Momentum and collisions: the momentum equation p = mv, conservation of momentum in a closed system, force as the rate of change of momentum, and how safety features reduce force.

What this dot point is asking

Edexcel wants you to recall and use the momentum equation, to apply the conservation of momentum to collisions and explosions in a closed system, to use force as the rate of change of momentum, and to explain how safety features such as crumple zones, air bags and seat belts reduce the force in a crash.

The momentum equation

Because momentum is a vector, direction matters: objects moving in opposite directions have momenta of opposite sign. A heavy, fast object has a large momentum and is hard to stop, which is why a lorry is far more dangerous in a crash than a bicycle moving at the same speed.

Conservation of momentum

Conservation of momentum is one of the most powerful tools in mechanics. Add up the momentum of every object before the event (taking direction into account with signs), and that total must equal the momentum afterwards. In an explosion starting from rest the total momentum is zero, so the fragments must move off in opposite directions with equal-sized momenta.

Force and the rate of change of momentum

This is another form of Newton's second law: a force is whatever changes an object's momentum, and the bigger the change or the shorter the time, the bigger the force. Rearranged, it explains every vehicle safety feature: for a fixed change in momentum, increasing the time of the change reduces the force.

How Edexcel examines this

Momentum is a Higher-tier focus and a frequent source of four to six mark questions. Conservation-of-momentum calculations are the staple: you are given the masses and velocities before a collision (often two trolleys, with one stationary) and asked for the velocity afterwards, sometimes when the objects stick together. The mark scheme rewards writing total momentum before equals total momentum after, substituting carefully with the correct signs for direction, and remembering to combine the masses when objects join. The other common style is an explanation question on safety features, where the full-mark answer must connect a longer collision time to a smaller rate of change of momentum and therefore a smaller force, quoting $F = \dfrac{m \Delta v}{t}$. Examiners penalise the loose claim that air bags or crumple zones "reduce the momentum change"; the change in momentum is fixed by the velocity lost, and it is the force that is reduced by spreading that change over more time.

Try this

Q1. Calculate the momentum of a $1500\,\text{kg}$ car moving at $12\,\text{m/s}$. [2 marks]

• Cue. $p = mv = 1500 \times 12 = 18000\,\text{kg m/s}$.

Q2. State what happens to the total momentum of a closed system during a collision. [1 mark]

• Cue. It is conserved (stays the same).