Question

The input force of a pulley system must move 8.0 m to lift a 3,000-n engine a distance of 2.0 m. what is the ima of the system?

Answer 1

The IMA (ideal mechanical advantage) of a single pulley is the ratio between the output force and the input force:

`IMA= (F_(out))/(F_(in))`
Moreover, for the law of conservation of energy, the work done in input to lift the lift must be equal to the output work:

`W_(in)=W_(out)`

`F_(in) d_(in)=F_(out) d_(out)`
where the
`d_(in)` is the distance for which the input force is applied while
`d_(out)` is the distance of which the lift is lifted.
Substituting
`F_(out)=3000 N`,
`d_(out)=2 m` and
`d_(in)=8 m` into the previous equation, we find the value of the input force:

`F_(in)= (F_(out) d_(out))/(d_(in)) = ((3000 N)(2 m))/(8 m)=750 N`
And now we can find the IMA of the pulley:

`IMA= (F_(out))/(F_(in))= (3000 N)/(750 N)=4`

As we can see, the IMA is also equal to the ratio between the input and output distance:

`IMA= (d_(in))/(F_(out))= (8m)/(2m)=4`