A tennis ball is dropped from rest onto a hard floor and bounces back to a height lower than the release height. Explain, using Newton's third law and the concept of impulse, why the ball does not return to its original height.

IB DP Physics Higher 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).

Model answer (4 marks)

1. When the ball strikes the floor, the ball exerts a downward force on the floor and the floor exerts an equal‑magnitude upward force on the ball (Newton’s third law). 2. The impulse delivered to the ball is the integral of this upward force over the brief contact time. 3. Because some of the ball’s kinetic energy is lost to internal deformation, heat and sound, the impulse is smaller than the impulse that would be required to restore the ball’s original downward momentum. 4. Consequently the ball leaves the floor with a smaller upward momentum and speed, giving it less kinetic energy and it rises to a lower height than it fell from.

Examiner tips

  • Use the phrase "Newton’s third law" and describe the equal and opposite forces.
  • Explain that impulse = change in momentum and that the upward impulse is less than the downward impulse.
  • Show the link between reduced kinetic energy and lower maximum height.
  • Keep the answer concise and use correct physics terminology.

Common mistakes

  • Confusing force with impulse; writing that the forces are different in magnitude.
  • Forgetting to mention energy loss to internal/thermal/sound energy.
  • Not linking the reduced upward speed to the lower maximum height.

Mark scheme (4 marks)

  1. Newton's third law: the ball exerts a force on the floor equal in magnitude and opposite in direction to the force the floor exerts on the ball.
  2. During contact, the impulse (force × time) delivered to the ball is less than the impulse needed to restore the original momentum magnitude, because some energy is transferred to internal energy / thermal energy / sound during the collision.
  3. The impulse equals the change in momentum of the ball; the upward impulse is smaller in magnitude than the downward impulse on impact, so the ball's upward momentum is less than its downward momentum before the bounce.
  4. Because the ball leaves the floor with a smaller upward speed, it has less kinetic energy and therefore reaches a lower maximum height (since gravitational potential energy gained equals kinetic energy at floor level).

Key terms in this question

Newton's third law · impulse

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