Conservation of momentum in collisions revision notes

Edexcel International GCSE Physics (4PH1), chapter 4: Momentum, specification point 1.27P. Free lesson.

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In a collision, total momentum before equals total momentum after if no external force acts. You can use this rule to find an object's velocity after a collision, including when objects move in opposite directions.

What conservation of momentum means

Momentum is conserved when the total stays the same. In a collision, the total momentum before equals the total momentum after, provided no external force acts. An external force comes from outside the colliding objects, such as friction. State the full rule: total momentum before = total momentum after. Saying only “momentum is conserved” repeats the question and does not state the rule.

How to solve a collision question

Keep track of every object's momentum before and after the collision. If the objects stick together, they have one shared velocity, so treat them as one combined mass.

When two trolleys stick together

A 2 kg trolley moving at 3 m/s hits a stationary 1 kg trolley. They stick together, so their combined mass is 3 kg and they share one velocity, v. Before: 2 × 3 + 1 × 0 = 6 kg m/s. After: (2 + 1) × v = 3v. Set before equal to after: 3v = 6, so v = 2 m/s. The positive result means the trolleys move in the same direction as trolley A.

Count every object after the collision

A 0.4 kg ball moving at 5 m/s hits a stationary 0.6 kg ball. After the collision, ball A is still moving at 0.5 m/s, while ball B moves at an unknown velocity, v. Both balls must be included in the total after. Before: ball A has momentum 0.4 × 5 = 2 kg m/s. Ball B has momentum 0.6 × 0 = 0. After: ball A has momentum 0.4 × 0.5 = 0.2 kg m/s. Ball B has momentum 0.6v. Equate the totals: 2 = 0.2 + 0.6v. So 1.8 = 0.6v, giving v = 3 m/s.

Use negative velocity for the opposite direction

Choose one direction as positive. An object moving the other way has a negative velocity, so its momentum is negative too. This lets the total before account for both directions. Take right as positive. For a 3 kg trolley moving right at 4 m/s and a 1 kg trolley moving left at 6 m/s, their velocities are +4 m/s and −6 m/s. Before: 3 × 4 + 1 × (−6) = 6 kg m/s. They stick together, so after: (3 + 1) × v = 4v. Equate: 4v = 6, so v = 1.5 m/s. The result is positive, so the joined trolleys move to the right.