Question

Why is the actual mechanical advantage of a simple machine different from the ideal mechanical advantage?

Answer 1

`AMA=(F_(out))/(F_(i.n))`
`IMA=s_(i.n)/s_(out)`

Explanation:

The Actual Mechanical Advantage AMA is equal to:
`AMA=(F_(out))/(F_(i.n))` that is, the ratio between the output and input force.

The ideal mechanical advantage, IMA, is the same but in absence of FRICTION!

In this case you can use the concept known as CONSERVATION of ENERGY.

So, basically, the energy you put in must be equal to the energy delivered (this, obviously, is quite difficult in reality where you have friction that "dissipates" part of the energy to change it into, say, heat!!!).
But energy in/out may be called WORK and indicated by `W` as:
`W=`force`xx`distance`=F*s`:

So, from conservation of energy:
`W_(out)=W_(i.n)`
`F_(out)*s_(out)=F_(i.n)*s_(i.n)`
and:
`F_(out)/F_(i.n)=s_(i.n)/s_(out)=IMA` or:
IMA = (input distance)/(output distance)
Friction acts upon the ratio of forces (reducing it) but leaves the ratio of distances as it is so this ratio is used to define IMA.

hope it helps!