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?

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

Moreover, for the law of conservation of energy, the work done in input to lift the lift must be equal to the output work:


where the is the distance for which the input force is applied while is the distance of which the lift is lifted.
Substituting , and into the previous equation, we find the value of the input force:

And now we can find the IMA of the pulley:


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