Explain why a person standing on a bathroom scale in a lift (elevator) that is accelerating downwards reads a value less than their true weight.

IB DP Physics Standard Level (2023 syllabus) — A.2 Forces and momentum · Explain · 4 marks · View as Markdown

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

A person stands on a bathroom scale inside a lift. The lift begins to accelerate downwards from rest.

Model answer (4 marks)

The weight of the person, (mg), acts downward at all times. The scale measures the normal (contact) force it exerts upward on the person – this is the reaction force in Newton’s third law. In the accelerating lift the net downward force is (mg-N), which equals (ma) (Newton’s second law). Because the lift is accelerating downward, (a>0) and therefore (mg-N=ma>0), so (N<mg). The scale displays the normal force, so it reads a value smaller than the true weight.

Examiner tips

  • State the weight and the normal force, linking them via Newton’s third law.
  • Apply Newton’s second law to show (N<mg).
  • Explain that the scale reads the normal force, not the weight.
  • Keep the answer concise and use correct symbols.

Mark scheme (4 marks)

  1. Weight (gravitational force) acts downward on the person at all times
  2. The scale reads the normal/contact force that it exerts upward on the person (Newton's third law pair / reaction force)
  3. Applying Newton's second law: the net downward force provides the downward acceleration, so the normal force N must be less than the weight mg (i.e. mg − N = ma)
  4. Because the contact/normal force is less than the weight, the scale displays a value smaller than the person's true weight

Key terms in this question

weight

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