Momentum and Collisions

Abstract

Momentum is the product of the mass of a body and its velocity. It is therefore a vector. We first mentioned momentum in Chapter 4 as the seed whose germination led to modern thoughts on the mechanical behavior of newtonian bodies. In our description of this development, however, we did not consider with sufficient care what was meant by a body. In many cases it is an assembly of particles. In this chapter we will first show how such an assembly can be mathematically represented by a point mass, called the center of mass. We will then show that the motion of the center of mass is that predicted by Newton’s second law for a particle whose mass is the sum of the masses of the individual particles and is acted on by the resultant of the forces acting on the body. Having established these facts, we will turn our attention to the momentum changes of colliding bodies with confidence, knowing that the treatment of bodies is as mathematically sound as if they were very small masses. Collision theory is very important in our later analysis of conduction electrons in solids.