Two girls each carry a box up to the fourth floor of a building. The total mass of each girl and the box she is carrying is the same. Rachel makes the trip in 35 seconds while Madison takes 50 seconds.
Which of the following statements best describes this task?
a. Rachel has greater power output than Madison.
b. Madison has a greater power output than Rachel.
c. Madison does more total work than Rachel.
d. Rachel does more total work than Madison.
I would say option A. because, considering that Rachel does the work faster than Madison, she has more power being exerted, or output.
The total work is the same for both girls. The one with the shorter time is higher power output.
To determine which statement is correct, we need to understand the concepts of power and work in physics.
Power is the rate at which work is done or energy is transferred. It is calculated as the work done divided by the time taken.
Work, on the other hand, is the transfer of energy to an object by the application of a force. It is calculated as the force applied multiplied by the distance over which the force is applied.
In this scenario, both girls are carrying the same mass of the box, which means the force they apply to lift the box is the same. However, Rachel takes less time to make the trip than Madison, which means she does the same amount of work in less time. Therefore, Rachel has a higher power output than Madison.
So, the correct statement is a. Rachel has greater power output than Madison.
To determine which statement is correct, we need to understand the concepts of power output and total work done.
Power output is the rate at which work is done or energy is transferred. It is calculated by dividing the amount of work done by the time taken to do that work. Power is measured in watts (W). The formula for calculating power is:
Power = Work / Time
Total work done is the sum of the work done by each individual. Work is defined as the force applied over a distance, and it is measured in joules (J). The formula for calculating work is:
Work = Force × Distance
Given that both girls carry the same box with the same mass, we can assume that the distance traveled is the same for both. Therefore, the comparison between Rachel and Madison can be made based on the time it took for them to complete the task.
In this scenario, Rachel completes the task in 35 seconds, while Madison takes 50 seconds. Since both girls carry the same box with the same mass, we can conclude that Rachel does the work in a shorter time, resulting in a greater power output. Therefore, the correct statement is:
a. Rachel has greater power output than Madison.