A-level · Momentum

Conservation of linear momentumExam-style questions

The principle that the total momentum of a system is unchanged by a direct collision — how to set it up with a consistent positive direction, the special case where the bodies coalesce (stick together) and move with a common velocity, and how to read the sign of the answer as a direction.

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19 questions · A Level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A light inextensible string has particle $P$ , of mass $5m$ , attached to one end and particle $Q$ , of mass $3m$ , attached to the other. The particles are on a smooth horizontal table, and the string is slack.

$P$ is at rest and $Q$ is sliding across the table, directly away from $P$ , with speed $8u$ . When the string becomes taut, $P$ is jerked into motion, and from then on the two particles move with a common speed.
(a) Find, in terms of $u$ , the speed of $P$ immediately after the string becomes taut.

(2 marks)
(b) Find the magnitude of the impulse that the string exerts on $Q$ as it becomes taut, giving your answer in terms of $m$ and $u$ .

(3 marks)
Level 2 · 5 marksTry it
2
A particle $A$ of mass $4\text{ kg}$ moving at $5\text{ m s}^{-1}$ collides directly with a stationary particle $B$ of mass $2\text{ kg}$ . After the collision $A$ continues in the same direction at $2\text{ m s}^{-1}$ . Find the speed of $B$ after the collision. (3 marks)
Level 2 · 3 marksTry it
3
A truck of mass $2000\text{ kg}$ moving at $6\text{ m s}^{-1}$ collides with a stationary truck of mass $1000\text{ kg}$ . The trucks couple together on impact. Find their common speed after coupling. (3 marks)
Level 2 · 3 marksTry it
4
A particle of mass $3\text{ kg}$ moving at $6\text{ m s}^{-1}$ collides directly with a particle of mass $5\text{ kg}$ moving in the same direction at $2\text{ m s}^{-1}$ . The particles coalesce.

Find the speed of the combined particle after the collision. (3 marks)
Level 2 · 3 marksTry it
5
A railway truck of mass $1500\text{ kg}$ moving at $4\text{ m s}^{-1}$ catches up and couples with a truck of mass $2500\text{ kg}$ moving at $1.2\text{ m s}^{-1}$ in the same direction.

Find their common speed after coupling. (3 marks)
Level 2 · 3 marksTry it

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