A student wants to estimate the power output of a person walking up a flight of stairs. Explain how the student could arrive at a reasonable estimate, including any values they would need to use.

AQA A-Level Physics (7408) — 3.1.3 Estimation of Physical Quantities · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (5 marks)

Estimate a reasonable mass for the person – about 60–80 kg.
Estimate the height of the flight of stairs – roughly 3–5 m.
Estimate the time taken to climb – about 5–10 s.
Use the relation for gravitational potential energy:
E = m g h (with g ≈ 10 N kg⁻¹).
Calculate the power: P = E / t, giving a value in the range 200–700 W.

Examiner tips

  • Mention the typical ranges for mass, height and time to show realistic assumptions. Show the formulae mgh and P=E/t explicitly. Include the value g≈10 N kg⁻¹. Give a numerical estimate within the expected range.
  • common_mistakes
  • :
  • Using g = 9.8 N kg⁻¹ instead of the rounded 10 N kg⁻¹. Omitting the time factor when calculating power. Choosing unrealistic values for mass, height or time (e.g. 200 kg or 50 s).

Mark scheme (5 marks)

  1. Estimate a reasonable value for the mass of a person (e.g. 60–80 kg)
  2. Estimate a reasonable value for the height of the flight of stairs (e.g. 3–5 m)
  3. Estimate a reasonable time to climb the stairs (e.g. 5–10 s)
  4. State that gravitational potential energy gained equals mass × gravitational field strength × height (or work done = mgh), using g ≈ 10 N/kg
  5. State that power = energy / time (or work done / time), leading to a reasonable calculated estimate (e.g. 200–700 W)

Key terms in this question

power

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