Momentum and collisions, solved with clear bookkeeping
Collision problems are accounting problems: define a positive direction, total before, total after. Sign errors cause most lost marks.
What this covers
- Momentum p = mv and impulse
- Conservation in collisions
- Elastic vs inelastic collisions
- Explosions and recoil
- Two-dimensional collisions
Worked example
Problem
A 2 kg cart at 3 m/s hits a stationary 1 kg cart and they stick together. Final speed?
- 1Momentum before(2 × 3) + (1 × 0) = 6 kg·m/s.
- 2Momentum afterCombined mass 3 kg moving at v: 3v.
- 3Set equal and solve3v = 6 → v = 2.
Answer: 2 m/s in the original direction
Mistakes that cost marks
- Assuming kinetic energy is conserved in an inelastic collision.
- Forgetting that velocity is a vector — direction needs a sign.
- Using masses separately after objects stick together.
Questions students ask
Is momentum always conserved?
Yes, when no external force acts on the system — which is why choosing the system boundary matters.
Practise mechanics until it sticks
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