The Work and Power of Cyclists Riding Up a Mountain
Two Cyclists Riding Up a Mountain
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?
Question:
Which one of the following statements is true regarding the amount of work done and the average power exerted by Joe and Bob?
Final answer:
The correct answer is c. 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.
Explanation:
Work done: Work is defined as force times displacement. Both cyclists experience the force of gravity pulling them down the mountain, but the displacement (distance traveled) is different for each. Since Joe takes the shorter route, his displacement is less than Bob's.
Therefore, the work done by Joe (force x shorter distance) will be less than the work done by Bob (force x longer distance).
Power: Power is defined as work done per unit time. Since Joe takes less time to reach the top due to the shorter distance, his average power (work done / time taken) will be greater than Bob's, who took a longer time despite doing more work.
Therefore, both statements in option c are true: Joe did less work but had a higher average power than Bob.
Option a is incorrect because Bob actually did more work due to the longer distance.
Option b is incorrect because the amount of work and average power differ for each cyclist.
Option d is incorrect because Bob did more work and took longer to do it, resulting in a lower average power.