Conservation of Momentum (OCR A Level Physics)

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Dan MG

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Dan MG

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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:

p subscript A i end subscript plus space p subscript B i end subscript space equals space p subscript A f end subscript plus space p subscript B f end subscript

  • Where:
    • p subscript A i end subscript = initial momentum of A, measured in kg m s−1
    • p subscript B i end subscript = initial momentum of B, measured in kg m s−1
    • p subscript A f end subscript = final momentum of A, measured in kg m s−1
    • p subscript B f end subscript = final momentum of B, measured in kg m s−1

Conservation of momentum example: collision

  • Ball A moves with an initial velocity of u subscript A
  • 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

p subscript b e f o r e end subscript space equals space m subscript A u subscript A space plus space 0

    • The total momentum after the collision is

p subscript a f t e r end subscript space equals space minus m subscript A v subscript A space plus thin space m subscript B v subscript B

    • 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

m subscript A u subscript A space equals space m subscript B v subscript B space minus space m subscript A v subscript A

Conversation of Momentum, downloadable AS & A Level Physics revision notes

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:

4-5-external-and-internal-forces-on-a-mass-on-a-spring

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

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.

Worked example - 1D momentum quesions solution

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Dan MG

Author: Dan MG

Expertise: Physics

Dan graduated with a First-class Masters degree in Physics at Durham University, specialising in cell membrane biophysics. After being awarded an Institute of Physics Teacher Training Scholarship, Dan taught physics in secondary schools in the North of England before moving to SME. Here, he carries on his passion for writing enjoyable physics questions and helping young people to love physics.