Momentum

Momentum

We consider the idea of momentum. Suppose a body has a mass m and a velocity v. Then the momentum of the body is the product of mass and velocity, mv.

The purpose of this quantity is to measure (that is, to tell us) the amount of motion in a body. This means that we want to use momentum to compare two bodies, and say which one has more motion.

To understand this better, consider two bodies A and B with the same mass. Suppose that B moves faster than A. It is reasonable to think that B has more motion than A. Notice that the momentum (mv) of B is also larger than the momentum for A.

Next, suppose that A has a larger mass than B, and that they both move equally fast. Since they are equally fast, it looks that they have the same amount of motion. However, imagine trying to stop them. It would be easier to stop B because it has a smaller mass. In this sense, it is reasonable to say that B has less motion than A. Notice that in this case, the momentum of B is smaller than the momentum for A.

From these two examples, we see that a larger mass or a larger velocity means a larger amount of motion. So it seems reasonable to use the product of mass and velocity as a measure of the quantity of motion in a body.

We could of course make up other combinations to measure motion, like m²v or mv². The reason for choosing just mv is not because it is simple, but because it can be related to the force applied on the body. This relation is given by Newton's second law, which states that:

"The rate of change of momentum of a body is proportional to the resultant force acting on the body."

Neither the rate of change of m²v nor mv² nor any other combination would work. Only mv is found experimentally (by measuring many different masses, velocities and forces) to be to be proportional to the force.

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