mass
steel wire
rigid beam
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The 25 g mass is released and falls freely until the wire becomes taut. The kinetic energy of the
falling mass is converted to elastic potential energy in the wire as the wire extends to a
maximum of 1.0 mm. Energy converted to other forms is negligible.
For maximum extension of the wire, complete parts (i) to (v).
(i) Show that the elastic potential energy stored by the extended wire is 0.29 J.
.....................................................................................................................................
.....................................................................................................................................
(ii) Calculate the tension in the wire.
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(iii) Calculate the stress in the wire.
.....................................................................................................................................
.....................................................................................................................................
(iv) Calculate the strain of the wire.
.....................................................................................................................................
.....................................................................................................................................
(v) Hence, calculate the Young modulus for the steel of the wire.
.....................................................................................................................................
..................................................................................................................................... (Total 9 marks)
7. A student carries out an experiment to investigate how the extension of a steel wire varies with
an increasing tensile force. The results of the experiment are shown plotted on the graph. The
initial length of the wire is 0.50m and its diameter is 0.80 mm. The wire breaks at an extension
of 1.46 mm.
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110
100
90
80
70
60
50
40
30
20
10
0
force/N
0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60extension/mm
Use information from the graph to determine
the Young modulus for the material,
...............................................................................................................................................
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...............................................................................................................................................
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...............................................................................................................................................
...............................................................................................................................................
an estimate of the yield stress for the material.
...............................................................................................................................................
............................................................................................................................................... (Total 6 marks)
8. (a) When determining the Young modulus for the material of a wire, a tensile stress is
applied to the wire and the tensile strain produced is measured.
(i) State the meaning of
tensile stress .....................................................................................................
...........................................................................................................................
tensile strain .....................................................................................................
...........................................................................................................................
(ii) Define the Young modulus.
...........................................................................................................................
........................................................................................................................... (3)
(b) The graph represents tensile stress-tensile strain curves for two different materials A and
B. X and Y are the respective points at which each material fractures.
tensile stress
material A
material B
tensile strain00
X
Y
(i) One of the materials is brittle, the other ductile. State which material is brittle.
...........................................................................................................................
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(ii) Making use of the curves in the graph, describe the behaviour of each material as it
is stretched from its original state to breaking point.
material A .........................................................................................................
...........................................................................................................................
material B .........................................................................................................
...........................................................................................................................
(iii) State, giving a reason, which material has the greater value of the Young modulus.
...........................................................................................................................
........................................................................................................................... (5)
(c) A vertical steel piano wire of length 1.5 m and cross-sectional area 1.3 × 10–6
m2 supports
a load of 80N.
Given that the Young modulus for steel = 2.10 × 1011
Pa, calculate the extension in the
wire produced by this load.
.....................................................................................................................................
.....................................................................................................................................
..................................................................................................................................... (2)
(Total 10 marks)
9. (a) (i) Draw and label suitable apparatus required for measuring the Young modulus of a
material in the form of a long wire.
(ii) List the measurements you would make when using the apparatus described in part
(i).
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...........................................................................................................................
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(iii) Describe briefly how the measurements listed in part (ii) would be carried out.
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(iv) Explain how you would calculate the Young modulus from your measurements.
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........................................................................................................................... (13)
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(b) A uniform heavy metal bar of weight 250 N is suspended by two vertical wires, supported
at their upper ends from a horizontal surface, as shown.
T T
brass steel
A B
250 N
One wire is made of brass and the other of steel. The cross-sectional area of each wire is
2.5 ×10–7
m2 and the unstretched length of each wire is 2.0 m.
the Young modulus for brass = 1.0 × 1011
Pa
the Young modulus for steel = 2.0 × 1011
Pa
(i) If the tension, T, in each wire is 125 N, calculate the extension of the steel wire.
...........................................................................................................................
...........................................................................................................................
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(ii) Estimate how much lower the end A will be than the end B.
...........................................................................................................................
........................................................................................................................... (3)
(Total 16 marks)
10. (a) (i) Define the Young modulus for a material.
...........................................................................................................................
...........................................................................................................................
(ii) Explain what is meant by the elastic limit for a wire.
...........................................................................................................................
........................................................................................................................... (2)
(b) A wire supported at its upper end, hangs vertically. The table shows readings obtained
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when stretching the wire by suspending masses from its lower end.
load/N 0 2.0 4.0 6.0 7.0 8.0 9.0 10.0 10.5
extension/mm 0 1.2 2.4 3.6 4.2 4.9 5.7 7.0 8.0
(i) Plot a graph of load against extension.
(Allow one sheet of graph paper)
(ii) Indicate on your graph the region where Hooke’s law is obeyed.
(iii) The unstretched length of the wire is 1.6m and the area of cross-section
8.0 × 10–8
m2. Calculate the value of the Young modulus of the material.
...........................................................................................................................
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...........................................................................................................................
........................................................................................................................... (8)
(c) (i) By considering the work done in stretching a wire, show that the energy stored is
given by 21 Fe, where F is the force producing an extension e.
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(ii) Calculate the energy stored in the wire in part (b) when the extension is 4.0 mm.
