Using a simply pulley/rope system, a crewman on an Arctic expedition is trying t

Question

Using a simply pulley/rope system, a crewman on an Arctic expedition is trying to lower a 5.13 kg crate to the bottom of a steep ravine of height 23.2 meters. The 45.0 -kg crewman is walking along holding the rope, being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point on a slick patch of ice and slips. The crate immediately accelerates toward the ground, dragging the hapless crewman across the ice and toward the edge of the cliff. If we assume the ice is perfectly slick (that is, no friction between the crewman and the ice one he slips and falls down), at what speed will the crate hit the ground? Assume also that the rope is long enough to allow the crate to hit the ground before the crewman slides over the side of the cliff.

Explanation / Answer

Let tension be T.

Since acceleration of both bodies has to be equal,

T/45 = [5.13*9.8 -T]/5.13

5.13 T = 2262 - 45 T

T = 2262/50.13

= 45.12 m/s^2

a = T/45 = 1.003 m/s^2

using third equation of motion,

v = sqrt(u^2+2as)

= sqrt(1.5^2+2*1.003*12.9)

= 5.3035 m/s

for crewman, v=sqrt(5.3035^2+2*9.8*23.2)

= 21.97 m/s

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