AS and A Level Physics Original material Cambridge University Press 2010 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 Hookes 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]

A WY = 21 WX

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]

3 The force on a sample of a material is slowly increased and then slowly decreased. The

forceextension 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

F

A B C D

d l 2d d 2d

2l

2F

F 2F

8 Worksheet

AS and A Level Physics Original material Cambridge University Press 2010 2

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 forceextension graph and the extension axis. B The area between a stressstrain graph and the stress axis. C The gradient of a forceextension graph. D The gradient of a stressstrain graph.

6 Springs and wires obey Hookes law. State Hookes 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 m1. [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 stressstrain 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]

8 Worksheet

AS and A Level Physics Original material Cambridge University Press 2010 3

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]

8 Worksheet

AS and A Level Physics Original material Cambridge University Press 2010 4

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 m1. 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 forceextension 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:

k = l

EA

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 forceextension graph would change for a wire of the same material but: i twice the length [1] ii twice the radius. [1]

Total: 49

Score: %