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Further Mechanics

Conservation of momentum in two dimensions

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  • Papers 1 and 3

Overview

Recall questions on resolving momenta into components, why magnitudes cannot simply be added, and applying conservation to an explosion or a glancing collision.

What you need to know

Answer each one before you reveal it.

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Key term

What does conservation of linear momentum state, and why can momenta in two dimensions not simply be added as magnitudes?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    A tennis ball of mass 0.058 kg leaves a racket at 45 m s⁻¹ from rest after a contact time of 5.0 ms. What average force acted on it?

    Model answer

    The change of momentum is 0.058 × 45 = 2.61 kg m s⁻¹, so the average force is 2.61 ÷ (5.0 × 10⁻³) = 522 N, or 520 N to 2 significant figures.

  2. 2

    State the principle of conservation of linear momentum:

    Model answer

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

  3. 3

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

    Model answer

    Two interacting bodies exert equal and opposite forces on each other for the same length of time, so they receive equal and opposite impulses and their momentum changes cancel exactly.

  4. 4

    How is conservation of momentum applied to a collision that is not along a single line?

    Model answer

    Momentum is conserved independently in two perpendicular directions, so the momenta are resolved into components and the totals before and after are equated in each direction separately.

  5. 5

    Why can momenta in two dimensions not simply be added as magnitudes?

    Model answer

    Momentum is a vector, so only components along a common axis may be added arithmetically; otherwise vector addition is required.

  6. 6

    A stationary object explodes into exactly two fragments. What can be said about their momenta?

    Model answer

    The two fragments must carry equal magnitudes of momentum in exactly opposite directions, so that the total remains zero.

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