A stationary ice skater catches a heavy ball thrown horizontally towards them. Explain why the skater and ball move together at a lower speed than the ball had just before the catch, and identify the type of collision that has occurred.

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).

An ice skater standing at rest on a frictionless ice surface catches a heavy ball moving horizontally. After the catch, the skater and ball move together as one system.

Model answer (4 marks)

The ball has a certain momentum before the catch. When the skater catches it, the ball and skater become one system, so the total momentum of the system must be the same as before the catch (momentum is conserved). The mass of the system after the catch is the sum of the ball’s mass and the skater’s mass – a larger mass than the ball alone. Because momentum p = mv, keeping p constant while m increases forces the velocity v to decrease: v = p/m. Therefore the skater and ball move together at a lower speed than the ball had just before the catch.

The ball and skater stick together after the collision, so kinetic energy is not conserved. This is a perfectly inelastic collision.

Examiner tips

  • Show the conservation of momentum equation before and after the catch; include the mass increase; calculate v = p/m to explain the speed drop; state the collision type and why kinetic energy is not conserved.
  • Use the exact terms "conserved momentum", "mass increases", "v = p/m", "perfectly inelastic collision" – these are the phrases the mark scheme rewards.

Common mistakes

  • Assuming the skater’s mass is negligible and ignoring the mass increase; "the ball slows down" instead of explaining the combined system’s speed; claiming the collision is elastic because momentum is conserved, forgetting kinetic energy loss.

Mark scheme (4 marks)

  1. The total momentum of the system is conserved, so the momentum of ball before equals the momentum of ball plus skater after.
  2. The total mass of the system increases when the skater catches the ball, since the skater's mass is added to the ball's mass.
  3. Since momentum = mass × velocity, a larger mass with the same momentum means a smaller velocity / v = p/m so v decreases as m increases.
  4. This is a perfectly inelastic collision because the two objects stick together and kinetic energy is not conserved / is lost.

Related

More Forces and momentum questions

▶ Try answering this question with AI marking (free) →