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AS · Practice questions · Elastic potential energy

Store it in the stretch.

Six original Cambridge-style questions on energy stored, the force-extension graph, and elastic versus plastic behaviour.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Area under the line.

01
Analysis
[2 marks]

State how the work done in stretching a spring can be found from its force-extension graph.

  • It is the area under the force-extension graph ✓
  • For a Hooke-law spring this is the area of a triangle, ½Fx ✓
02
Analysis
[2 marks]

A spring of constant 300 N m⁻¹ is stretched by 0.080 m. Find the elastic potential energy stored.

  • Eₚ = ½kx² = ½ × 300 × 0.080² ✓
  • Eₚ = 0.96 J ✓
03
Analysis
[3 marks]

A force-extension graph for a spring is a straight line reaching 20 N at an extension of 0.050 m. Find the energy stored at this extension.

  • Energy = area of the triangle = ½ × force × extension ✓
  • Eₚ = ½ × 20 × 0.050 ✓
  • Eₚ = 0.50 J ✓
04
Analysis
[3 marks]

A spring obeying Hooke law stores 4.5 J of energy when stretched by 0.30 m. Find its spring constant.

  • Eₚ = ½kx², so 4.5 = ½ × k × 0.30² ✓
  • 4.5 = 0.045k ✓
  • k = 100 N m⁻¹ ✓
05
Analysis
[2 marks]

Explain why, when a wire is stretched beyond its elastic limit and the load removed, the energy recovered is less than the work done in stretching it.

  • Beyond the elastic limit the deformation is partly plastic (permanent) ✓
  • Some of the work done goes into rearranging the structure and heating, and is not returned, so less energy is recovered ✓
06
Analysis
[3 marks]

A catapult's stretched elastic stores 8.0 J of elastic potential energy. It launches a 0.040 kg stone. Assuming all the stored energy becomes kinetic energy, find the launch speed.

  • Energy conservation: ½mv² = 8.0 ✓
  • v² = (2 × 8.0) / 0.040 = 400 ✓
  • v = 20 m s⁻¹ ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.