A-level · Momentum

Linear momentumExam-style questions

Linear momentum p = mv as a vector quantity in one dimension — how the sign carries the direction of motion, how to combine the momenta of several particles, and how to find a change in momentum by working with velocities (with signs) rather than speeds.

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

DifficultyAll Level 1 Level 2 Level 3 Level 4

1
Figure 1Diagram not accurately drawn.

Two particles, $P$ and $Q$ , have masses $4m$ kg and $3m$ kg respectively. Initially both particles are stationary on a rough horizontal surface, with $PQ = 2$ m, as shown in Figure 1. The coefficient of friction between each particle and the surface is $\mu$ .

$P$ is given an impulse of magnitude $J$ N s, which sets it moving along the surface towards $Q$ with speed $5\text{ m s}^{-1}$
(a) Find $J$ in terms of $m$ .

(2 marks)

When $P$ reaches $Q$ , its speed has fallen to $3\text{ m s}^{-1}$
(b) Find the value of $\mu$

(7 marks)

$P$ then collides directly with $Q$ . Immediately after the impact, $Q$ is moving with speed $3.2\text{ m s}^{-1}$
(c) Find the speed of $P$ at this instant.

(3 marks)
Level 4 · 12 marksTry it
2
A particle of mass $2\text{ kg}$ moves in a straight line with velocity $v = 3t^{2}\text{ m s}^{-1}$ at time $t$ seconds.
(a) Find the momentum of the particle when $t = 2$ . (3 marks)
(b) Find the change in momentum between $t = 1$ and $t = 2$ . (2 marks)
Level 4 · 5 marksTry it
3
Two ice skaters, of masses $60\text{ kg}$ and $75\text{ kg}$ , stand at rest facing each other. They push apart, and the lighter skater moves off at $1.5\text{ m s}^{-1}$ .
(a) Find the speed of the heavier skater. (4 marks)
(b) State the total momentum of the two skaters after they separate, justifying your answer. (1 mark)
Level 4 · 5 marksTry it