# How can simple machines trade force for distance?

Mar 19, 2018

The short answer is that the same work is done in both cases.

#### Explanation:

It is the principle of conservation of energy.

#"work" = "force"*"distance".

As an example, assume you want to raise a 1000 kg car 0.1 m to do some repair underneath. Let's calculate the work required to lift it 0.1 m without a simple machine.

The weight of the car is $m \cdot g = 9800 N$. That is the force required to lift it. Get a team of men to lift it and slip blocks under it to hold it during the repair. The work done using this method would be

$\text{work} = 9800 N \cdot 0.1 m = 980 J$

Now, get a fulcrum and a long pole with a cradle that fits under the car. Find the best spot for the fulcrum so that the end of the lever would have to move down 1.96 m to raise the car 0.1 m. Then have a 500 N woman sit on the end. The work done by that woman would be

$\text{work} = 500 N \cdot 1.96 m = 980 J$

I hope this helps,
Steve