7 -2 points CJ10 9.P047 My Notes The crane shown in the drawing is lifting a 182

Question

7 -2 points CJ10 9.P047 My Notes The crane shown in the drawing is lifting a 182-kg crate upward with an acceleration of 1.2 m/s2. The cable from the crate passes over a solid cylindrical pulley at the top of the boom. The pulley has a mass of 130 kg. The cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the crane. The mass of the drum is 150 kg, and its radius is 0.76 m. The engine applies a counterclockwise torque to the drum in order to wind up the cable. What is the magnitude of this torque? Ignore the mass of the cable. N·m Pul Boom Drum Additional Materials Section 9.4

Explanation / Answer

on crate : T1 - m g = m a

T1 = 182 (9.8 + 1.2) = 2002 N

on pulley:

Net torque = I alpha

r (T2 - T1) = ( M r^2 /2 ) (a / r)

T2 - 2002 = (130 x 1.2 / 2)

T2 = 2080 N

Now on drum,

M - (R T2) = ( M' R^2) (a / R)

M - ( 1580.8) = 136.8

M = 1717.6 N m ........ans

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