Question

Over the course of 30 seconds, a crane lifts a 20kg object to the roof of a 55-meter building. How much power did the crane use, assuming no friction or other mechanism or thermal loss? What formula is used to solve?

Answer 1

To calculate the power used by the crane, we use the formula Power = Work / Time. The work done is equal to the force applied multiplied by the distance moved. In this case, the power used by the crane is approximately 359.3 Watts.

Step-by-step explanation:

To calculate the power used by the crane to lift the object, we need to use the formula:

Power = Work / Time

First, we need to calculate the work done by the crane. The work done is equal to the force applied multiplied by the distance moved. In this case, the force applied is equal to the weight of the object, which is the mass multiplied by the gravitational acceleration (9.8 m/s^2). The distance moved is given as 55 meters. So, the work done is:

Work = Force x Distance = (20 kg x 9.8 m/s^2) x 55 m = 10,780 J

Next, we need to calculate the power by dividing the work by the time taken (30 seconds):

Power = Work / Time = 10,780 J / 30 s = 359.3 W

Therefore, the crane used approximately 359.3 Watts of power to lift the object.