Final answer:
Scenario (b) involves carrying a load up two flights of stairs, potentially resulting in more work done if each flight is of equal height. Power is determined by the rate of work done; carrying a lighter object (like a watermelon) quickly can generate more power than carrying a heavier object (like a TV) slowly, even if the work done is the same, because power accounts for the time taken to do the work.
Step-by-step explanation:
To determine which scenario involves the most amount of work, we must understand the definition of work in a physical context. Work is defined as the product of the force applied to an object and the displacement of that object in the direction of the force. Mathematically, work (W) is expressed as W = force (F) × displacement (s). In scenarios (a) and (b), the force remains the same along each flight of stairs, and the displacement is vertically upwards. If we assume each flight of stairs is of equal height, then scenario (b) involves carrying a load up a greater total displacement, resulting in more work being done. Therefore, the correct answer is (b). However, the question also presents an option (d) that says it depends on the height of the stairs, which is indeed true. If the flights of stairs have different heights, the work done would depend on the total vertical displacement for each scenario. Since we do not have exact heights, we can only definitively say scenario (b) involves more work if we assume equal height per flight.
Identifying Higher Power Generation
Power is the rate of doing work or the amount of energy transferred per unit time. The formula for power is P = work (W) / time (t). Let's compute the power for both objects:
- For the 100 N TV: Power = Work / Time = (100 N × height) / 50 s
- For the 24 N watermelon: Power = Work / Time = (24 N × height) / 10 s
Without the exact height, we cannot compute the exact values of power, but we can compare the two. The 100 N TV takes 50 seconds to carry to the second floor whereas the 24 N watermelon takes only 10 seconds. Given that the height is the same in both scenarios, the watermelon's action generates more power due to the shorter time interval, even though it involves less force.