The IMA (ideal mechanical advantage) of a single pulley is the ratio between the output force and the input force:
[tex]IMA= \frac{F_{out}}{F_{in}} [/tex]
Moreover, for the law of conservation of energy, the work done in input to lift the lift must be equal to the output work:
[tex]W_{in}=W_{out}[/tex]
[tex]F_{in} d_{in}=F_{out} d_{out}[/tex]
where the [tex]d_{in}[/tex] is the distance for which the input force is applied while [tex]d_{out}[/tex] is the distance of which the lift is lifted.
Substituting [tex]F_{out}=3000 N[/tex], [tex]d_{out}=2 m[/tex] and [tex]d_{in}=8 m[/tex] into the previous equation, we find the value of the input force:
[tex]F_{in}= \frac{F_{out} d_{out}}{d_{in}} = \frac{(3000 N)(2 m)}{8 m}=750 N [/tex]
And now we can find the IMA of the pulley:
[tex]IMA= \frac{F_{out}}{F_{in}}= \frac{3000 N}{750 N}=4 [/tex]
As we can see, the IMA is also equal to the ratio between the input and output distance:
[tex]IMA= \frac{d_{in}}{F_{out}}= \frac{8m}{2m}=4 [/tex]
