# 5.9.2 Conservation of Momentum

Higher Tier Only

### Conservation of Momentum

• The principle of conservation of momentum states that:

In a closed system, the total momentum before an event is equal to the total momentum after the event

• A closed system means the energy within the system is constant and the absence of external forces (e.g. friction)
• In other words:

The total momentum before a collision = The total momentum after a collision

• A system is a certain number of objects under consideration
• This can be just one object or multiple objects
• Since momentum is a vector quantity, a system of objects moving in opposite directions (e.g. towards each other) at the same speed will have an overall momentum of 0 since they will cancel out
• Momentum is always conserved over time
• The diagram below shows two masses with velocity u and M at rest (ie. zero velocity) The momentum of a system before and after a collision

• Before the collision:
• The momentum is only of mass m which is moving
• If the right is taken as the positive direction, the total momentum of the system is m × u
• After the collision:
• Mass M also now has momentum
• The velocity of m is now –(since it is now travelling to the left) and the velocity of M is V
• The total momentum is now the momentum of M + momentum of m
• This is (M × V) + (m × –v) or (M × V) – (m × v)

#### Worked Example

The diagram shows a car and a van, just before and just after the car collided with the van, which is initially at rest. Use the idea of conservation of momentum to calculate the velocity of the van when it is pushed forward by the collision.  #### Exam Tip

If it is not given in the question already, drawing a diagram of before and after helps keep track of all the masses and velocities (and directions) in the conversation of momentum questions. ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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