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
Two particles, $P$ and $Q$ , of masses $3m$ and $4m$ respectively, move on a smooth horizontal surface. They travel along a straight line towards each other, $P$ at speed $5u$ and $Q$ at speed $2u$ , and collide directly.

The collision reverses the direction of motion of both particles. Immediately after the collision, the speed of $P$ is $v$ and $Q$ is moving twice as fast as $P$ .
(a) Show that $v = \dfrac{7}{5}u$

(3 marks)
(b) Find, in terms of $m$ and $u$ , the magnitude of the impulse that $P$ exerts on $Q$ in the collision.

(3 marks)
Level 3 · 6 marksTry it
2
Two particles move towards each other along the same straight line. $P$ (mass $5\text{ kg}$ ) moves at $4\text{ m s}^{-1}$ and $Q$ (mass $3\text{ kg}$ ) moves at $6\text{ m s}^{-1}$ . They collide and coalesce. Find the speed and direction of the combined particle. (4 marks)
Level 3 · 4 marksTry it
3
A particle $A$ of mass $2\text{ kg}$ moving at $8\text{ m s}^{-1}$ collides directly with a stationary particle $B$ of mass $6\text{ kg}$ . After the collision $B$ moves in $A$ 's original direction at $3\text{ m s}^{-1}$ . Find the velocity of $A$ after the collision, and state whether $A$ has reversed its direction. (4 marks)
Level 3 · 4 marksTry it
4
A particle $P$ of mass $4\text{ kg}$ moving at $5\text{ m s}^{-1}$ collides directly with a stationary particle $Q$ of mass $m\text{ kg}$ . The particles coalesce and move on together at $2\text{ m s}^{-1}$ . Find $m$ . (3 marks)
Level 3 · 3 marksTry it
5
Particles $P$ (mass $2\text{ kg}$ ) and $Q$ (mass $6\text{ kg}$ ) move towards each other along the same straight line, $P$ at $7\text{ m s}^{-1}$ and $Q$ at $3\text{ m s}^{-1}$ . They collide and coalesce.

Find the velocity of the combined particle, and state its direction. (4 marks)
Level 3 · 4 marksTry it

4 more questions on conservation of linear momentum

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