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 6.95 kg crate to the bottom of a steep ravine of height 22.0 meters. The 45.0 kg crewman is being careful to lower the crate at a constant speed of 1.50 m/s. Unfortunately, when the crate reaches a point 12.2 meters above the ground, the crewman slips and 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 once 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. At what speed will the crewman hit the bottom of the ravine? (Assume no air friction.)

Explanation / Answer

Ans.) From basic mechanics of motion constrained by ropes and pulleys, we know that acceleration of the block,

a = m1/(m1+m2) *g ; where m1 = mass of block, m2 = mass of man; g = acceleration due to gravity.

Therefore, a = 0.9015 m/s^2

Now, the block was at a height of 12.8 m and is falling with an acceleration of 0.9051 m/s^2

Hence, from the equation, V^2 - U^2 = 2*a*H; whre V is the final velocity; U is the initial velocity = 0 ; a = 0.9051; H = 12.8m

SOlving for V, we get(U3 + U4 ) - (U2+ U1)

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