A tennis ball travelling at 20 m/s strikes a stationary wall and bounces back in the opposite direction at 15 m/s. The contact time between the ball and the wall is very short. Explain, using Newton's laws of motion and the concept of momentum, what happens to the tennis ball during and after the collision, and why the wall does not appear to move.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A tennis ball of mass 0.06 kg strikes a wall and bounces back. The ball is in contact with the wall for 0.005 s.
Model answer (5 marks)
The ball’s momentum changes from 0.06 kg×20 m s⁻¹=1.2 kg m s⁻¹ to 0.06 kg×(−15 m s⁻¹)=−0.9 kg m s⁻¹, a change of 2.1 kg m s⁻¹. This change is produced by an impulse during the 0.005 s contact, so the average force on the ball is F=Δp/Δt=2.1/0.005=420 N. By Newton’s second law the ball experiences this force and its velocity reverses.
According to Newton’s third law the ball exerts an equal and opposite force on the wall. The wall’s momentum changes by the same amount but in the opposite direction, so the total momentum of the ball‑wall system remains zero. Because the wall is attached to a very large mass (the building/Earth), its change in velocity is v=Δp/M≈2.1/(10⁵ kg)≈2×10⁻⁵ m s⁻¹, which is imperceptible, so the wall does not appear to move.
According to Newton’s third law the ball exerts an equal and opposite force on the wall. The wall’s momentum changes by the same amount but in the opposite direction, so the total momentum of the ball‑wall system remains zero. Because the wall is attached to a very large mass (the building/Earth), its change in velocity is v=Δp/M≈2.1/(10⁵ kg)≈2×10⁻⁵ m s⁻¹, which is imperceptible, so the wall does not appear to move.
Examiner tips
- Show the momentum change and calculate Δp; link Δp to impulse via Δp=FΔt; mention Newton’s 2nd and 3rd laws; state conservation of momentum; explain negligible wall motion due to large mass
Common mistakes
- Using the wrong sign for the final momentum; forgetting to include the negative sign for the rebound velocity; neglecting to calculate the force or to mention the impulse; claiming the wall moves significantly because of the force
Mark scheme (5 marks)
- The ball experiences a change in momentum (impulse) because its velocity changes direction
- A resultant force acts on the ball during contact (Newton's second law links force to rate of change of momentum)
- By Newton's third law, the ball exerts an equal and opposite force on the wall
- The total momentum of the ball-wall system is conserved (the change in momentum of the ball is equal and opposite to the change in momentum of the wall)
- The wall does not appear to move because it is attached to a very large mass (the Earth/building), so its change in velocity is negligibly small
Key terms in this question
Related
- All Edexcel A-Level Physics (9PH0) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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