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Answer :
Yes, it is possible for the 185-lb woman to hoist the 100-lb boy up. The smallest force she needs to exert is slightly greater than half of the boy's weight due to the mechanical advantage provided by the rope passing over the quarter circular cliff rock.
To determine if the 185-lb woman can hoist the 100-lb boy up, we consider the mechanical advantage provided by the rope system. In simple systems, such as a rope passing over a pulley, the force needed to lift a weight is effectively reduced by half. However, the scenario involves a quarter circular cliff rock, which adds some friction and changes the force dynamics slightly but still offers a significant mechanical advantage.
Assuming minimal friction and an ideal mechanical system, the force exerted by the woman would need to be slightly greater than half the weight of the boy to overcome gravitational forces. This is due to the redistribution of the boy’s weight across the rope length that passes over the cliff rock. Thus, she would need to exert a force greater than 50 lbs to begin lifting the boy.
Calculating roughly, if the woman weighs 185 lbs and can exert a force equal to her body weight, this far exceeds the minimal force required to lift the boy, even when considering realistic factors like friction and the efficiency of the force transfer over the cliff rock. Given these considerations, it's clear that the woman has the capability to hoist the boy up without exceeding her own weight limit or requiring an unreasonable amount of force.
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