Elastic strain energyEdexcel International A Level Physics: Subtopic test

1. 1
   A spring of stiffness 250 N m⁻¹ is stretched by 0.080 m from its natural length. The spring obeys Hooke's law throughout.

   (a)

   What force is needed to hold the spring at this extension?

   [1 mark]

   • A3.2 × 10⁻⁴ N
   • B20 N
   • C3.1 × 10³ N
   • D2.0 N

   (b)

   What is the elastic strain energy stored in the spring at this extension?

   [1 mark]

   • A0.80 J
   • B1.6 J
   • C10 J
   • D20 J

   (c)

   The spring is now stretched by a further 0.040 m. Calculate the additional elastic strain energy stored.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student stretches a strip of polymer, keeping it within its elastic limit. She records the force at each extension: 0 N at 0 m, 3.0 N at 0.050 m, 5.0 N at 0.100 m, 6.0 N at 0.150 m and 6.5 N at 0.200 m. The force is not directly proportional to the extension.

   (a)

   Which feature of a force-extension graph represents the elastic strain energy stored in the strip?

   [1 mark]

   • AThe gradient of the graph
   • BThe intercept on the force axis
   • CThe area under the graph
   • DThe maximum force reached

   (b)

   Why can the strain energy of the polymer strip not be found using ½Fx?

   [1 mark]

   • AThe extension is too small to measure.
   • BEnergy is not stored in a polymer.
   • CThe force is constant during the extension.
   • DThe force is not proportional to the extension, so the graph is not a straight line through the origin.

   (c)

   Estimate the elastic strain energy stored in the strip when its extension is 0.100 m.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A toy launcher contains a spring of stiffness 600 N m⁻¹. The spring is compressed by 0.050 m and then released, firing a ball of mass 0.025 kg along a horizontal barrel. The spring obeys Hooke's law throughout.

   (a)

   Calculate the elastic strain energy stored in the compressed spring and hence the maximum speed of the ball, assuming all of the energy is transferred to the ball as kinetic energy.

   [3 marks]

   (b)

   The ball is measured leaving the barrel at 6.5 m s⁻¹. Calculate the efficiency of the launcher, and suggest one reason why it is less than 100%.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An engineer is assessing an elastic rope for a bungee jump. The rope has a natural length of 20 m and a stiffness of 150 N m⁻¹, and obeys Hooke's law up to an extension of 25 m, beyond which it would be permanently stretched. A jumper of mass 70 kg falls from a platform that is 45 m above the water. Take g = 9.81 N kg⁻¹.

   (a)

   Explain how the elastic strain energy stored in the rope is found from its force-extension graph, show that it equals ½kx² for a rope that obeys Hooke's law, and describe how it would be found if the graph were curved.

   [6 marks]

   (b)

   Evaluate whether this rope is suitable for the jump, by calculating how far below the platform the jumper falls before first coming to rest.

   [6 marks]

   Total for question 4: 12 marks

End of questions