Explain why the elastic potential energy stored in a compressed spring is equal to the work done by the external force used to compress it, and describe how this stored energy changes as the spring is released and accelerates a trolley from rest on a frictionless surface.

IB DP Physics Higher Level (2023 syllabus) — A.3 Work, energy and power · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A spring is initially compressed by a fixed amount against a stationary trolley on a horizontal, frictionless surface. The spring is then released, pushing the trolley until the spring reaches its natural length.

Model answer (4 marks)

The work done by the external force equals the elastic potential energy stored because the compression is carried out quasi‑statically, so the net force on the spring is zero and all the work done against the spring force is stored as elastic potential energy.
When the spring is released it expands back to its natural length. The elastic potential energy stored in the spring decreases.
As the spring does work on the trolley, the trolley’s kinetic energy increases. Because the surface is frictionless, no energy is lost to heat.
By conservation of energy the total mechanical energy (elastic potential + kinetic) remains constant, so the loss of elastic potential energy equals the gain in kinetic energy of the trolley.

Examiner tips

  • Use the term ‘quasi‑static’ to justify zero net force and full energy storage.
  • Show the energy transfer: U_elastic → K_trolley.
  • Mention frictionless surface to avoid energy loss.
  • State conservation of energy explicitly to link the two energy changes.

Common mistakes

  • Confusing work done by the spring with work done by the external force.
  • Assuming energy is lost to friction when the surface is frictionless.
  • Not linking the decrease in elastic potential to the increase in kinetic energy explicitly.

Mark scheme (4 marks)

  1. The work done by the external force equals the elastic potential energy stored because the net force on the spring is zero (quasi-static compression), so all the work done against the spring force is transferred into stored elastic potential energy.
  2. As the spring extends back to its natural length, elastic potential energy decreases (is converted/transferred).
  3. The kinetic energy of the trolley increases as the spring does work on it, since the surface is frictionless so no energy is lost to thermal energy.
  4. By conservation of energy, the total mechanical energy (elastic potential energy plus kinetic energy) remains constant throughout the release, so the decrease in elastic potential energy exactly equals the increase in kinetic energy.

Key terms in this question

elastic potential energy · work done · frictionless surface

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