Editing Lever (section)

== Law of the lever {{anchor|Law}} ==
{{See also|Mechanical advantage#Lever}}
The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot.

As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity.<ref>{{cite book
  | last1 = Uicker
  | first1 = John
  | last2 = Pennock
  | first2 = Gordon
  | last3 = Shigley
  | first3 = Joseph
  | title = Theory of Machines and Mechanisms
  | publisher = Oxford University Press USA
  | edition = 4th
  | year = 2010
  | isbn =978-0-19-537123-9 
}}</ref>

If ''a'' and ''b'' are distances from the fulcrum to points ''A'' and ''B'' and the force ''F<sub>A</sub>'' applied to ''A'' is the input and the force ''F<sub>B</sub>'' applied 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:
<math display="block">MA = \frac{F_B}{F_A} = \frac{a}{b}.</math>

This is the ''law of the lever'', which was proven by [[Archimedes]] using geometric reasoning.<ref name="Usher1954">{{cite book|author=Usher, A. P.|author-link=Abbott Payson Usher|title=A History of Mechanical Inventions|url=https://books.google.com/books?id=Zt4Aw9wKjm8C&pg=PA94|page=94|access-date=7 April 2013|year=1929|publisher=Harvard University Press (reprinted by Dover Publications 1988)|isbn=978-0-486-14359-0|oclc=514178|archive-date=26 July 2020|archive-url=https://web.archive.org/web/20200726002155/https://books.google.com/books?id=Zt4Aw9wKjm8C&pg=PA94|url-status=live}}</ref> 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. On the other hand, if the distance ''a'' from the fulcrum to the input force is less than the distance ''b'' from the fulcrum to the output force, then the lever reduces the input force.

The use of velocity in the static analysis of a lever is an application of the principle of [[virtual work#Law of the Lever|virtual work]].