A football of mass 0.45 kg is moving at 12 m/s when it strikes a goalkeeper's hands and comes to rest. State what is meant by the principle of conservation of momentum and use it to explain what happens to the momentum of the football–goalkeeper system during this collision.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A goalkeeper of mass 75 kg is initially standing still on a football pitch. A football of mass 0.45 kg travels towards the goalkeeper at 12 m/s. The goalkeeper catches the ball and both come to rest together immediately after the catch.
Model answer (4 marks)
The principle of conservation of momentum states that the total momentum of a system remains constant if no external force acts on it.
Before the catch the football has momentum p=0.45×12=5.4 kg·m s⁻¹ in the direction of motion. The goalkeeper is stationary, so his initial momentum is 0 kg·m s⁻¹. Thus the total initial momentum of the football–goalkeeper system is 5.4 kg·m s⁻¹.
After the catch both ball and goalkeeper are at rest, so the final momentum of the system is 0 kg·m s⁻¹. The change in momentum is therefore –5.4 kg·m s⁻¹, which is produced by an external force (the reaction of the ground and friction on the goalkeeper’s feet). Because an external force acts, the system is not isolated and the total momentum is not conserved during the collision.
Before the catch the football has momentum p=0.45×12=5.4 kg·m s⁻¹ in the direction of motion. The goalkeeper is stationary, so his initial momentum is 0 kg·m s⁻¹. Thus the total initial momentum of the football–goalkeeper system is 5.4 kg·m s⁻¹.
After the catch both ball and goalkeeper are at rest, so the final momentum of the system is 0 kg·m s⁻¹. The change in momentum is therefore –5.4 kg·m s⁻¹, which is produced by an external force (the reaction of the ground and friction on the goalkeeper’s feet). Because an external force acts, the system is not isolated and the total momentum is not conserved during the collision.
Examiner tips
- State the principle first, then give the numerical momentum of the ball, note the goalkeeper’s zero momentum, calculate the total initial momentum, state the final momentum and explain the role of the external force.
Common mistakes
- Calculating the ball’s momentum incorrectly (e.g. 0.45×12=5.4 kg·m s⁻¹ but writing 5.4 kg m s⁻¹ incorrectly), forgetting to mention the goalkeeper’s initial momentum is zero, or claiming the system is isolated and that momentum is conserved when an external force is present.
Mark scheme (4 marks)
- The principle of conservation of momentum states that the total momentum of a system remains constant / is conserved, provided no external force acts on it.
- The football has momentum before the collision (momentum = mass × velocity, in the direction of travel).
- The goalkeeper is initially stationary, so the goalkeeper's initial momentum is zero; therefore the total initial momentum of the system equals only the football's momentum.
- After the catch, both the ball and goalkeeper are at rest, so the final momentum of the system is zero; this is consistent with conservation of momentum because an external force (friction / ground reaction) acts to bring the system to rest, meaning the system is not closed/isolated.
Key terms in this question
momentum · principle of conservation of momentum
Related
- All Cambridge International IGCSE Physics (0625) revision notes →
- How to answer a "State and Explain" question →
- Decode the mark scheme abbreviations →
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