Question

use the scenario to answer the following question.
a football team is investigating which of three players has the most power when running up a 3.0 m flight of stairs. assume that the horizontal motion is constant and all the force from the steps is used to elevate the player upward at a constant speed. assume the weight of the player is equal to the force that does the work on the player and the height of the staircase is the upward displacement (3.0 m).
how should the team best conduct this investigation to determine the player with the most power?
a take the weight of each player. have all three players run up the stairs at the same time to see who reaches the top first.
b take the weight of each player. one at a time, have each player run up the stairs and record the time and describe how much effort it took to reach the top of the stairs.
c take the weight of each player. one at a time, have each player run up the stairs and record the time. then, multiply the player’s weight by 3.0 m and divide that by the time it took for them to reach the top of the stairs. repeat this calculation for all players and compare.
d take the weight of each player. one at a time, have each player run up the stairs and record the time. then, multiply the player’s weight by the time it took for them to reach the top of the stairs, then divide by 3.0 m. repeat this calculation for all players and compare.

Explanation:

To determine power, we use the formula \( P=\frac{W}{t}=\frac{Fd}{t} \), where \( F \) (force) is the player's weight, \( d \) (distance) is the stair height (3.0 m), and \( t \) is time.

• Option A: Having all run at the same time measures speed (who finishes first), not power (which depends on work and time, and work depends on weight too).
• Option B: Describing "effort" is vague; power needs quantitative calculation (\( P=\frac{weight \times height}{time} \)), not qualitative description.
• Option C: The formula for power is \( P = \frac{W}{t}=\frac{weight \times height}{time} \). By taking each player’s weight, recording their time to climb 3.0 m, calculating \( weight \times 3.0\space m \) (work) and dividing by time (to get power), then comparing, we can find who has the most power.
• Option D: Multiplying weight by time (\( weight \times time \)) and dividing by height is not the correct power formula (power is \( \frac{work}{time}=\frac{weight \times height}{time} \)), so this would give an incorrect value.

Answer:

C. Take the weight of each player. One at a time, have each player run up the stairs and record the time. Then, multiply the player’s weight by 3.0 m and divide that by the time it took for them to reach the top of the stairs. Repeat this calculation for all players and compare.