1. 8 Worksheet (AS)
Data needed to answer questions can be found in the Data, formulae and relationships sheet.
1 Two springs X and Y have spring constants k and 2k respectively.
Spring X is stretched by a force F and spring Y is stretched by a force 2F. Each spring obeys
Hooke’s law during the extension.
The work done in stretching spring X is WX and the work done in stretching spring Y is WY.
What is the relationship between WX and WY? [1]
1
A WY = WX
2
B WY = WX
C WY = 2WX
D WY = 4WX
2 Four wires A, B, C and D have diameters, lengths and are stretched by forces as shown. All the
wires are made of the same material.
Which wire has the smallest extension? [1]
A B C D
l d 2d d 2d
2l
F
2F
F 2F
3 The force on a sample of a material is slowly increased and then slowly decreased. The
force–extension graph is shown in the diagram.
Which area represents the net work done on the sample during the complete process? [1]
A P+Q B Q+R C P+Q–R D P+Q+R
AS and A Level Physics Original material © Cambridge University Press 2010 1

2. 8 Worksheet
4 Which statement is true about rubber, a polymeric material? [1]
A A normal rubber band breaks when the strain is greater than 1.
B A normal rubber band breaks when the strain is less than 10%.
C When a small amount of sulfur is added, to provide cross-links between molecules in
rubber, the elastic limit is reduced.
D When a small amount of sulfur is added, to provide cross-links between molecules in
rubber, the ultimate tensile stress is reduced.
5 What is equal to the Young modulus? [1]
A The area between a force–extension graph and the extension axis.
B The area between a stress–strain graph and the stress axis.
C The gradient of a force–extension graph.
D The gradient of a stress–strain graph.
6 Springs and wires obey Hooke’s law. State Hooke’s law. [1]
7 A spring has a natural length of 2.5 cm. A force of 4.0 N extends the spring to a length
of 6.2 cm.
a What is the extension of the spring? [1]
b Determine the force (spring) constant k for the spring in N m−1. [3]
c Calculate the extension of the spring when a tensile force of 6.0 N is applied. You may
assume that the spring has not exceeded its elastic limit. [2]
8 The diagram shows the stress–strain graphs for two wires A and B made from different materials.
The wires have the same length and cross-sectional area. Explain which of the materials is:
a brittle [1]
b stiffer [1]
c stronger. [1]
AS and A Level Physics Original material © Cambridge University Press 2010 2

3. 8 Worksheet
9 A graph of force F against extension x is shown for a spring.
a Use the graph to determine the force (spring) constant k of the spring. [2]
b Calculate the energy stored (elastic potential energy) in the spring when its extension is
5.0 cm. [3]
10 A length of cable of diameter 1.2 mm is under a tension of 150 N. Calculate the stress in the
cable. [3]
11 A metal wire of diameter 0.68 mm and natural length 1.5 m is fixed firmly to the ceiling at one
end. When a 6.8 kg mass is hung from the free end, the wire extends by 2.8 mm. Calculate:
a the stress in the wire [3]
b the Young modulus of the material of the wire. [4]
12 The diagram shows two springs X and Y connected
in series and supporting a weight of 8.0 N. The force
constants of the springs are shown on the diagram.
a Calculate the extension of each spring. [2]
b Determine the force (spring) constant for the
combination. [2]
c According to a student, the force constant for the
springs in series is the sum of the force constants
of the individual springs. Is the student correct? [1]
AS and A Level Physics Original material © Cambridge University Press 2010 3

4. 8 Worksheet
13 A 180 g trolley is placed on a frictionless air track. One end of the trolley is attached to a spring
of force constant 50 N m−1. The trolley is pushed against a fixed support so that the compression
of the spring is 8.0 cm. The trolley is then released.
a What is the initial acceleration of the trolley when it is released? [3]
b What is the initial energy stored in the spring? [3]
c Calculate the final speed of the trolley along the air track. You may assume that there is
100% transfer of energy from the spring to the trolley. [2]
14 The force–extension graph for a length of metal wire is shown below.
a The gradient of the graph is equal to the
force constant k of the wire. Show that
the force constant k is given by:
EA
k=
l
where E is the Young modulus of the metal,
A is the cross-sectional area of the wire and
l is the natural length of the wire. [4]
b Explain how the gradient of the force–extension
graph would change for a wire of
the same material but:
i twice the length [1]
ii twice the radius. [1]
Total: Score: %
49
AS and A Level Physics Original material © Cambridge University Press 2010 4