SITEMAP   Physics: Forces & motion 6.2 Conservation of momentum, elastic/inelastic collisions

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Forces and Newton's Laws of Motion 6.2 Explaining the Law of Conservation of Momentum and explaining the difference between elastic and inelastic collisions

Doc Brown's Physics exam study revision notes

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

Keywords, phrases and learning objectives for elastic/inelastic collisions and momentum

Be able to explain and use the Law of Conservation of Momentum.

Know that momentum is conserved in both elastic collisions and inelastic collisions.

Be able to describe and explain the difference between elastic collisions, where kinetic energy is conserved and inelastic collisions in which kinetic energy is not conserved.

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