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Space, Time and Motion

Conservation of momentum and collisions

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on the conservation of momentum and why it follows from Newton's third law, the condition for it, trolleys sticking together and the kinetic energy lost, elastic and inelastic collisions, trolleys pushed apart by a spring, signs for direction, head-on collisions, gun and rifle recoil, air track tests, and the Earth's unnoticed momentum change.

What you need to know

Answer each one before you reveal it.

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Key term

Why do momentum directions need signs, and how fast does a 3.2 kg rifle recoil firing a 4.0 g bullet at 400 m s⁻¹?

Key term

State the principle of conservation of momentum.

Key term

Why does conservation of momentum follow from Newton's third law?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the principle of conservation of momentum.

    Model answer

    The total momentum of a system stays constant provided that no resultant external force acts on it.

  2. 2

    Why does conservation of momentum follow from Newton's third law?

    Model answer

    The forces two colliding bodies exert on each other are equal and opposite and act for the same time, so the impulses are equal and opposite and the momentum changes cancel.

  3. 3

    What condition must a system satisfy if its momentum is to be conserved?

    Model answer

    No resultant external force may act on it, so it must be isolated from outside influences such as friction.

  4. 4

    A 2.0 kg trolley moving at 3.0 m s⁻¹ collides with a stationary 1.0 kg trolley and the two move off together. What is their common velocity?

    Model answer

    The total momentum of 6.0 kg m s⁻¹ is shared by 3.0 kg, so the common velocity is 2.0 m s⁻¹.

  5. 5

    A 2.0 kg trolley at 3.0 m s⁻¹ sticks to a stationary 1.0 kg trolley and they move off at 2.0 m s⁻¹. What is the kinetic energy lost?

    Model answer

    Before the collision the kinetic energy is ½ × 2.0 × 3.0² = 9.0 J and afterwards it is ½ × 3.0 × 2.0² = 6.0 J, so 3.0 J is lost.

  6. 6

    What distinguishes an elastic collision from an inelastic one?

    Model answer

    Kinetic energy is conserved in an elastic collision but not in an inelastic one, although momentum is conserved in both.

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