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FORCE SYSTEMS Levers Types of Levers
Examples
A pull of 80 pounds is exerted at the end of the lever, at W; l = 12 inches and L = 32 inches. Find the value of force F required to balance the lever. F:W = l:L W×l F = -----------L W×a W×l L = --------------- = -----------W+F F
F×L = W×l F×L W = ------------l
80 × 12 960 F = ------------------ = --------- = 30 pounds 32 32
If F = 20; W = 180; and l = 3; how long must L be made to secure equilibrium?
F×a F×L l = --------------- = ------------W+F W
180 × 3 L = ------------------ = 27 20
Total length L of a lever is 25 inches. A weight of 90 pounds is supported at W; l is 10 inches. Find the value of F.
F:W = l:L W×l F = -----------L W×a W×l L = -------------- = -----------W–F F
90 × 10 F = ------------------ = 36 pounds 25 F×L = W×l If F = 100 pounds, W = 2200 pounds, and a = 5 F×L W = ------------- feet, what should L equal to secure equilibrium? l 2200 × 5 L = --------------------------- = 5.24 feet F×a F×L 2200 – 100 l = -------------- = ------------W–F W
Let W = 20, P = 30, and Q = 15 pounds; a = 4, b = 7, and c = 10 inches. If x = 6 inches, find F. When three or more forces act on lever: F×x = W×a+P×b+Q×c W×a+P×b+Q×c x = ----------------------------------------------------F W×a+P×b+Q×c F = ----------------------------------------------------x
1 20 × 4 + 30 × 7 + 15 × 10 F = ------------------------------------------------------------- = 73 --- lbs 3 6
Assuming F = 20 in the example above, how long must lever arm x be made? 20 × 4 + 30 × 7 + 15 × 10 x = ------------------------------------------------------------- = 22 ins 20
The above formulas are valid using metric SI units, with forces expressed in newtons, and lengths in meters. However, it should be noted that the weight of a mass W kilograms is equal to a force of Wg newtons, where g is approximately 9.81 m/s2. Thus, supposing that in the first example l = 0.4 m, L = 1.2 m, and W = 30 kg, then the weight of W is 30g newtons, so that the 30g × 0.4 1.2
× - = 10g = 98.1 newtons. force F required to balance the lever is F = ----------------------
This force could be produced by suspending a mass of 10 kg at F.