Deformation of Solids June 03

6. A suspended copper wire is gradually loaded until it is stretched

May 02 just beyond the elastic limit, and it is then gradually unloaded.
1. Which of the following correctly defines the terms stress, Which graph (with arrows indicating the sequence) best illustrates
strain and Young modulus? the variation of the tensile stress with longitudinal strain?

2. A wire is stretched by 8 mm when a load of 60 N is applied. 7. What is the ultimate tensile stress of a material?
What will be the extension of a wire of the same material having A the stress at which the material becomes ductile
four times the cross-sectional area and twice the original length, B the stress at which the material breaks
when the same load is applied? C the stress at which the material deforms plastically
A 2 mm B 4 mm C 8 mm D 16 mm D the stress at which the material reaches its elastic limit

3. The tension in a spring of natural length l0 is first increased 8. A beam, the weight of which may be neglected, is supported by
from zero to T1, causing the length to increase to l1. The tension three identical springs. When a weight W is hung from the middle of
is then reduced to T2, causing the length to decrease to l2 (as the beam, the extension of each spring is x.
shown).

Which area of the graph represents the work done by the spring
The middle spring and the weight are removed.
during this reduction in length?
What is the extension when a weight of 2W is hung from the middle
A MLP B MNQP C MNSR D MPLU of the beam?
A 3x/2 B 4x/3 C 2x D 3x
Nov 02 Nov 03
4. The variation of the extension x of a spring with applied force 9. What is the Young modulus of a metal?
F is shown. A extension / force B force / extension
C strain / stress D stress / strain

10. The graph shows how the extension of a spring varies with the
force used to stretch it.

Which shaded area represents the work done when the

extension is increased from x1 to x2?

What is the strain energy stored in the spring when the extension is
4.0 cm?
A 60 J B 120 J C 600 J D 1200 J

June 04
11. The graph shown was plotted in an experiment on a metal wire.

The shaded area represents the

total strain energy stored in
stretching the wire.
How should the axes be labelled?
5. Two springs P and Q both obey Hooke’s law. They have
spring constants 2k and k respectively.
The springs are stretched, separately, by a force that is
gradually increased from zero up to a certain maximum value,
the same for each spring. The work done in stretching spring P
is WP, and the work done in stretching spring Q is WQ.
How is WP related to WQ?
 9
12. Nylon breaks when the stress within it reaches 1 x 10 Pa. Which row correctly relates the graphs to the materials?
Which range includes the heaviest load that could be lifted by a
nylon thread of diameter 1 mm?
A 2 N to 20 N B 20 N to 200 N
C 200 N to 2000 N D 2000 N to 20 000 N
Nov 04
13. Which two substances are normally both crystalline?
A copper and diamond B copper and glass
C diamond and glass D diamond and rubber 18. Two steel wires P and Q have lengths l and 2l respectively, and
cross-sectional areas A and A/2 respectively. Both wires obey
14. The table shows a load applied to four wires and the cross-
Hooke’s law.
sectional area of each.
Which of the wires is subjected to the greatest stress?
What is the ratio

when both wires are stretched to the same extension?

Nov 05
19. When white sugar granules are heated, they melt. When the
melt is cooled quickly, a brittle solid form of toffee is produced.
15. The force F required to extend a sample of rubber by a How does the structure of the sugar change?
distance x is found to vary as shown. A amorphous to polymeric B crystalline to amorphous
C crystalline to polymeric D polymeric to amorphous

20 A ductile material is stretched by a tensile force to a point beyond

its elastic limit. The tensile force is then reduced to zero. The graph
of force against extension is shown below.

The energy stored in the rubber for an extension of 5 m is

A less than 100 J. B 100 J.
C between 100 J and 200 J. D more than 200 J
June 05
16. A number of similar springs, each having the same spring
constant, are joined in three arrangements X, Y and Z. The
same load is applied to each.
Which area represents the net work done on the sample?
AX BX+Y CY+Z DZ
21 A wire stretches 8 mm under a load of 60 N.
A second wire of the same material, with half the diameter and a
quarter of the original length of the first wire, is stretched by the
same load. Assuming that Hooke’s law is obeyed, what is the
extension of this wire?
A 1 mm B 4 mm C 8 mm D 16 mm
June 06
22. In describing the behaviour of a spring, the spring constant is
used. Different loads are used to extend the spring by different
amounts. To find the spring constant, which quantities are required?
What is the order of increasing extension for these A the elastic limit and the loads
arrangements? B the elastic limit, extensions and the length of the spring
C the loads and the extensions of the spring
D the loads and the length of the spring

23. The graph shows the behaviour of a sample of a metal when it is

stretched until it starts to undergo plastic deformation.

17. Cylindrical samples of steel, glass and rubber are each

subjected to a gradually increasing tensile force F. The
extensions e are measured and graphs are plotted as shown
below.
What is the total work done in stretching the sample from zero Nov. 07
extension to 12.0 mm? 30. What is plastic deformation?
Simplify the calculation by treating the region XY as a straight A Plastic deformation occurs when strain is not proportional to stress
line. but when the load is removed the material returns to its original
A 3.30 J B 3.55 J C 3.60 J D 6.60 J length.
Nov 06 B Plastic deformation occurs if, when the load is removed, the
material contracts but a permanent stretching has occurred.
24. What is represented by the gradient of a graph of force
C Plastic deformation occurs until the extension is no longer
(vertical axis) against extension (horizontal axis)?
proportional to the load.
A elastic limit B spring constant
D Plastic deformation occurs when the material extends so that
C stress D the Young modulus
strain is directly proportional to stress.
25. What is the unit of the Young modulus?
–1 –2 2
ANm BNm CNm DNm 31.The graph shows how the length of a particular rubber cord
varies as force is applied.
June 07
26. A piece of copper is drawn into a continuous wire.
What behaviour is the copper exhibiting?
A brittle only B elastic only
C plastic only D both brittle and elastic
27. The force-extension graph of a particular sample of rubber
as a load is applied and then removed is shown.

