153.  Applications of the Lever.  By means of a lever, a 600-pound bowlder can be easily pried out of the ground.  Let the lever, any strong metal bar, be supported on a stone which serves as fulcrum; then if a man exerts his force at the end of the rod somewhat as in Figure 91 (p. 154), the force arm will be the distance from the stone or fulcrum to the end of the bar, and the weight arm will be the distance from the fulcrum to the bowlder itself.  The man pushes down with a force of 100 pounds, but with that amount succeeds in prying up the 600-pound bowlder.  If, however, you look carefully, you will see that the force arm is 6 times as long as the weight arm, so that the smaller force is compensated for by the greater distance through which it acts.

At first sight it seems as though the man’s work were done for him by the machine.  But this is not so.  The man must lower his end of the lever 3 feet in order to raise the bowlder 6 inches out of the ground.  He does not at any time exert a large force, but he accomplishes his purpose by exerting a small force continuously through a correspondingly greater distance.  He finds it easier to exert a force of 100 pounds continuously until his end has moved 3 feet rather than to exert a force of 600 pounds on the bowlder and move it 6 inches.

By the time the stone has been raised the man has done as much work as though the stone had been raised directly, but his inability to put forth sufficient muscular force to raise the bowlder directly would have rendered impossible a result which was easily accomplished when through the medium of the lever he could extend his small force through greater distance.

154.  The Wheelbarrow as a Lever.  The principle of the lever is always the same; but the relative position of the important points may vary.  For example, the fulcrum is sometimes at one end, the force at the opposite end, and the weight to be lifted between them.

[Illustration:  FIG. 98.—­A slightly different form of lever.]

Suspend a stick with a hole at its center as in Figure 98, and hang a 4-pound weight at a distance of 1 foot from the fulcrum, supporting the load by means of a spring balance 2 feet from the fulcrum.  The pointer on the spring balance shows that the force required to balance the 4-pound load is but 2 pounds.

The force is 2 feet from the fulcrum, and the weight (4) is 1 foot from the fulcrum, so that

  Force x distance = Weight x distance,
  or 2 x 2 = 4 x 1.

Move the 4-pound weight so that it is very near the fulcrum, say but 6 inches from it; then the spring balance registers a force only one fourth as great as the weight which it suspends.  In other words a force of 1 at a distance of 24 inches (2 feet) is equivalent to a force of 4 at a distance of 6 inches.

[Illustration:  FIG. 99.—­The wheelbarrow lightened labor.]

One of the most useful levers of this type is the wheelbarrow (Fig. 99).  The fulcrum is at the wheel, the force is at the handles, the weight is on the wheelbarrow.  If the load is halfway from the fulcrum to the man’s hands, the man will have to lift with a force equal to one half the load.  If the load is one fourth as far from the fulcrum as the man’s hands, he will need to lift with a force only one fourth as great as that of the load.