Engineering Application One of the most powerful cranes in the world operates in
ID: 2055325 • Letter: E
Question
Engineering Application One of the most powerful cranes in the world operates in Switzerland. It can slowly raise a 6000-t load to a height of 12.0 m. (Note that 1 t = one tonne is equal to 1000kg) (a) How much work is done by the crane during this lift? (b) If it takes 1.00 min to lift this load to this height at constant velocity, and the crane is 20 percent efficient, find the total (gross) power rating of the crane.
I tried to solve it like this, but i don't know if it's correct:
m=6.0*106kg, y=12.0m, t=1.00min=60.00s
Wapp = Fapp y y = (10kN)(12.0k) = 120kJ
Wnet = Wapp + Wg = 120kJ + (-706320kJ) = -706200kJ = -706.2MJ
Explanation / Answer
The ay you calculated is incorrect. Because the crane lifts the mass with constant velocity, the acceleration is constant for the duration of the operation.
Because the velocity is constant, no net force is acting on the body. Thus the crane applies a force equal to the weight of the load.
Thus, work= load* displacement= mg*h=(6x106 x9.8) N * 12m= 705.6 MJ
the gross power applied by the crane= force*velocity=(mg)*vf
you have calculated vf correctly as 0.2 m/s.
Thus power, P=(6x106 x9.8) N * 0.2 m/s=11.76 MW
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