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Topic 6 of 8 · Form 6

Momentum, impulse and collisions

Momentum = mv (N s). Impulse = force × time = change in momentum.

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  1. PDFMomentum, impulse and collisions – Mechanical Mathematics notes (ZIMSEC A Level)45.8 KB

Impulse and momentum

Momentum = mv (N s). Impulse = force × time = change in momentum.

Conservation of momentum

In a collision or explosion with no external impulse, total momentum is conserved.

Newton's law of restitution

Speed of separation = e × speed of approach, where 0 ≤ e ≤ 1 (e = 1 perfectly elastic; e = 0 particles coalesce).

Worked example: A 2 kg sphere moving at 6 m s⁻¹ hits a 4 kg sphere at rest; e = 0.5. Find the velocities after impact.

Momentum: 12 = 2v₁ + 4v₂

Restitution: v₂ − v₁ = 0.5 × 6 = 3

Solving: v₁ = 0, v₂ = 3 m s⁻¹

Kinetic energy lost = 36 − 18 = 18 J

Impact with a wall

The rebound speed = e × approach speed; the impulse on the wall = m(v + ev) for perpendicular impact.

Jerk in strings

When a string tightens suddenly, the connected particles acquire a common speed (momentum conserved along the string).

Exam tip: Use a consistent positive direction and draw before-and-after diagrams for every collision.

Check yourself

  1. A 0.2 kg ball hits a wall at 10 m s⁻¹ and rebounds with e = 0.6. Find the impulse.
  2. Two particles stick together after collision. What is e?
  3. A 3 kg gun fires a 0.01 kg bullet at 600 m s⁻¹. Find the recoil speed.
Show answers
  1. 0.2 × (10 + 6) = 3.2 N s
  2. e = 0
  3. 0.01 × 600 ÷ 3 = 2 m s⁻¹
Next topicMoments and centres of mass

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