Explain why two ice skaters, initially at rest, move in opposite directions after pushing off from each other.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Two ice skaters stand face-to-face on a frictionless ice rink. Skater A has a greater mass than Skater B. They push off from each other and move apart.
Model answer (4 marks)
The total momentum of the two‑skater system is zero before the push because they are initially at rest.
No external horizontal force acts on the system, so by conservation of momentum the total momentum must remain zero after the push.
During the push the skaters exert equal and opposite forces on each other (Newton’s third law).
Because the forces are equal and act for the same time, the changes in momentum of the two skaters are equal in magnitude and opposite in direction. Thus each skater gains a momentum that cancels the other’s, giving opposite directions of motion.
Since Skater A has a larger mass, the equal magnitude of momentum gives Skater A a smaller speed than Skater B (p = mv).
No external horizontal force acts on the system, so by conservation of momentum the total momentum must remain zero after the push.
During the push the skaters exert equal and opposite forces on each other (Newton’s third law).
Because the forces are equal and act for the same time, the changes in momentum of the two skaters are equal in magnitude and opposite in direction. Thus each skater gains a momentum that cancels the other’s, giving opposite directions of motion.
Since Skater A has a larger mass, the equal magnitude of momentum gives Skater A a smaller speed than Skater B (p = mv).
Examiner tips
- Use the conservation of momentum to justify the zero total momentum after the push.
- Mention Newton’s third law to explain equal and opposite forces.
- Show that equal magnitude momenta give opposite directions.
- Explain the speed difference using p = mv and the mass ratio.
Common mistakes
- Claiming the skaters move in the same direction; they move opposite due to equal and opposite momenta.
- Forgetting to state that no external horizontal force acts on the system.
- Confusing momentum with force magnitude; the forces are equal but the resulting speeds differ because of mass.
Mark scheme (4 marks)
- The total momentum of the system before the push is zero, so the total momentum must remain zero after the push (conservation of momentum / no external horizontal force acts on the system).
- By Newton's third law, the force Skater A exerts on Skater B is equal in magnitude and opposite in direction to the force Skater B exerts on Skater A.
- Since the forces are equal and opposite, the momenta gained are equal in magnitude and opposite in direction, so the skaters move in opposite directions.
- Because Skater A has greater mass, Skater A moves with a smaller speed than Skater B (since momentum = mass × velocity and both momenta are equal in magnitude).
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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