cistG
2021-04-21
Answered

The crane shown in the drawing is lifting a 182-kg crate upward with an acceleration of $1.5\frac{m}{{s}^{2}}$ . 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 ontoa 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 counter clockwise torque to the drum in order towind up the cable. What is the magnitude of this torque? Ignore the mass of the cable.

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Derrick

Answered 2021-04-23
Author has **94** answers

Let us represent

the net torque is calculated accordingto the equation

so the net torque exerted on the drum will be

Where

if we take that the cable does not slip then we can write

in the above equation

T is the counter clockwise torque providedby the motor and a is the acceleration of the cord as from the given we can see that

in the next step we take

apply newtons second law oftranslational motion to the crate then we get

now solving for

= ....... N.m

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