Two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that
Has a lower grade. Joe gets to the top before Bob. Ignoring friction and wind resistance, which one
Of the following statements is true?
A) The amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob.
B) The average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there.
C) Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same.
D) The amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob.

Question

Quizplus · Accepted Answer

The work done is defined as the force times the distance moved in the direction of the force. Since both cyclists are moving to the same height against gravity, and they weigh the same, the work done against gravity is the same for both. However, Joe, who arrives first, does this work in a shorter time, meaning his average power (work done per unit time) is higher than Bob's.

Two Cyclists Who Weigh the Same and Have Identical Bicycles