A ski racer descends a snow-covered slope. As she moves down the slope, her gravitational potential energy decreases and her speed increases. Explain, in terms of work done and energy transfers, why the ski racer's kinetic energy at the bottom of the slope is less than the loss in her gravitational potential energy.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A ski racer of mass 65 kg descends a slope. At the top of the slope her speed is negligible. By the time she reaches the bottom, she has descended a vertical height of 40 m but her kinetic energy is only 18 500 J.
Model answer (4 marks)
The skier loses gravitational potential energy equal to mgh = 65 kg × 9.8 m s⁻² × 40 m = 25 480 J. This energy is the work done by gravity. Part of this work increases the skier’s kinetic energy (18 500 J). The remainder, 25 480 J – 18 500 J = 6 980 J, is expended as work against friction and air resistance. That work is transferred to the surroundings as thermal energy, so the skier’s kinetic energy is less than the loss in potential energy.
Examiner tips
- Show the calculation of mgh to justify the 25 480 J loss. Explain that friction/air resistance takes the ‘missing’ energy. Mention energy transfer to surroundings as heat. Use terms: work, kinetic energy, potential energy, resistive forces.
Common mistakes
- Calculating mgh incorrectly or omitting the 9.8 m s⁻². Forgetting to subtract the kinetic energy from the loss in potential energy. Using the wrong sign for work done by friction (should be negative).
Mark scheme (4 marks)
- Work is done against friction (or air resistance / resistive forces) as the ski racer moves down the slope
- This work done against friction transfers energy away from the skier (as a waste/thermal energy transfer to the surroundings)
- The work done by gravity (equal to the loss in gravitational potential energy) is shared between increasing kinetic energy and doing work against resistive forces
- By the conservation of energy, the total energy is conserved — the 'missing' energy equals the work done against resistive forces (transferred as thermal energy)
Key terms in this question
work done · gravitational potential energy · kinetic energy
Related
- All Pearson Edexcel International GCSE Physics (4PH1) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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