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## An Example

Let us take two bodies say two balls. We assume that these balls are in a place where no external forces are acting on them.
Such a place would be called an isolated system. Let one ball be moving along a straight line with velocity v_{1}
and let the other ball be moving with a velocity v_{2}. Now these velocities are different.
So, as both balls are moving along the same line, they will hit each other at some point of time if the ball,
which is following is moving at a faster speed. If you were to walk exactly behind some one, and walk faster than,
you will run into this person ahead of you if you do not take evasive action!

After the collision the balls will move with new velocities v_{1}' and v_{2}'.
What is the relation between the way the balls move before and after the collision?

The answer lies in the law of conservation of momentum

## Law of conservation of momentum

In the absence of external forces, the total momentum of the system is conserved.

So using this law we can write the following equation about the two colliding balls,
having mass m_{1} and m_{2}.

### m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1}' + m_{2}v_{2}'

This is a very neat and a universally applicable law. It is true whether the balls are planets! or atoms!

## Question and Answer

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s,
what is the recoil speed of the gun?

Let m and v be the mass and velocity of the shell and M and V the mass and velocity of the gun.

V = mv/M

=0.020 x 80/100 = 0.016 m/s