Conservation of Momentum (WJEC GCSE Physics)

• The principle of conservation of momentum states that:

The total momentum before an interaction is equal to the total momentum after an interaction, if no external forces are acting on the objects

• In this context, an interaction can be either:
  • A collision i.e. where two objects collide with each other
  • An explosion i.e. where a stationary object explodes into two (or more) parts

Collisions

• For a collision between two objects:

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

• Before the collision:
  • The momentum is only generated by mass m  because it is the only moving object
  • 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 -v  (since it is now travelling to the left) and the velocity of M  is V
  • The total momentum is now the momentum of M + the momentum of m
  • This is (M  × V) + (m  × -v) or (M  × V) – (m × v) written more simply

Momentum Before and After a Collision

The momentum of a system before and after a collision where the momentum before equals the momentum after

 Newton's Third Law in Collisions

• According to Newton's Third Law:
  • When two objects collide, both objects will react, generally causing one object to speed up (gain momentum) and the other object to slow down (lose momentum)

Equal and Opposite Forces on Two Colliding Objects

Newton's third law can be applied to collisions. Here the force of trolley A on B is equal and opposite to the force of trolley B on A.

• Consider the collision between two trolleys, A and B:
  • Trolley A exerts a force on trolley B
  • Trolley B exert an equal force on trolley A in the opposite direction

• This can be written as:

Higher Tier

Explosions

• Examples of explosions include:
  • A person jumping off a skateboard
  • A cannon or bullet being fired
  • A firework exploding
  • A person being thrown from a vehicle
  • The separation of space vehicles
• As with collisions, the principle of conservation of momentum equations can be applied:
  • The mass of the separate objects = the mass of the original object
  • The initial velocity (and therefore, momentum) of the object is 0

• Remember that velocity is a vector, so it considers the direction of the speed of each component
  • Some will travel in a positive direction and others in a negative direction
  • When they are all added together the resultant velocity = 0

Momentum of a Dynamite Explosion

The sum of the masses of the exploded pieces equals the mass of the original dynamite and the sum of the velocities of the separate pieces equals zero.

Higher Tier

• In both collisions and explosions, momentum is always conserved
  • Energy is always conserved too, but kinetic energy might not always be conserved

• A collision (or explosion) is either:
  • Elastic – if the kinetic energy is conserved
  • Inelastic – if the kinetic energy is not conserved

• Collisions are instances when objects collide with each other:
  • Elastic collisions are usually when the colliding objects do not stick together and then they move in opposite directions
  • Inelastic collisions are usually when colliding objects stick together after the collision

  Elastic and Inelastic Collisions

Elastic collisions are where two objects move in opposite directions. Inelastic collisions are where two objects stick together

• To find out whether a collision is elastic or inelastic, compare the kinetic energy before and after the collision
• The equation for kinetic energy is:

• Where:
  • KE = kinetic energy (J)
  • m = mass (kg)
  • v = velocity (m/s)