Question

A 120-meter-long ski lift carries skiers from a station at the foot of a slope to a second station 40m above. what is the ima of the lift?

Answer 1

The ideal mechanical advantage of a slope is given by the ratio between the output load, which is simply the weight of the object ($F_w$), and the input force $F_i$ applied to move the object along the slope:
$ima= \frac{F_w}{F_i}$

The energy conservation law states that the potential energy of the object when it reaches the final height h is equal to the work done to move the object along the distance of the slope $l$, i.e.
$F_w h = F_i l$
From this we find
$\frac{F_w}{F_i} = \frac{l}{h}$
Therefore, we can substitute this into the formula of the ideal mechanical advantage and calculate its value:
$ima= \frac{l}{h} = \frac{120~m}{40~m}=3$