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Cambridge IGCSE Physics · 0625

Chapter 1: Motion, forces and energy — Part 8

Topic 1.6 · Momentum

Momentum and impulse

Momentum p = mv. Unit: kg m/s. Momentum is a vector — give a direction (or use + and − in one dimension).

Impulse = force × time for which the force acts = FΔt = Δ(mv). Impulse equals change in momentum.

A 0.50 kg ball moves at 8.0 m/s to the right. Calculate its momentum.

Worked example: momentum is 0.50 times 8.0 equals 4.0 kilogram metres per second to the right
p = mv = 4.0 kg m/s to the right.

A resultant force of 15 N acts on a 0.60 kg object for 0.20 s, starting from rest. Calculate the impulse and the speed reached.

Worked example: impulse 3.0 kilogram metres per second, speed 5.0 metres per second
Impulse F Δt = 3.0 kg m/s = Δ(mv), so v = 5.0 m/s.

Conservation of momentum

In a closed system (no external resultant force), total momentum is conserved in one dimension.

total momentum before = total momentum after. Take one direction as positive.

A 2.0 kg trolley moving at 3.0 m/s collides with a 1.0 kg trolley at rest. They stick together. Calculate their speed after the collision.

Worked example: conservation of momentum, combined speed 2.0 metres per second
Total momentum before = 6.0 kg m/s = 3.0 v, so v = 2.0 m/s.

Resultant force is also the change in momentum per unit time: F = Δp / Δt.

One-dimensional collision: two trolleys before and after impact, with arrows for velocity, showing total momentum before equals total momentum after (including a rebound with a negative velocity).
Diagram 1: One-dimensional collision: two trolleys before and after impact, with arrows for velocity, showing total momentum before equals total momentum after (including a rebound with a negative velocity).

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