# If you have a simple machine with a large machanical advantage what does that mean for the input force you have to apply to the machine?

The ideal mechanical advantage for a simple machine is the ratio of the output force to the input force.

MA = Fo/Fi.  Applying the mulitiplicative property of equality we get

Fi = Fo/MA

This is telling us that as the MA increased, the input decreases to cause the same amount of output force.  Or another way to look at it is that for any input force, increasing the MA increases the amount of output force you can apply to doing work.

Work/energy of course has to be conserved.  Mechanical work is the force applied multiplied by the distance of movement

W = Fd

So, if we are increasing the amount of output force by increasing the MA, we must be doing the same amount of work.

MA = Fo/Fi and MA = Di/Do

Therefore, you must either decrease the output distance or increase the distance the object that is providing the input force must move.

For example, to lift a large mass, a First Class lever must have the mass close to the fulcrum and the applied force a long way from the fulcrum.

Approved by eNotes Editorial Team