Force and work

Mechanical advantage, and the catch

Every simple machine makes the same deal: less force, more distance. Here is the arithmetic.

How this site works. Every fact is in our own words and linked to its source, beside it. Where good sources disagree, we show each version in a “Sources differ” box.

Mechanical advantage

Mechanical advantage is how many times a machine multiplies the force you put in: the output force divided by the input force. OpenStax

The theoretical mechanical advantage assumes no friction; in practice friction makes the actual mechanical advantage smaller. Britannica

The trade-off

Machines multiply force at the expense of distance: you push with less force, but over a longer distance. OpenStax

A US Navy manual puts it this way: a machine lets you gain force, but only at the expense of speed. US Navy

A machine cannot do more work than the energy put into it, so energy is still conserved. OpenStax

Ignoring friction, the work you put into a machine equals the work you get out. US Navy

What physicists mean by work

In physics, work is force multiplied by the distance moved in the direction of the force: W = fd. Britannica

Work is measured in joules. One joule is the work done by a force of one newton moving something one metre. Britannica

A force of 10 newtons that moves something 3 metres does 30 joules of work. Science Trek

So a ramp doesn’t cut the work of lifting a box onto a table; it spreads the same work over a longer distance, so each step takes less force.

Work that isn’t work

Holding a heavy object still, however tiring, does no work in the physics sense. Britannica

Push on a brick wall until you sweat and, unless it moves, you have done no work; nudge a computer mouse and you have. Science Trek

Friction takes its cut

The theoretical mechanical advantage assumes no friction; in practice friction makes the actual mechanical advantage smaller. Britannica

Screw jacks lose a lot to friction, on purpose: without it, the weight of the load would spin the jack straight back down. US Navy

Who worked it out

It credits Archimedes, in the third century BCE, with first developing the idea of mechanical advantage. Ohio Univ.

In Le Meccaniche, around 1600, Galileo was the first to show that simple machines do not create energy, only transform it. Ohio Univ.

Machines can move force around, but they can’t make energy. Engines are the other half of the story: see how a steam engine works on our sister site, steam.mechanics.im.

Next: Archimedes →