## Friday, 9 February 2007

### Friday's Physical Law - Conservation of Momentum

Well all have experience Newton's Third Law of Motion in action, every time we push on something like a door we can feel it pushing back on us.

What we have here is action and reaction, and as it is normally put Newton's third law reads every action has an equal and opposite reaction. So if I push the door with a force of 5 N the door pushes back with the same force.

Of course the main thing to note about these forces is that they operate on different objects. Many people seem to get this confused by thinking that the forces cancel out, which can only happen when forces are acting on the same object, which is not the case here. To use my previous example: I push on the wall and the wall pushes back on me.

Of course the action and reaction occur at the same time, they start at the same time and they finish at the same time. So this gives us another measure of the motion that results from these forces. Remember that as we saw a couple of weeks ago

• F = ma,

and since we know the force applied in the action and reaction and the mass of each object and now the time over which the force acts we can work out the change in velocity (remember that a = v/t). So this gives us what we refer to as impulse:

• F t = mΔv = Δp
What we have here is another measure of motion, momentum (p) which is equal to an objects mass times its velocity. And from Newton's third law we see that when ever we have to objects interacting (action and reaction) then their is a change in momentum is equal (and opposite). That is the total (nett) momentum of two interacting objects is conserved (the same before and after the interaction).

As we progress through this series we will see many more examples of the idea of conservation of quantities. But in this case we have a very good means to analyse the interaction of objects (the idea of two objects interacting can be extended to multiple objects where momentum will still be conserved) such as in collisions.