Conservation of Momentum (OCR AS Physics)

• 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