This is also termed mechanical advantage.
The earliest remaining writings regarding levers are provided by Archimedes ("Give me a place to stand, and I will move the Earth.", a remark of Archimedes quoted by Pappus of Alexandria[?]) who formally stated the correct mathematical principle of levers.
The force applied (at end points of the lever) is proportional to the ratio of the lever arms measured between the fulcrum and application point of the force applied at each end of the lever.
Insert a better freebody diagram here when one is available.
Example:
1000 lb boulder 50 lb force applied down  \_____/ \/ lllllllllllllllllllllllllllllllllllllllllllll ^ Fulcrum
The principle of the lever tells us that the above would be in static equilibrium with all forces balancing.
The force applied upwards on the boulder is equal to the ratio of the lever arms times the force applied at the other end by the operator. (40/2)*50 = 1000.
Increase the downward force a trifle and the boulder begins to move. By applying a fifty pound force plus a little more we can lift thousand pound boulders!
A pulley assembly (see also block and tackle[?]) made of different size pulleys exploits this fundamental principle, as do gear assemblies or mechanical transmissions.
The principle of leverage can also be derived using Newton's laws of motion and modern statics.
Modern examples of the lever in use include: the crowbar[?], a steam shovel[?], an adjustable teeter totter[?] and the cantilever.
See also engineering mechanics
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