Chapter 9, Problem 44A

Two people who weigh the same amount climb a flight of stairs. The first person climbs the stairs in 30 s, while the second person climbs them in 40 s. person does more work? Which uses more power?

To determine

The person who does more work and who uses more power when the two equally weighing people climb a flight of stairs in $30\text{s}$ and $40\text{s}$ , respectively.

Answer to Problem 44A

Both the persons do an equal amount of work; however, the power used by the first person is more as compared to the second person.

Explanation of Solution

Introduction:

When an object moves a distance d by the application of the forceF , then the work done is:

  $W=F\times d$

The power used in the process is given by:

  $\text{Power =}\frac{\text{work done}}{\text{time taken}}$

Since the weight of the person is the same, hence the force on both the persons will be the same andthe distance moved by both persons is also the same. Hence, the work done by both persons isthe same.

However, as implied from the above formula of power, the power r consumed is inversely proportional to the time taken when the work done is constant. Therefore, the power consumed by the first person, who takes 30 s, will be more as compared to the second person.

Conclusion:

Hence, the power consumed by the first person is more than that by the second person, however, the work done by both the persons isthe same.