Question

One of the most powerful cranes in the world operates in Switzerland. It can slowly raise a 5707-t load to a height of 12.9 m (Note that 1 t = one tonne is sometimes called a metric ton. It is a unit of mass, not force, and is equal to 1000 kg.) How much work is done by the crane during this lift.

7.22×108 J
You are correct.

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Problem 6-58b:
If it takes 1.15 min to lift this load at constant velocity, and the crane is 19.9 percent efficient, find the total (gross) power rating of the crane.

Answer 1

Efficiency: \(\eta\) is defined as follows:\[\eta = \frac{P_\text{out}}{P_\text{in}}\]Also, \(P = \vec F \cdot \vec v\) for moving the object.

Answer 2

@yakeyglee is correct, but let me expand but explaining how to find the power.

There are two ways. We can find the constant velocity as\[v = {\rm distance \over time} = {12.9 \over 1.15 \cdot 60}\]and the force the crane exerts a force of\[F = 5707 [tonnes] \cdot 1000 [kg/tonne] \cdot 9.81 [m/s^2]\]Power output can be found from\[P_{out} = F \cdot v\]

The second way is directly from the definition of power\[P = {\rm Work \over time}\]Therefore, the power output of the crane becomes\[P_{out} = {W \over 1.15 \cdot 60}\]where work is what you found in the previous question.

As yakeyglee already said, the gross power can be found from\[\eta = {P_{out} \over P_{ i n}}\]\(P_{i n}\) is the gross power.