Only Part D Needs to be worked You work in a construction company which has just

Question

Only Part D Needs to be worked

You work in a construction company which has just built a new crane. The duty cycle of the crane is constant: every upward journey needs to lift a load of 1 towne (metric) of bricks from the ground to a height h_top = 100 m using its motorised pulley. The motorised pulley consists of an electric motor, a transmission and a negligible-mass pulley, with the following characteristics: The acceleration/speed profiles chosen to perform the upward journey are qualitatively sketched on the right with a_max = 10 m/s^2. They should consider that: the cable cannot transmit any compression force to slow down the mass in the final stage of the upward journey therefore, some time (from t_off to t_trip) needs to be allowed for the mass to decelerate and reach the top with zero final speed. Neglecting the motor power constraint, calculate the values t_trip (total time for lifting) and the time t_off (when the motor should stop pulling). In the choice of the cable, which is the minimum rated load of the cable T_rated you will look for? Will the motor have sufficient power to perform the task (calculations required)? How would you modify the shape of the acceleration/speed profile to reduce the power requirements without increasing the total time t_trip (only qualitative answer required)? During a night, the load is oscillating in the top position, swinging at a constant cable length of L_top = 6 m. The cable snaps when perfectly vertical, and with an angular speed omega = 0.5 rad/s. How far will the body impact with the ground and with which speed?

Explanation / Answer

here, speed of load at vertical = 0.5 * 6

                                                    =   3 m/sec

Applying equation of motion

=>     100 =   1/2 * g * t2

=>   t   =   4.517 sec

=> far will the body impact with ground = 3 * 4.517 = 13.551 m

=>    speed   =   sqrt(32 + 44.262)

                      = 44.36   m/sec

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