What is the maximum strain energy in this deformed rubber cord?

A 2.5 J B 5.0 J C 7.5 J D 10 J
June 08
32. A sample of metal is subjected to a force which increases to a
maximum value and then decreases back to zero. A force-extension
graph for the sample is shown.
What does the shaded area represent?
A the energy transformed into heat during the complete cycle
B the recoverable elastic potential energy stored at maximum
extension
C the work done on the sample while loading
D the work done on the sample while unloading

28.A spring of unextended length 0.50 m is stretched by a force

of 2.0 N to a new length of 0.90 m.
The variation of its length with tension is as shown.
When the sample contracts it follows the same force-extension
curve as when it was being stretched.
What is the behaviour of the metal between X and Y?
A both elastic and plastic B elastic but not plastic
C plastic but not elastic D not elastic and not plastic
33. A spring of original length 100 mm is compressed by a force.
The graph shows the variation of the length L of the spring with the
compressing force F.

How much strain energy is stored in the spring?

A 0.40 J B 0.80 J C 0.90 J D 1.8 J

29. A simple crane consists of a rigid vertical pillar supporting a

horizontal beam.

What is the energy stored in the spring when the length is 70 mm?
A 0.090 J B 0.21 J C 0.27 J D 0.63 J
34. The Young modulus of steel is determined using a length of steel
A weight W is lifted by a rope at the end of the beam. wire and is found to have the value E.
What are the forces at points X, Y and Z due to the weight W? Another experiment is carried out using a wire of the same steel, but
force at X force at Y force at Z of twice the length and half the diameter.
A tension compression tension What value is obtained for the Young modulus in the second
B tension tension compression experiment?
C compression tension compression
D compression compression compression
Nov 08 Nov 09
35. Which properties best describe modelling clay? 42. Which row best defines elastic and plastic behaviour of a material?
A brittle and ductile B ductile and elastic elastic behaviour of a material plastic behaviour of a material
C elastic and plastic D plastic and ductile A extends only within the limit of extends beyond the limit of
proportionality proportionality
36. A number of similar springs, each having the same spring B has a linear force-extension has a horizontal force-extension
constant, are joined in four arrangements. The same load is curve curve
applied to each. Which arrangement gives the greatest C obeys Hooke’s Law extends continuously under a
extension? steady load
D returns to its original shape suffers permanent deformation
and size
43. The graph shows the non-linear force-extension curve for a wire
made from a new composite material.

37. The graphs show how force varies with extension and stress
varies with strain for the loading of a metal wire.

What could be the value of the strain energy stored in the wire when
it is stretched to point P?
A 0.09 J B 0.10 J C 0.11 J D 0.20 J
44. A steel string on an electric guitar has the following properties.
diameter = 5.0 × 10–4m Young modulus = 2.0 × 1011Pa tension = 20 N
The string snaps, and contracts elastically.
The Young modulus for this wire is equal to By what percentage does a length l of a piece of the string contract?
A the gradient of the force-extension graph. A 5.1×10 %
–4
B 5.1×10 %
–2
C 1.3×10 %
–4
D 1.3×10 %
–2
B the area between the force-extension graph and the extension axis.
C the gradient of the stress-strain graph. June 10
D the area between the stress-strain graph and the strain axis. 45. In stress-strain experiments on metal wires, the stress axis is
8
often marked in units of 10 Pa and the strain axis is marked as a
38. For a wire, Hooke’s law is obeyed for a tension F and percentage. This is shown for a particular wire in the diagram.
extension x. The Young modulus for the material of the wire is E.
Which expression represents the elastic strain energy stored in
the wire?

June 09
39. Four materials are formed into rods of the same dimensions.
At room temperature, which can sustain the largest plastic What is the value of the Young modulus for the material of the wire?
7 8 9 9
deformation? A 6.0×10 Pa B 7.5 × 10 Pa C 1.5×10 Pa D 6.0×10 Pa
A the ductile material aluminium 46. A spring is compressed by a force. The graph shows the
B the brittle material carbon compressing force F plotted against the length L of the spring.
C the brittle material glass
D the ductile material steel

40. Two steel wires P and Q have lengths l and 2l respectively,

and cross-sectional areas A and A/2 respectively. Both wires
obey Hooke’s law.

What is the ratio when both wires are

stretched to the same extension? What is the spring constant of this spring?
–1 –1 –1 –1
A 0.2 N m B5Nm C 100 N m D 200 N m
47. Which graph represents the force-extension relationship of a
rubber band that is stretched almost to its breaking point?
41. A rubber band is stretched by hanging weights on it and the
force-extension graph is plotted from the results.

Answers

What is the best estimate of the strain energy stored in the

rubber band when it is extended 30 cm?
A 2.0 J B 2.6 J C 5.1 J D 200 J