Pearson Edexcel IAL Mathematics M1.4.3 Momentum & impulse

Practise one-dimensional collisions and impulses, using momentum equations to find speeds, directions, constants and impulses after impact.

Exam points

use impulse-momentum for one particle, with signs showing direction before and after collision
apply conservation of linear momentum to two particles to find a speed or unknown mass constant
combine suvat with impulse when a particle hits the ground and rebounds

[Maximum number: 7]

A particle P has mass k m and a particle Q has mass m. The particles are movide direct each other in opposite directions along the same straight line when they collide directis

Immediately before the collision, P has speed 3 u and Q has speed u.
As a result of the collision, the direction of motion of each particle is reversed and the speed of each particle is halved.

(a)

Find the value of k.

[ 4 ]

Figure for Answer to Question (a) — Edexcel A-Level Mathematics AS

CLM: $k m \times 3 u-m u=-k m \times \frac{3}{2} u+m \times \frac{1}{2} u$

M1 A1 A1

$k=\frac{1}{3}$

A1

(4)

(b)

Find, in terms of m and u, the magnitude of the impulse exerted on Q in the collision.

[ 3 ]

$I=m\left(\frac{1}{2} u--u\right) \quad$ OR $\quad I=\frac{1}{3} m\left(\frac{3}{2} u--3 u\right)$

M1 A1

$I=\frac{3}{2} m u \quad$ must be positive

A1

(3)

(7)

Notes for question 2

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M1.4.3 - Momentum and impulse question 1

Question (a)

Question (b)