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. A revolving fly wheel will run machinery for some time after the application of force has ceased. This is doing work, and represents energy. A bullet fired from a gun will accomplish destruction before having its motion arrested. This is work--energy. If a boy throw a ball into a snow bank, its motion will sink it into the snow, but not far, the resistance of the snow will soon bring the ball to rest. The ball overcomes resistance in passing through the snow until it is brought to rest, and thus it does the _work_ of forcing itself through the snow, and possesses the _energy_ necessary to do that work.