9. Conservation of momentum.

Momentum is the crashing force a body has. Think about this for a minute, what if it hit you would hurt you?

Describe it ...................

A Big mass (weight) would hurt, but only if it was __________ , something standing at rest would not hurt!

A smaller mass travelling at a great ________ would also hurt.

or in symbols

Momentum is a Vector, as you well know, this means its direction is important. For simple 1-D problems it is enough to say that 1 direction is +ive and the other -ive. For higher dimension problems we have to use a number of axis. In the following treatment we shall not deal with anything beyond 2-D, but if you must then all the rules stay the same. This is not complicated.

Simple problems involving momentum

Conservation of momentum

There is the law of Conservation of momentum that says the amount of momentum in a system is constant. So what ever amount of momentum was there in a closed system before a particular collision (or at any time) is the same as it will be after the interaction.


Impulse is defined as the change in momentum

This is very close to the definition for Force,

as a is acceleration which is defined as

Therefore sub this definition of a into the definition of force and you get

Rearrange this to give


Remember this as in questions they may say that there was an impulse of .......

This impulse will come from outside the closed system.

Now do Qs 1 & 2 pg 170

So in the examples in we have to calculate the Impulse for each body in the system, we do this by calculating mv - mu, for each body where u is its original velocity and V its final velocity. The Sum of the Impulses will always add up to zero in a closed system so the Impulse gained by one body is equal to the loss of Impulse by the other body.

Again in 2-D problems we have to break the velocity of the bodies into i & j vectors. The Impulse in each vector will be conserved, that is the amount of Impulse in i before the interaction will be equal to the amount of impulse after the interaction.

Worked Example 7.3

Newtons 3rd law states that for every action there is an equal and opposite reaction

Now go and do the questions 3,4 & 5

Worked Example 7.5

The idea of conservation of momentum means that no external force is applied. In the problem there is no horizontal force being applied.

Conservation of momentum with 2 bodies

This is the 1st equation that you will NEED to use in Every question, usually solving this leads to 5 marks.

Conservation of momentum with 2 bodies problem scenarios

  1. Both moving before hand, both moving after,
  2. 1 body moving the other at rest, both move after,
  3. 2 bodies move and they stick together
  4. 2 bodies at rest, then one is fired ....

So how would you solve these?

Now go and do the rest of the questions on page 171.

Q10 Calculate the velocity that the block and bullet will have initially, remember the conservation of energy ½mv2 = mgh, et woila !!!

If there are no forces in a plane

then the bodies in that plane will have their

momentum conserved

If the only force externally applied is gravity then the potential energy will be turned into kinetic energy at the lowest point, but the amount of energy will be conserved.