A railway carriage of mass 4000 kg is moving at 3 m/s along a level track. It collides with a stationary carriage of mass 2000 kg. After the collision the two carriages join together and move as one. Explain what happens to the total momentum of the two carriages during the collision, and describe how the velocity of the joined carriages after the collision compares to the velocity of the moving carriage before the collision. Give reasons for your answers.

WJEC A-Level Physics (Wales) — 1.4 Momentum (A-Level only) · Explain · 5 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Model answer (5 marks)

The total momentum of the two carriages is conserved during the collision because no external horizontal force acts on the system. The initial momentum is 4000 kg × 3 m s⁻¹ = 12000 kg m s⁻¹. After the collision the two carriages are joined, so the total mass is 4000 kg + 2000 kg = 6000 kg. By conservation of momentum 12000 kg m s⁻¹ = 6000 kg × v, giving v = 2 m s⁻¹. Thus the velocity of the joined carriages after the collision is 2 m s⁻¹, which is lower than the original 3 m s⁻¹ because the mass has increased while momentum is unchanged.

Examiner tips

  • Show the initial momentum calculation and state conservation of momentum explicitly
  • Explain that the system is closed – no external horizontal force
  • Use the increased total mass to justify the lower final speed
  • Give the numerical final speed 2 m s⁻¹

Common mistakes

  • Confusing momentum with kinetic energy and claiming energy is conserved
  • Failing to calculate the final speed correctly (e.g. using 4000 kg instead of 6000 kg)
  • Not recognising that the system is closed and therefore momentum is conserved

Mark scheme (5 marks)

  1. The total momentum of the two carriages is conserved / stays the same / does not change during the collision
  2. This is because no external (resultant) force acts on the system / it is a closed system
  3. The total mass after the collision is greater than the mass of the moving carriage alone
  4. Because momentum is conserved and the total mass has increased, the velocity after the collision is lower / smaller than 3 m/s
  5. The velocity of the joined carriages is 2 m/s (correct value obtained by applying conservation of momentum: 4000 × 3 = 6000 × v)

Key terms in this question

momentum · velocity · mass

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