Answer to Question #219002 in Physics for ran li

Question

An electric motor has a power rating of 1.60 kW and operates at 75% efficiency. The amount of work that it can do in 1.0 hrs is ___x10⁶ J. Give your answer with the correct number of sig digs and do not include units)

Answer 1

By the definition of the power, we have:

$$P_{total}=\dfrac{W}{t}.$$

From the definition of the efficiency, we have:

$$\eta=\dfrac{P_{useful}}{P_{total}},$$ $$P_{useful}=\eta\cdot P_{total}.$$

Finally, we can find the amount of work done:

$$W=\eta P_{total}t=0.75\cdot1.60\cdot10^{3}\ W\cdot3600\ s=4.32\cdot10^6\ J.$$