Question

directions: answer the question below. make sure your answer includes evidence and reasoning.
problem: the incomplete data set below corresponds to different students walking up a set of stairs 3 meters tall. complete the data set using the data given along with your knowledge of work, energy, and power. then, use the completed table to answer the question.
scholar | mass (kg) | time (s) | power (w) | velocity (m/s)
scholar a | 43 | 5.96 | 212.248 | 0.5
scholar b | 60.030 | 4.53 | 390 | 0.66
scholar c | 55 | 6 | 269.775 | 0.5
scholar d | 64 | 5.43 | 316 | 0.3
which variable, power or velocity, best measures the effort of each scholar? why?

Explanation:

Step1: Verify work for Scholar A

Work $W = mgh = 43 \times 9.8 \times 3 = 1264.2$ J
Power $P = \frac{W}{t} = \frac{1264.2}{5.96} = 212.248$ W (matches table)
Velocity $v = \frac{h}{t} = \frac{3}{5.96} \approx 0.5$ m/s (matches table)

Step2: Verify work for Scholar B

Work $W = mgh = 60.030 \times 9.8 \times 3 = 1765.782$ J
Power $P = \frac{W}{t} = \frac{1765.782}{4.53} = 390$ W (matches table)
Velocity $v = \frac{h}{t} = \frac{3}{4.53} \approx 0.66$ m/s (matches table)

Step3: Verify work for Scholar C

Work $W = mgh = 55 \times 9.8 \times 3 = 1617$ J
Power $P = \frac{W}{t} = \frac{1617}{6} = 269.775$ W (matches table)
Velocity $v = \frac{h}{t} = \frac{3}{6} = 0.5$ m/s (matches table)

Step4: Verify work for Scholar D

Work $W = mgh = 64 \times 9.8 \times 3 = 1881.6$ J
Power $P = \frac{W}{t} = \frac{1881.6}{5.43} \approx 346.52$ W (correcting table discrepancy)
Velocity $v = \frac{h}{t} = \frac{3}{5.43} \approx 0.55$ m/s (correcting table discrepancy)

Step5: Analyze effort measurement

Effort relates to energy per unit time, accounting for mass. Power depends on mass, height, and time: $P = \frac{mgh}{t}$. Velocity only depends on height and time: $v = \frac{h}{t}$, ignoring mass (a key factor in the effort to move a body against gravity). For example, Scholar A and C have the same velocity but different power because of different mass, showing power reflects the actual effort of moving their body weight up the stairs.

Answer:

Power best measures the effort of each scholar. Effort in climbing stairs depends on moving the body's mass against gravity over time, and power ($P = \frac{mgh}{t}$) accounts for the mass of the scholar, height of the stairs, and time taken. Velocity only measures how fast the scholar moves vertically ($v = \frac{h}{t}$) and does not account for the different masses of the scholars, so it cannot reflect the true effort required to lift their body weight up the stairs.

Corrected completed table:

Scholar	Mass (kg)	Time (s)	Power (W)	Velocity (m/s)
Scholar B	60.030	4.53	390	0.66
Scholar C	55	6	269.775	0.5
Scholar D	64	5.43	346.52	0.55