3.2.1 Conservation of Momentum

• The principle of conservation of momentum is:
  • The total momentum of a system remains constant provided no external force acts on it

• For example if two objects collide:

the total momentum before the collision = the total momentum after the collision

• Remember momentum is a vector quantity. This allows oppositely-directed vectors to cancel out so the momentum of the system as a whole is zero
• Momentum is always conserved over time

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
• Which forces 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

• You may also come across a system with no external forces being described as a ‘closed’ or ‘isolated’ system
• These all still refer to a system that is not affected by external forces
• For example, a swimmer diving from a boat:
  • The diver will move forward, and, to conserve momentum, the boat will move backwards

• This is because the momentum beforehand was zero and no external forces are present to affect the motion of the diver or the boat

One-dimensional momentum problems

• Momentum (p) is equal to: p = m × v
• Using the conversation of linear momentum, it is possible to calculate missing velocities and masses of components in the system. This is shown in the example below

• To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
  • If the kinetic energy is conserved, it is an elastic collision
  • If the kinetic energy is not conserved, it is an inelastic collision

• Elastic collisions are commonly those where objects colliding do not stick together and then move in opposite directions
• Inelastic collision are where objects collide and stick together after the collision

Two-dimensional momentum problems

• Since momentum is a vector, in 2D it can be split up into its x and y components
• Review revision notes 1.3 Scalars & Vectors on how to resolve vectors