The Law of Equilibrium of the Lever
المؤلف:
GEORGE A. HOADLEY
المصدر:
ESSENTIALS OF PHYSICS
الجزء والصفحة:
p-100
2025-11-05
36
By applying the principle of moments, we can readily find an expression for the law of the lever. As F is fixed in every case, it is the center of moments, and when the lever is in equilibrium, the moment of P equals the moment of W. Hence 
Writing this as a proportion, we have
Or 
in which "arm " means the perpendicular from the fulcrum to the direction of the force. Using the more general term Resistance in place of Weight, we write the formula thus: 
The mechanical advantage of any lever is the ratio of the longer arm to the shorter arm.
If additional forces are applied at different points along the lever, equilibrium will be maintained when the sum of the moments producing clockwise rotation is equal to the sum of the moments producing counterclockwise rotation. Moments producing counterclockwise rotation are sometimes called positive, and those producing clockwise rotation negative: if this is done, equilibrium will be maintained whenever the sum of all the moments is zero.
If a body is acted on by a number of forces and is in equilibrium, any point at which force is applied may be taken as the center of moments, when the sum of the clockwise
moments with reference to this point will be equal to the sum of the counterclockwise moments. This is true however great the number of forces, and whether they are parallel or not. If A in Fig. 1 is taken as the center of moments, W tends to produce a counterclockwise rotation which is counterbalanced by the pressure of the fulcrum upon the lever at F. This pressure at F is upward in direction, and is equal to P+W,. the pressure that P and W exert upon the fulcrum.
Fig.1
Demonstration. - The equality of moments may be demonstrated by the use of the algebraic balance (Fig.2).
The moments of the weights hung directly on the bar are clockwise. The moment of the weight hanging from the cord passing over the fixed pulley is counterclockwise. To produce equilibrium these must counterbalance each other. By different arrangements of the weights the three classes of levers can be illustrated.
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