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

1. 1
   A helical spring obeys Hooke's law. A tensile force of 4.0 N extends it by 25 mm.

   (a)

   What is the stiffness of the spring?

   [1 mark]

   • A160 N m⁻¹
   • B6.3 × 10⁻³ N m⁻¹
   • C0.16 N m⁻¹
   • D16 N m⁻¹

   (b)

   What extension would a tensile force of 10 N produce, assuming the spring still obeys Hooke's law?

   [1 mark]

   • A6.3 mm
   • B40 mm
   • C62.5 mm
   • D625 mm

   (c)

   The spring is instead compressed by 15 mm. Calculate the force needed, assuming Hooke's law is obeyed in compression.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A metal wire is loaded in steps and the extension is measured. The graph of force against extension is a straight line through the origin up to a force of 12 N, where the extension is 1.5 mm. Beyond 12 N the line curves so that its gradient decreases. When the wire is unloaded from a force of 12 N it returns to its original length. When it is unloaded from a force of 14 N it is found to be 0.30 mm longer than at the start.

   (a)

   What does the graph show at a force of 12 N?

   [1 mark]

   • AThe wire breaks
   • BThe limit of proportionality: beyond it, force is no longer proportional to extension
   • CThe wire starts to obey Hooke's law
   • D12 N is the largest force the wire can ever support

   (b)

   What is the stiffness of the wire in its straight-line region?

   [1 mark]

   • A1.3 × 10⁻⁴ N m⁻¹
   • B8.0 N m⁻¹
   • C8.0 × 10⁶ N m⁻¹
   • D8.0 × 10³ N m⁻¹

   (c)

   Explain what the 0.30 mm permanent extension shows about the wire.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A car suspension spring has a stiffness of 4.5 × 10⁴ N m⁻¹. When the car is parked, the spring supports one quarter of the car's mass of 1200 kg. The spring obeys Hooke's law up to a compression of 0.18 m. Take g = 9.81 N kg⁻¹.

   (a)

   Calculate the compression of the spring when the car is parked.

   [3 marks]

   (b)

   Calculate the largest extra mass the spring can carry, in addition to its share of the car, before its limit of proportionality is reached.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A steel wire is loaded until it breaks. The force–extension graph is a straight line through the origin up to a force of 400 N, which is the limit of proportionality. The elastic limit is only just above this force. At 450 N the wire reaches its yield point, where it extends a large amount for very little increase in force. The force then rises to a maximum of 520 N and the wire breaks.

   (a)

   Describe and explain how the wire behaves as the force is increased from zero to 480 N and then removed.

   [6 marks]

   (b)

   A designer proposes that a lifting cable made from this wire should have a safe working load of 450 N, because it does not break until 520 N. Evaluate this proposal.

   [6 marks]

   Total for question 4: 12 marks

End of questions