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.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A skier slides down a straight, frictionless slope inclined at an angle to the horizontal. The skier moves along the slope surface.
Model answer (4 marks)
The normal force acts perpendicular to the slope surface, i.e. perpendicular to the skier’s displacement along the slope. Work is W=Fd cosθ; with θ=90° cosθ=0, so the normal force does no work.
Gravity acts vertically downward. The skier’s displacement along the slope has a vertical component, so the angle between the gravitational force and the displacement is less than 90°. Hence cosθ≠0 and the work done by gravity is non‑zero.
Gravity acts vertically downward. The skier’s displacement along the slope has a vertical component, so the angle between the gravitational force and the displacement is less than 90°. Hence cosθ≠0 and the work done by gravity is non‑zero.
Examiner tips
- Use the definition W=Fd cosθ and state the angle for each force.
- Show that the normal force is perpendicular to displacement (θ=90°).
- Show that gravity has a component along the displacement (θ<90°).
Common mistakes
- Confusing the direction of the normal force with the slope direction.
- Assuming gravity is perpendicular to the slope and thus does no work.
- Neglecting to mention the angle or the cosine factor in the work formula.
Mark scheme (4 marks)
- The normal contact force acts perpendicular to the slope surface, which is the same direction as perpendicular to the skier's displacement.
- 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.
- Gravitational force acts vertically downward, and the skier's displacement along the slope has a non-zero component in the vertical (downward) direction.
- 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 in this question
normal contact force · work · gravitational force
Related
- All IB DP Physics Higher Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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