The big idea: Click two pool balls together and they swap speeds; a Newton's cradle sends one ball off the far end. Nothing gets lost — the motion just gets shared out.
That's conservation of momentum: with no outside push, the total momentum before a collision equals the total after (momentum = mass × velocity, and mind the directions).
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Spot it — and mind the signs: Velocity has a direction, so give one way + and the other −. A cart moving left at 2 m s⁻¹ has velocity −2 m s⁻¹.
Add up m × v for every object before, and it must equal the same total after.
Two kinds of collision: Momentum is always conserved in both — but kinetic energy is not.
- Elastic: kinetic energy is also conserved (KE before = KE after). Things bounce cleanly. - Inelastic: some KE turns into heat/sound. If they stick together it is perfectly inelastic (most KE lost).
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Momentum of one object is mass × velocity. This one is given in the data booklet:
- momentum (kg m s⁻¹)
- mass (kg)
- velocity — carries a sign for direction (m s⁻¹)
Conservation of momentum then says the total before equals the total after. (This is a principle — it is not printed as an equation, so you write it out yourself.)
- the two masses (kg)
- velocities before the collision (m s⁻¹)
- velocities after the collision (m s⁻¹)
How to use it: 1. Pick a positive direction.
2. Write m × v for everything before and add them.
3. Set that equal to the total after, then solve for the unknown.
Keep every minus sign.
A 2.0 kg trolley moving right at 3.0 m s⁻¹ hits a stationary 1.0 kg trolley. They do not stick: the 2.0 kg trolley continues at 1.0 m s⁻¹. Find the velocity of the 1.0 kg trolley afterwards.
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How this is tested — collisions appear as a full Paper 2 calculation and quick Paper 1A MCQs. Two flavours:
Paper 1A
- Read cart velocities off a v–t graph.
- Quick 'is it elastic?' or stick-together question.
Paper 2
- 'Show that' a collision is elastic (compare KE before and after).
- Find a common speed after two things stick.
The classic trap: Assuming kinetic energy is conserved. Momentum is always conserved; KE is conserved only if the collision is elastic. When objects stick, KE is lost.
Testing for elastic — use kinetic energy: Kinetic energy is the energy of motion. It is given in the booklet:
- kinetic energy (J)
- mass (kg)
- speed (m s⁻¹)
Work out the total KE before and the total KE after. If they're equal, the collision is elastic.
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Watch the graph build step by step in study mode.
Two 1.5 kg trolleys: X moves at 5.0 m s⁻¹ toward a stationary Y. After colliding, X moves at 1.0 m s⁻¹ and Y at 4.0 m s⁻¹ (same direction). Show that the collision is elastic.
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See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.