# 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

> 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.

## 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

- [elastic potential energy](https://www.gradenine.co.uk/glossary/elastic-potential-energy)
- [work done](https://www.gradenine.co.uk/glossary/work-done)
- [frictionless surface](https://www.gradenine.co.uk/glossary/frictionless-surface)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-the-elastic-potential-energy-c9d1018e) · Published by Druglandscape Ltd.