# Explain why the total mechanical energy of a ball undergoing simple harmonic motion on a frictionless horizontal surface, attached to a spring fixed at one end, remains constant even though both its kinetic energy and elastic potential energy change continuously.

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

> A ball of mass m is attached to a horizontal spring fixed to a wall. The ball oscillates back and forth on a frictionless surface with amplitude A, undergoing simple harmonic motion.

## Mark scheme (4 marks)

1. The total mechanical energy is the sum of kinetic energy and elastic potential energy, and no non-conservative (dissipative) forces act on the system.
2. As the ball moves away from the equilibrium position, the spring does negative work on the ball, decreasing its kinetic energy while increasing the elastic potential energy stored in the spring.
3. As the ball moves back towards the equilibrium position, the spring does positive work on the ball, converting elastic potential energy back into kinetic energy by the same amount.
4. Since the decrease in kinetic energy exactly equals the increase in elastic potential energy at every instant (and vice versa), the total mechanical energy remains constant throughout the motion.

## Key terms

- [total mechanical energy](https://www.gradenine.co.uk/glossary/total-mechanical-energy)
- [elastic potential energy](https://www.gradenine.co.uk/glossary/elastic-potential-energy)
- [kinetic energy](https://www.gradenine.co.uk/glossary/kinetic-energy)
- [simple harmonic motion](https://www.gradenine.co.uk/glossary/simple-harmonic-motion)

## 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-total-mechanical-energy-a10736bb) · Published by Druglandscape Ltd.