All problems in leverage may be solved by arithmetic and without using a model.

Suppose that two weights are balanced as in Fig. 9 at the distances shown therein. As 11 times 18 equals 12 times 16 1/2 (198) it follows that the weight of one side times its distance from the fulcrum is equal to the weight on. the other side times its distance from the fulcrum.

W X D = W' X D'

This rule always holds true for all classes of levers. If, therefore, the amount of both weights and one distance are known, the other distance can always be found; or if any three of the four quantities are known, the fourth can always be found. As an example, if we know all but the 16 1/2 lbs. in Fig. 9 we can find this figure in the following way:

18 X 11 / 12---------- = 16 lbs.

In all classes of levers the weight or force times its perpendicular distance from the fulcrum is called the moment.

Thus in the above problem, 12 X 16 1/2 is one moment and 18 X 11 the other. As another example: What force will balance a weight of 100 lbs., 12 in. from a fulcrum located at the short end of a lever? The long end of the lever is 24 in. in length.

100 X 12 = moment of acting force W X 24 = moment of resisting force

But, when a lever is balanced, the moments of forces are equal, according to the rule explained above.

Fig. 9.   The Moment of Forces.

Fig. 9. - The Moment of Forces.

W X 24 = 100 X 12 24W = 1200 W = 50 lbs.

That is to say, it will take 50 lbs. at the long end of the lever to balance the 100 lbs. at the short end.*