How do you calculate momentum and use conservation of momentum?
Short answer
Momentum = mass × velocity, written p = mv, in kilogram metres per second (kg m/s). In a collision or explosion with no external forces, total momentum before equals total momentum after. Because velocity has a direction, momentum does too: give one direction a negative sign.
Step by step
- Choose a positive direction.
- Calculate the momentum of each object before the event, using negative signs for the opposite direction.
- Add them to get the total momentum before.
- Write the total momentum after in terms of the unknown.
- Set before equal to after and solve.
Worked example
A 2 kg trolley at 3 m/s hits a stationary 1 kg trolley and they move off together
- Before: 2 × 3 + 1 × 0 = 6 kg m/s
- After: (2 + 1) × v = 3v
- 3v = 6, so v = 2 m/s
Common mistakes
- Ignoring direction, so momenta that should cancel are added.
- Forgetting to combine masses when objects stick together.
- Confusing momentum with kinetic energy. Kinetic energy is often lost in collisions; momentum is conserved.
Useful for:GCSEA LevelWAECMatric
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