First: Look at [Fig. 127]; the distance traveled. The long end of the lever is at its highest point, which is A; and the short end of the lever is at its lowest point C. When the long end of the lever is pushed down, so it is at B, it moves four times farther than the short end moves upwardly, as the distance from C to D is just one-fourth that from A to B. The energy expended in moving four times the distance balances the power gained.
Power vs. Distance Traveled.—From this the following law is deduced: That whatever is gained in power is lost in the distance traveled
Second: Using the same figure, supposing it was necessary to raise the short end of the lever, from C to D, in one second of time. In that case the hand pressing down the long end of the lever, would go from A to B in one second of time; or it would go four times as far as the short end, in the same time.
Power vs. Loss in Time.—This means another law: That what is gained in power is lost in time.
Distinguish clearly between these two motions. In the first case the long end of the lever is moved down from A to B in four seconds, and it had to travel four times the distance that the short end moves in going from C to D.
In the second case the long end is moved down, from A to B, in one second of time, and it had to go that distance in one-fourth of the time, so that four times as much energy was expended in the same time to raise the short end from C to D.
Wrongly Directed Energy.—More men have gone astray on the simple question of the power of the lever than on any other subject in mechanics. The writer has known instances where men knew the principles involved in the lever, who would still insist on trying to work out mechanical devices in which pulleys and gearing were involved, without seeming to understand that those[p. 132] mechanical devices are absolutely the same in principle.
This will be made plain by a few illustrations. In [Fig. 128], A is a pulley four times larger, diametrically, than B, and C is the pivot on which they turn. The pulleys are, of course, secured to each other. In this case we have the two weights, one of four pounds on the belt, which is on the small pulley (B), and a one-pound weight on the belt from the large pulley (A).