As long as no external forces are acting on the objects involved, the total momentum stays the same in explosions and collisions. We say that momentumA quantity relating to a moving object that is calculated by multiplying its mass by its velocity. is conserved.
You can use this idea to work out the massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g)., velocityThe speed of an object in a particular direction. or momentum of an object in an explosion or collision.
Momentum calculations
Here is a worked example.
Two railway carriages collide and move off together. Carriage A has a mass of 12,000 kg and moves at 5 m/s before the collision. Carriage B has a mass of 8,000 kg and is stationary before the collision. What is the velocity of the two carriages after the collision?
Step one
Work out the total momentum before the event (before the collision).
\(\text{p} = {\text{m}}\times{\text{v}}\)
Momentum of carriage A before = 12,000 × 5 = 60,000 kg m/s
Momentum of carriage B before = 8,000 × 0 = 0 kg m/s
Total momentum before = 60,000 + 0 = 60,000 kg m/s
Step two
Work out the total momentum after the event (after the collision).
Because momentum is conserved, total momentum afterwards = 60,000 kg m/s.
Step three
Work out the total mass after the event (after the collision).
Total mass = mass of carriage A + mass of carriage B = 12,000 + 8,000 = 20,000 kg
Step four
Work out the new velocity.
p = m × v, but we can rearrange this equation so that v = p ÷ m
Velocity (after the collision) = 60,000 ÷ 20,000 = 3 m/s
Watch this illustrated podcast on momentum for a summary of how momentum and motion are related.