Energy and momentum

Let us be sure that we understand the differences between energy and momentum, because we shall be concerned with this later on.

Energy is 1/2 mv2. Momentum is mv.

So the mass of 2 kg, moving at 10 m/s, has 100 units of energy (joules), but 2 X 10, i. e. 20 units, of momentum (kg X m/s).

Yes, but there is more to it than that.

Consider two bodies colliding, e. g. billiard balls.

The total momentum after the collision is the same as the total momentum before; the momentum lost by one ball is exactly the same as the momentum gained by the other. This is the principle of the conservation of momentum. (In considering this it must be remembered that momentum has direction, because velocity has direction.) The law will apply whether the balls rebound, or whether they stick together, or whatever they do.

But the total mechanical energy after the collision will not be the same as before; energy will be dissipated, it will go into the air in the form of heat, sound, etc.; the total energy of the universe will not be changed by the colli­sion – but that of the balls will be.

So momentum is a more permanent property than energy, the latter is often wasted and we shall sometimes find it unfortunate that in order to give a body momentum we must also give it energy.