Answer :
Final answer:
To find the average power output of the crane, you need to calculate the work done and divide it by the time taken. The work done is equal to the force applied times the distance lifted, and the force applied is equal to the weight of the mass being lifted. Substituting the given values into the formula gives an average power output of 32 kW.
Explanation:
To calculate the average power output of the crane, we need to use the formula P = W/t, where P is power, W is work done, and t is time. The work done is equal to the force applied times the distance lifted, so W = Fd. In this case, the force applied is equal to the weight of the mass being lifted, which is given by F = mg, where m is mass and g is the acceleration due to gravity. The distance lifted is given as 31 m.
So, the work done is W = Fd = (mg)(d) = (6000 kg)(9.8 m/s^2)(31 m) = 1,805,200 J.
The time taken to lift the mass is given as 56 s.
Now, we can substitute the values into the formula P = W/t to find the average power output of the crane:
P = (1,805,200 J)/(56 s) = 32,232.14 W.
Rounded to the nearest whole number, the average power output of the crane is 32,232 W, which is approximately 32 kW.
