The Principle of Conservation of Momentum
- The principle of conservation of linear momentum states:
The total momentum before a collision = the total momentum after a collision provided no external force acts
- Linear momentum is the momentum of an object that only moves in one dimension
- Momentum is a vector quantity
- This means oppositely-directed vectors can cancel each other out resulting in a net momentum of zero
- If after a collision an object starts to move in the opposite direction to which it was initially travelling, its velocity will now be negative
- Momentum, just like energy, is always conserved
The conservation of momentum for two objects A and B colliding then moving apart
External and Internal Forces
- External forces are forces that act on a structure from outside e.g. friction and weight
- Internal forces are forces exchanged by the particles in the system e.g. tension in a string
- Forces which are internal or external will depend on the system itself, as shown in the diagram below:
Internal and external forces on a mass on a spring
- Systems with no external forces may be described as ‘closed’ or ‘isolated’
- These are keywords that refer to a system that is not affected by external forces
- For example, a swimmer diving from a boat:
- The diver will move forwards, and, to conserve momentum, the boat will move backwards
- This is because the momentum beforehand was zero and no external forces were present to affect the motion of the diver or the boat
Worked example
Trolley A of mass 0.80 kg collides head-on with stationary trolley B whilst travelling at
3.0 m s–1. Trolley B has twice the mass of trolley A. On impact, the trolleys stick together.
Using the conservation of momentum, calculate the common velocity of both trolleys after the collision.