Conservation of Momentum (AQA A Level Physics)

The Principle of Conservation of Momentum

• The principle of conservation of linear momentum states:

  The total momentum before a collision is equal to the total momentum after a collision, provided no external force acts

• Therefore:

  momentum before = momentum after

• Momentum is a vector quantity, therefore:

  • opposing vectors can cancel each other out, resulting in a net momentum of zero

  • an object that collides with another object and rebounds, has a positive velocity before the collision and a negative velocity after 

• Momentum, just like energy, is always conserved

• If objects A and B collide, their momenta before and after are related by the following equation:

• Where:

  • = initial momentum of A, measured in kg m s⁻¹

  • = initial momentum of B, measured in kg m s⁻¹

  • = final momentum of A, measured in kg m s⁻¹

  • = final momentum of B, measured in kg m s⁻¹

Conservation of momentum example: collision

• Ball A moves with an initial velocity of

• Ball A collides with Ball B which is stationary

• After the collision, both balls travel in opposite directions

  • Taking the direction of the initial motion of Ball A as the positive direction (to the right) 

  • The total momentum before the collision is

    

  • The total momentum after the collision is

    

  • The minus sign shows that Ball A travels in the opposite direction to the initial travel 

  • If an object is stationary like Ball B is before the collision, then it has a momentum of 0

• From the conservation of momentum, one can equate these expressions

The conservation of momentum for two objects A and B colliding then moving apart

External and Internal Forces

• Note that the definition of the law of conservation of momentum states that it only applies when no external forces act

  • External forces are forces that act on a structure or system 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

  • In these systems, total momentum is conserved

• 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 horizontal motion of the diver or the boat