Question

How do pulleys provide mechanical advantage?

Answer 1

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 = Fxxd`

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

`W = F_"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="weight" xx 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 `2h` length of rope.

But the amount of work done must remain the same.

`W = "weight"xx h = F xx 2h`

Now divide both sides by `2h` 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.