Impulse, Momentum, and Collisions

So far, we've applied two sets of tools to understand what happens when objects interact:

1. forces and acceleration
2. (conservation of) energy

But there are some very common, very important situations in which we need a new tool -- momentum.

• A very large movie of two cars meeting

Let's look at things in a bit of detail ..

You know some equations which connect changes in velocity to forces and accelerations .... but that isn't the complete story. Do your kinematic equations help you to answer this question:

I'm driving a car at 55 mph along the highway. How big a force will it take to stop me and my car?

The answer is -- it depends.

• A big force could stop the car ... in a very short period of time.
• A small force could stop the car ... if you give it long enough.
• And what would happen if the size of the force changed while the car was skidding to a halt?

Your kinematic equations assume that the force is constant in size; what if it isn't? We can still use Newton's Second Law to say something about the behavior of the object under a time-variable force:

As long as the mass of the object(s) doesn't change, then we can take the m out of the integral:

And now, if we define momentum p as the product of mass and velocity, we have

In words, we can say that

the change of a body's momentum is equal to the integral of the forces on it over time

Some guy named Newton wrote something along these lines:

Physicists have given the name impulse to the quantity "force integrated over time". Today you will use impulse to solve some problems.

Note one special case: if the magnitude of a force is constant, then its impulse is simply the force multiplied by the time it acts.

• Example of impulse on a tennis ball
• Example of impulse on a baseball
• Example of impulse on the Genesis spacecraft

Momentum turns out to be enormously useful in solving problems which involve collisions, even when you don't know the details. Why? Because under very common circumstances, the total momentum of a set of colliding objects will be the same before and after they collide; in other words, momentum is conserved.

• Using momentum in collisions
• Using a pistol as an engine
• A collision on the highway

In a collision, as long as there are no net external forces, momentum will always be conserved. That makes momentum a very powerful tool for dealing with collisions. Kinetic energy, on the other hand, is not always conserved in collisions. Given the choice, then, it's usually better to try using momentum than kinetic energy if you face a complicated collision between several objects.

• Elasic and inelastic collisions

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.