Elastic strain energyAQA A-Level Physics: Subtopic test

1. 1
   A spring obeys Hooke's law within its limit of proportionality. A force of 8.0 N extends the spring by 0.040 m.

   (a)

   What is the elastic strain energy stored in the spring at an extension of 0.040 m?

   [1 mark]

   • A0.32 J
   • B0.16 J
   • C0.64 J
   • D0.0064 J

   (b)

   The spring is now stretched to an extension of 0.080 m, still within its limit of proportionality. By what factor does the stored energy increase compared with that at 0.040 m?

   [1 mark]

   • A2
   • B3
   • C4
   • D8

   (c)

   Calculate the additional energy that must be transferred to the spring to increase its extension from 0.040 m to 0.080 m.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A technician loads a steel wire with increasing weights until it has been stretched beyond its elastic limit, and then removes the weights one by one. After unloading, the wire is found to be permanently longer than at the start and feels slightly warm.

   (a)

   The area under the force–extension graph for the loading of the wire represents which quantity?

   [1 mark]

   • AThe spring constant of the wire
   • BThe stress in the wire
   • CThe maximum force the wire can withstand
   • DThe work done in stretching the wire

   (b)

   Which statement correctly describes the energy changes when the wire is unloaded after being stretched beyond its elastic limit?

   [1 mark]

   • AOnly the elastic part of the work done can be recovered, and the rest remains in the wire as internal (thermal) energy
   • BAll the work done in loading is recovered as elastic strain energy
   • CNone of the work done is recovered because the wire is permanently deformed
   • DMore energy is recovered than was supplied during loading

   (c)

   Explain, in terms of energy, why the wire is slightly warm after it has been unloaded.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A pinball machine launches a steel ball of mass 0.080 kg using a spring of spring constant 320 N m⁻¹. The spring is compressed by 0.045 m and then released. The ball leaves the spring when the spring reaches its natural length. Take g = 9.81 m s⁻².

   (a)

   Calculate the speed of the ball as it leaves the spring, assuming the spring energy is transferred entirely to the kinetic energy of the ball.

   [3 marks]

   (b)

   The machine is now tilted so that the ball is fired vertically upwards from the compressed position. Calculate the maximum height the ball reaches above the point where it leaves the spring, ignoring air resistance, and state one reason why the measured height would be smaller.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A city council is evaluating a prototype shuttle of mass 2400 kg that stores its braking energy in a large steel spring of spring constant 1.2 × 10⁵ N m⁻¹. When the shuttle brakes from 8.0 m s⁻¹ to rest, 80% of its kinetic energy is stored in the compressed spring. When the shuttle sets off again, 90% of the stored energy is transferred back to the shuttle as kinetic energy. The council must also consider the environmental and ethical effects of adopting the design.

   (a)

   Calculate the compression of the spring when the shuttle stops, and the speed the shuttle regains when the stored energy is released.

   [6 marks]

   (b)

   Evaluate whether the council should adopt the spring braking system, referring to energy conservation and the wider ethical issues.

   [6 marks]

   Total for question 4: 12 marks

End of questions