# How do pulleys provide mechanical advantage?

Nov 9, 2015

A pulley increases the distance over which a force does work.

#### Explanation:

Mechanical advantage comes from changing how work is being done on an object. Work is defined as a force exerted over a distance.

$W = F \times d$

When we use simple machines, such as pulleys, the total work done moving an object is the same. In other words;

$W = {F}_{\text{without" xx d_"without" = F_"with" xx d_"with}}$

Simple machines make work easier by either increasing the force applied to an object, as is the case with a lever, or increasing the distance over which that force is applied, which is the case with a pulley.

Consider a weight hanging at the end of a rope. If you want to lift the weight to a height, $h$ you need to pull up that much rope. The work done in this case is $W = \text{weight} \times h$.

Now suppose you attach a pulley to the top of the weight. In order to move the weight a distance $h$ you need to pull $2 h$ length of rope. But the amount of work done must remain the same.

$W = \text{weight} \times h = F \times 2 h$

Now divide both sides by $2 h$ to find the force.

F = 1/2 "weight'

The amount of force required to lift the weight with a pulley is equal to half the actual weight. That means that a single pulley can provide a 2 to 1 mechanical advantage. You do work over twice the distance you would normally have to in order to decrease the amount of force you put in.
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