A 1000 kg crate is being unloaded from a freighter by a winch. When the crate is

Question

A 1000 kg crate is being unloaded from a freighter by a winch. When the crate is 4.0 m above the dock, the gearbox shaft on the winch breaks and the crate falls from rest. The winch drum and pulley can be treated as uniform cylinders. The winch has a mass of 800 kg and a radius of 1.1 m. The pulley has a mass of 100 kg and a radius of .3 m. Assume that, during the fall, the rope does not slip over either the pulley or the winch. Find the speed of the crate just before it hits the dock. What is the net torque acting on the pulley during the fall?

Explanation / Answer

using law of conservation of energy

m*g*h = (0.5*I1*w1^2)+(0.5*I2*w2^2)+(0.5*m3*v^2)

1000*9.81*4 = (0.5*0.5*m1*r1^2*(v^2/r1^2))+(0.5*0.5*m2*r2^2*(v^2/r2^2))+(0.5*1000*v^2)

39240 = (0.25*800*v^2)+(0.25*100*v^2)+(0.5*1000*v^2)

v = 7.35 m/s

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B) Net torque is Tnet

accelaration of the system is a

then using v^2-u^2 = 2*a*S

7.35^2 = 2*a*4

a = 7.35^2/8 = 6.75 m/s^2

alpha = a/r

then Tnet = -(I1*alpha1) - (I2*alpha2) = -(0.5*800*1.1^2*(6.75/1.1))-(0.5*100*0.3^2*(6.75/0.3)) = -3071.25 N-m

negative sign indicates the torque into the page

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