 Power is the product of force and velocity, so forces applied to points farther from the pivot must be less than when applied to points closer in.If "a" and "b" are distances from the fulcrum to points "A" and "B" and if force "FA" applied to "A" is the input force and "FB" exerted at "B" is the output, the ratio of the velocities of points "A" and "B" is given by "a"/"b" so the ratio of the output force to the input force, or mechanical advantage, is given by

This is the "law of the lever", which was proven by Archimedes using geometric reasoning.It shows that if the distance "a" from the fulcrum to where the input force is applied (point "A") is greater than the distance "b" from fulcrum to where the output force is applied (point "B"), then the lever amplifies the input force.