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A 'closed system' is something that is not affected by external forces. In a closed system:

total momentum before an event = total momentum after the event

This is called the principle of conservation of momentum. Momentum is conserved in collisions and explosions.

Conservation of momentum explains why a gun or cannon recoils backwards when it is fired. When a cannon is fired, the cannon ball gains forward momentum and the cannon gains backward momentum. Before the cannon is fired (the ‘event’), the total momentum is zero. This is because neither object is moving. The total momentum of the cannon and the cannon ball after being fired is also zero, with the cannon and cannon ball moving in opposite directions.

Calculations involving collisions

Collisions are often investigated using small trolleys. The diagrams show an example.

Before collision

After collision

The principle of conservation of momentum can be used to calculate the velocity of the combined trolleys after the collision.

Example

Calculate the velocity of the trolleys after the collision in the example above.

First calculate the momentum of both trolleys before the collision:

2 kg trolley = 2 × 3 = 6 kgm/s

4 kg trolley = 8 × 0 = 0 kgm/s

Total momentum before collision = 6 + 0 = 6 kgm/s

Total momentum after collision = 6 kgm/s (because momentum is conserved)

Mass after collision = 10 kg

Next, rearrange momentum = mass × velocity to find velocity:

Note that the 2 kg trolley is travelling right before the collision. As its velocity and the calculated velocity after the collision are both positive values, the combined trolleys must also be moving to the right after the collision.