Multiply the weight of each by its motion after the striking, and it will be found that the sum of the products is two hundred. This may be illustrated by swinging balls like pendulums to cords of equal length from a beam, having the arrangement such that balls of different materials and sizes can be substituted at liberty. If a body be drawn back parallel to the beam, and released so as to swing against another swinging body, both will have motion. This motion will, in some cases be a rebounding motion, as in the case of a small elastic body swinging against and striking a larger elastic body, but in all cases the sum total of the momentum after the impingement is the same as before.
The following statement of the law then, is deducible:
The Momentum of one body in motion may be made to impart momentum to another body, the amount of momentum lost by the former being exactly equal to that thus acquired by the latter.
Before leaving these remarks on momentum the reader should observe carefully what momentum is and bear in mind it is the quantity of motion possessed by a moving body, and has to do only with mass and velocity—and takes no account of distance passed through.
Energy
Energy is the capacity to do work, and the energy of a moving body is the amount of work it will do, i. e., the distance it will move against a resistance by virtue of its tendency to move, before being brought to a state of rest.
Now note, and note carefully, that the amount of energy is proportional to the mass, and to the square of the velocity.
Note this carefully: Any body in motion has both momentum and energy. Its momentum is proportional to its velocity; its energy to the square of its velocity. If the velocity be doubled, the momentum will be doubled, but its energy quadrupled. If the velocity be trebled, its momentum will be trebled, but its energy increased nine-fold.
It is important that the student get clearly what is meant by saying that Energy is the capacity to do work, and is proportional to the square of the velocity.
The capacity to do work means the capacity to move against resistance, i. e., to overcome resistance. The word "work" being used in a purely mechanical sense and in that sense it is used whether the result accomplished is destructive or beneficial.