A ice skater of mass 60 kg is moving at 4 m/s across a frictionless ice rink when she collides with a stationary skater of mass 40 kg. After the collision, the two skaters move together. State the principle of conservation of momentum and use it to explain what happens to the velocity of the pair of skaters after the collision compared to the initial velocity of the moving skater.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A 60 kg ice skater moving at 4 m/s collides with a stationary 40 kg skater on a frictionless surface. After the collision, the two skaters move together as one combined mass of 100 kg.
Model answer (4 marks)
The total momentum before the collision equals the total momentum after the collision when no external forces act.
Momentum is the product of mass and velocity, so the same total momentum must be carried by a larger mass after the collision, which means a lower velocity.
Initial momentum = 60 kg × 4 m s⁻¹ = 240 kg m s⁻¹.
After the collision the combined mass is 100 kg, so v = 240 kg m s⁻¹ ÷ 100 kg = 2.4 m s⁻¹, which is less than the initial 4 m s⁻¹.
Momentum is the product of mass and velocity, so the same total momentum must be carried by a larger mass after the collision, which means a lower velocity.
Initial momentum = 60 kg × 4 m s⁻¹ = 240 kg m s⁻¹.
After the collision the combined mass is 100 kg, so v = 240 kg m s⁻¹ ÷ 100 kg = 2.4 m s⁻¹, which is less than the initial 4 m s⁻¹.
Examiner tips
- State the conservation principle first, then explain using m×v; calculate the initial momentum; show the division to find the final speed; mention it is lower than 4 m s⁻¹.
Common mistakes
- Using the wrong total mass (e.g. 60 kg instead of 100 kg); forgetting to divide by the combined mass; giving the final speed as 4 m s⁻¹ instead of a lower value.
Mark scheme (4 marks)
- States that the total momentum before a collision equals the total momentum after a collision (in the absence of external forces)
- States that momentum is a product of mass and velocity, so the combined (greater) mass must move at a lower velocity to conserve momentum
- Correctly identifies that the total momentum before the collision is 240 kg m/s (60 kg × 4 m/s)
- Correctly concludes that the velocity of the combined pair after the collision is less than 4 m/s (e.g. 2.4 m/s), because the same momentum is now shared by a greater total mass
Key terms in this question
momentum · conservation of momentum · velocity · mass
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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