Principle of Lever

Physical Law

Let $M$ be a lever in a state of equilibrium.

The mechanical advantage $\mathrm {MA}$ of $M$ is given by:

$\mathrm {MA} = \dfrac b a$

where:

$L$ is the load applied to the lever at point $A$

$E$ is the effort applied to the lever at point $B$

$a$ and $b$ are the distances from the fulcrum to points $A$ and $B$ respectively.

In equilibrium, the sum of all the moments of all the external forces acting on $M$ is zero.

The moment applied by $L$ about the fulcrum is $L a$.

The moment applied by $E$ about the fulcrum is $-E b$ as it is in the opposite direction to $L$.

The mechanical advantage of $M$ is defined as:

the ratio of the load on $M$ to the effort applied to $M$.

Hence:

$\ds L a - E b$

$=$

$\ds 0$

$\ds \leadsto \ \ $

$\ds \dfrac L E$

$=$

$\ds \dfrac b a$

Hence the result.

$\blacksquare$