# Explain why the work done by the normal contact force on a skier travelling down a frictionless slope is zero, whilst the work done by the gravitational force is non-zero.

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

> A skier slides down a straight, frictionless slope inclined at an angle to the horizontal. The skier moves along the slope surface.

## Mark scheme (4 marks)

1. The normal contact force acts perpendicular to the slope surface, which is the same direction as perpendicular to the skier's displacement.
2. Work is defined as W = Fd cos θ, and when the angle between the force and displacement is 90°, cos 90° = 0, so no work is done by the normal contact force.
3. Gravitational force acts vertically downward, and the skier's displacement along the slope has a non-zero component in the vertical (downward) direction.
4. Therefore the angle between the gravitational force and the skier's displacement is between 0° and 90°, giving a non-zero value of cos θ and hence non-zero work done by gravity.

## Key terms

- [normal contact force](https://www.gradenine.co.uk/glossary/normal-contact-force)
- [work](https://www.gradenine.co.uk/glossary/work)
- [gravitational force](https://www.gradenine.co.uk/glossary/gravitational-force)

## 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-work-done-by-5c171170) · Published by Druglandscape Ltd.