Fig. 87.—The two moments are equal about C. 100 × 15 = 50 × 30
From the experiment just described, the moment of the acting force equals the moment of the weight or f × Df = w × Dw, or the effort times the effort arm equals the weight times the weight arm. This equation is called the law of the lever. It corresponds to the general law of machines and may also be written w: f = Df: Dw.
123. Mechanical Advantage.—A lever often gives an advantage because by its use one may lift a stone or weight which the unaided strength of man could not move. If the lever is used in lifting a stone weighing 500 lbs., the force available being only 100 lbs., then its mechanical advantage would be 5, the ratio of w:f. In a similar way, the mechanical advantage of any machine is found by finding the ratio of the resistance or weight to the effort. What must be the relative lengths of the effort arm and resistance or weight arm in the example just mentioned? Since the effort times the effort arm equals the weight times the weight arm, if f × Df = w × Dw, then Df is five times Dw. Hence the mechanical advantage of a lever is easily found by finding the ratio of the effort arm to the weight arm.
Important Topics
1. Advantage of machines.
2. Machines cannot create energy.
3. Law of machines.
4. Six simple machines.
5. Lever and principle of moments.