Question

A crane moved a 200 kg hot tub from the ground to the top of the hotel, 53m above the ground. If the crane used 200,000J of energy, how efficient was the crane?

Answer 1

The crane did the following work against the gravity force

$$A = mgh = 200kg\cdot 9.81m/s^2 \cdot 53m = 103986J$$

The efficiency is defined as the ratio of usful and total work. Thus

$$\eta =\dfrac{103986J}{200000J}\times 100\% = 51.993\%$$

Answer. 51.993%.