6.2 The Law of Conservation of Momentum

Here we will consider collisions between two objects in a closed system.

Here a closed system here means no other external forces affect the situation e.g. a collision between two objects - the event.

If an external force like friction is involved, total momentum cannot be conserved.

The total momentum of an event in a closed system is the same before and after the event (e.g. a collision between two objects).

This is called the 'Law of Conservation of Momentum' and you can use it do lots of calculations!

e.g. total momentum of two colliding objects = total moment of objects after collision

e.g. for two colliding objects, where p = momentum: p₁ + p₂ = p₃ + p₄

substituting m and v for the mass and velocity gives ...

m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄

where v₁ and v₂ are the initial velocities and v₃ and v₄ the velocities after the collision,

(you are assuming there is no change in mass, i.e. no bits have flown off!)

and if two objects stick together' after the collision then: p₁ + p₂ = p₃

substituting m and v for the mass and velocity gives ...

m₁v₁ + m₂v₂ = m₃v₃   (where m₃ = m₁ + m₂)

where v₁ and v₂ are the initial velocities and v₃ and m₃ (m₃ = m₁ + m₂) are the final velocity and mass after the collision.

In other words the large object formed by collision has the momentum equal to the two momentums of the colliding objects added together.

 

Momentum is conserved for both elastic and inelastic collisions

For a perfect elastic collision, no kinetic energy is lost - kinetic energy conserved.

In an elastic collision, the total energy in the kinetic energy stores of the colliding objects is the same as before and after the collision.

You will not have to solve problems for elastic collisions - the maths is too difficult for GCSE level physics, with two sets of equations, for momentum (mv) and kinetic energy (E = ½mv²), to solve e.g. for the resultant velocities!

For an inelastic collision, kinetic energy is not conserved - kinetic energy is lost in some form e.g. heat or sound.

In an inelastic collision, some of the moving objects kinetic energy stores are lost and transferred to other energy stores of the objects themselves or the environment.

This is because the atoms are bashed together increasing their potential energy store (compressed for a fraction of a second). They 'relax' to their normal state by losing the energy as heat  (thermal energy) or sound.

For inelastic collisions you can solve a variety of problems using the principle of 'conservation of momentum'.

See 6.4 for more complex momentum calculations

 Problem solving questions of more complex momentum calculations

Using SEARCH some initial results may be ad links you can ignore - look for docbrown

INDEX physics notes: Conservation of momentum, elastic and non-elastic collisions, Newton's 2nd law calculations - problem solving