Hooke's law and force-extension graphsEdexcel International A Level Physics: Subtopic test

1. 1
   A student investigates a helical steel spring hung from a clamp. Masses are added one at a time to the lower end and the extension of the spring is measured after each addition. The spring obeys Hooke's law for all loads up to 8.0 N, at which load its extension is 0.20 m.

   (a)

   Calculate the stiffness of the spring.

   [1 mark]

   • A0.025 N m⁻¹
   • B1.6 N m⁻¹
   • C40 N m⁻¹
   • D160 N m⁻¹

   (b)

   Which statement is a correct statement of Hooke's law?

   [1 mark]

   • AThe extension is inversely proportional to the force applied.
   • BThe force is proportional to the square of the extension.
   • CThe extension is proportional to the force at every load, however large.
   • DThe extension is directly proportional to the force, provided the limit of proportionality is not exceeded.

   (c)

   The student adds further masses so that the force is 12 N. She finds that the extension is greater than the value predicted using the stiffness found from the first results. Explain this observation.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Spring X has a stiffness of 60 N m⁻¹ and spring Y has a stiffness of 20 N m⁻¹. Both springs obey Hooke's law for all the forces used in a test.

   (a)

   A force of 3.0 N is applied to spring Y. What is its extension?

   [1 mark]

   • A0.15 m
   • B0.050 m
   • C6.7 m
   • D60 m

   (b)

   A graph of force (vertical axis) against extension (horizontal axis) is plotted for spring X. What does the gradient of the graph represent?

   [1 mark]

   • AThe reciprocal of the stiffness
   • BThe stiffness of the spring
   • CThe energy stored in the spring
   • DThe limit of proportionality

   (c)

   A force of 3.0 N is applied to spring Y. Calculate the force that must be applied to spring X to produce the same extension as in spring Y.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A technician loads a metal wire, increasing the force steadily from zero. Up to 24 N the extension is directly proportional to the force, and at 24 N the extension is 1.2 mm. Between 24 N and 30 N the extension increases by larger amounts for each newton added, but the wire still returns to its original length when unloaded. Beyond 30 N the wire no longer returns to its original length when unloaded.

   (a)

   Describe how the behaviour of the wire changes as the force is increased from zero to 30 N and beyond, using the terms limit of proportionality, elastic limit and plastic deformation.

   [3 marks]

   (b)

   Calculate the stiffness of the wire in the region where Hooke's law is obeyed, and hence the extension that Hooke's law would predict at 30 N. The measured extension at 30 N is 1.9 mm. Comment on the difference.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A structural engineer tests a sample of ductile steel wire. The force is increased steadily from zero until the wire passes its yield point, and the extension is recorded throughout. A force-extension graph is plotted from the results and is later used to decide the safe working load for a cable made from the same steel.

   (a)

   Describe and explain how the force-extension graph for the wire shows the limit of proportionality, the elastic limit, the yield point and plastic deformation.

   [6 marks]

   (b)

   The cable will be loaded and unloaded many times in service. Evaluate whether its working load should be below the limit of proportionality, between the limit of proportionality and the elastic limit, or beyond the elastic limit.

   [6 marks]

   Total for question 4: 12 marks

End of questions