Linear Momentum

We will now begin to study momentum conservation in order to best establish an experimental link to Newton's Laws.

This will be done both with experiments using an Air Track as well as some conservation of momentum applets.

What is Momentum? Momentum is the tendency for an object in motion to stay in in motion.

We have already observed this behavior using a cart on an air track and we have seen this in Applet land with friction turned off on the surface.

If there are no forces acting on an object an object remains at constant velocity. This is Newton's First Law: The Law of Inertia

A more physical way to state Newton's First Law is to say that the momentum of an object remains constant unless a force acts on that object. This implies that a force produces a change in the momentum of an object. This is Newton's Second Law

Again, we have already explored Newton's Second Law when we did experiments with impulse. This was the focus of the third Applet assignment as well. Large impulses produced a larger velocity.

Linear momentum is defined as:

p = mv

Since velocity is part of momentum, then momentum has a direction and is thus a vector quantity.

The Kinetic energy of an object is 1/2 mv² as we have seen earlier. Since kinetic energy goes as v², the kinetic energy of an object moving at say -50 m/sec is identical to the kinetic energy of that object moving at +50 km/s. Thus kinetic energy doesn't have a direction associated with it and is therefore not a vector quantity. In physics we call this a scalar quantity.

Conservation of Momentum:

An important observation which we will make in the course of doing experiments is that momentum is conserved between collisions.

We will be observing this rule in both the applet activities as well as the in class air cart demonstration. The difference between momentum conservation and energy conservation was easily demonstrated in the air track experiment done at the end of class.

Suppose we have two identical mass objects, one moves a velocity of +v and one moves at velocity of -v. These two objects will collide. We observed that after the collision both objects were at rest. Why?

Conservation of momentum is a relatively straightforward concept if you simply calculate the momentum of the system before and after the collision.

In this case the momentum before the collision was +mv (for object 1) and -mv (for object two). Thus the total momentum of the system (the system being just these two objects) is zero. Whatever happens to this system, this total momentum must be conserved. Hence, when the objects collide we immediately see the manifestation of momentum conservation both objects stop.

What about energy conservation? Well the kinetic energy of both objects was the same (1/2 mv²) initially and so the total kinetic energy of the system is mv². After the collision, v is zero and hence the kinetic energy of the system is zero Energy was not conserved.