Mechanical Advantage of Type 3 Lever is Less than 1

Theorem

Let $M$ be a type $3$ lever.

Then the mechanical advantage of $M$ is less than $1$.

Hence, instead of amplifying the force applied, a type $3$ lever amplifies the distance moved.

Proof

From Principle of Lever:

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

where:

$b$ is the distance of the effort from the fulcrum

$a$ is the distance of the load from the fulcrum.

But in a type $3$ lever, the effort acts between the load and the fulcrum.

That is:

$a > b$

and hence the result.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): lever
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): lever