Question

in a physics class, two students volunteer to participate in an experiment about the rate of energy transfer (power). they find a set of stairs on campus and want to use them to determine how much power they exert. they conduct their investigation and collect the data shown.

student	weight	height of 1 stair	# of stairs climbed	time
student 2	700n	15cm	8	2.1s

which student exerts more power during the experiment?

• student 1 exerted more power because she was able to reach the top of the stairs more quickly than student 2.
• both students exerted equal power. student 1’s lighter mass but faster time equals student 2’s heavier mass and slower time.
• student 2 exerted more power because he had to lift a greater mass up the stairs than student 1 so he had to do more work
• both students exerted equal power. they both climb the same number of stairs.

Explanation:

Step1: Recall Power Formula

Power \( P \) is work \( W \) over time \( t \), \( P = \frac{W}{t} \). Work \( W \) against gravity is \( W = Fd \), where \( F \) is weight (force) and \( d \) is total height.

Step2: Calculate Total Height for Each

For 1 stair height \( h = 15\,\text{cm} = 0.15\,\text{m} \), number of stairs \( n = 8 \). Total height \( H = n \times h \).

• Student 1: \( H_1 = 8 \times 0.15 = 1.2\,\text{m} \)
• Student 2: \( H_2 = 8 \times 0.15 = 1.2\,\text{m} \)

Step3: Calculate Work for Each

\( W = F \times H \) (since \( F \) is weight, force against gravity).

• Student 1: \( W_1 = 500\,\text{N} \times 1.2\,\text{m} = 600\,\text{J} \)
• Student 2: \( W_2 = 700\,\text{N} \times 1.2\,\text{m} = 840\,\text{J} \)

Step4: Calculate Power for Each

\( P = \frac{W}{t} \).

• Student 1: \( P_1 = \frac{600\,\text{J}}{1.5\,\text{s}} = 400\,\text{W} \)
• Student 2: \( P_2 = \frac{840\,\text{J}}{2.1\,\text{s}} = 400\,\text{W} \)

Step5: Analyze Options

• Option 1: Wrong, power depends on work and time, not just time.
• Option 2: Correct, \( P_1 = P_2 = 400\,\text{W} \). Lighter weight (less work) but faster time, heavier weight (more work) but slower time balance out.
• Option 3: Wrong, Student 2’s power equals Student 1’s (calculations show equal power).
• Option 4: Wrong, same stairs don’t mean same work (different weights) or same power.

Answer:

B. Both students exerted equal power. Student 1’s lighter mass but faster time equals Student 2’s heavier mass and slower time.