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........................................................................................................................... (4)
(Total 14 marks)
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11. A material in the form of a wire, 3.0 m long and cross-sectional area = 2.8 × 10–7
m2 is
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.
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..................................................................................................................................... (4)
(c) Using the graph, determine a value of the Young modulus for the material of the wire.
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..................................................................................................................................... (3)
(d) State how the graph can be used to estimate the energy stored during the loading process.
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..................................................................................................................................... (1)
(Total 12 marks)
12. 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.
cable A cable B
beam
5.52 m
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
Figure 2.
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cable A cable B5.52 m
1.00 m
20.0 kg
Figure 2
(i) Show that the new tension in cable A is 332 N.
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(ii) Calculate the new tension in cable B.
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........................................................................................................................... (6)
(Total 12 marks)
13. (a) The graph shows the variation of tensile stress with tensile strain for two wires X and Y,
having the same dimensions, but made of different materials. The materials fracture at the
points FX and FY respectively.
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X
Y
F
FX
Y
tensile strain
tensilestress
You may be awarded marks for the quality of written communication provided in your
answer to the following questions.
State, with a reason for each, which material, X or Y,
(i) obeys Hooke’s law up to the point of fracture,
...........................................................................................................................
...........................................................................................................................
(ii) is the weaker material,
...........................................................................................................................
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(iii) is ductile,
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(iv) has the greater elastic strain energy for a given tensile stress.
...........................................................................................................................
........................................................................................................................... (8)
(b) An elastic cord of unstretched length 160 mm has a cross-sectional area of 0.64 mm2. The
cord is stretched to a length of 190 mm. Assume that Hooke’s law is obeyed for this
range and that the cross-sectional area remains constant.
the Young modulus for the material of the cord = 2.0 × 107 Pa
(i) Calculate the tension in the cord at this extension.
...........................................................................................................................
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(ii) Calculate the energy stored in the cord at this extension.
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........................................................................................................................... (5)
(Total 13 marks)
14. (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.
tensilestress
tensile strain
A
BC
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.
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(Total 7 marks)
15. (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 = 8.9 × 103 kg m
–3
density of zinc = 7.1 × 103 kg m
–3
(i) Determine the mass of copper and the mass of zinc required to make a rod of brass
of volume 0.80 × 10–3
m3.
.......................................................................................................................
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(ii) Calculate the density of brass.
.......................................................................................................................
....................................................................................................................... (4)
(Total 5 marks)
16. (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.
St Ivo School 20
steel brass
A B
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.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii) Calculate the cross-sectional area of the brass wire.
...........................................................................................................................
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(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)
St Ivo School 21
17. 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.
force/N
2400
1600
800
00 0.1 0.2 0.3 0.4 time/ms
(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.
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................................................................................................................................…
................................................................................................................................… (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)
(Total 7 marks)
18. (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
tensile stress .......................................................................................................
.............................................................................................................................
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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.
brass steel
M
(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
,SS
BB F
F
E
E
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.
the Young modulus for steel = 2.0 × 1011
Pa
the Young modulus for brass = 1.0 × 1011
Pa
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(iii) The cross-sectional area of each wire is 1.4 × 106
m2 and the unstretched length is
1.5 m. Determine the extension produced in either wire.
.............................................................................................................................
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............................................................................................................................. (6)
(Total 9 marks)
19. (a) State Hooke’s law for a material in the form of a wire and state the conditions under
which this law applies.
.....................................................................................................................................
..................................................................................................................................... (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.
steel
brass
80 N
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.
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(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
...........................................................................................................................
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...........................................................................................................................
........................................................................................................................... (7)
(c) A single brass wire has the same mass and the same cross-sectional area as the
combination wire described in part (b). Calculate its length.
.....................................................................................................................................
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.....................................................................................................................................
..................................................................................................................................... (2)
(Total 11 marks)
20. (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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tensilestress
tensile strainA
BC
D0
0
(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.
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(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.
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........................................................................................................................... (9)
(c) The wire described in part (b) has an unstretched length of 3.0 m and cross-sectional
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)
21. (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?
...........................................................................................................................
...........................................................................................................................
(ii) Explain how the student may obtain a value of the Young modulus.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
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...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(iii) How would a value for the elastic energy stored in the wire be found from the
results?
...........................................................................................................................
........................................................................................................................... (6)
(Total 11 marks)
22. 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.
14.0 m
P Q12.0
mast
38 m of copper wire
mast
(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 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.
...........................................................................................................................
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(ii) The copper wire has a diameter of 4.0 mm. Calculate the stress in the copper wire.
...........................................................................................................................
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...........................................................................................................................
...........................................................................................................................
(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
...........................................................................................................................
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(Total 8 marks)
23. (a) (i) Describe the behaviour of a wire that obeys Hooke’s law.
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(ii) Explain what is meant by the elastic limit of the wire.
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(iii) Define the Young modulus of a material and state the unit in which it is measured.
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St Ivo School 29
(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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(ii) Explain how the student may obtain a value of the Young modulus.
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(iii) How would a value for the elastic energy stored in the wire be found from the
results?
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(Total 11 marks)
