Question

In a physics lab, a 60-kg student runs up a 2.0-meter tall flight of stairs in 1.5 seconds. The work done to get to the top is 1200 Joules. The student's power rating is approximately _W.

Answer 1

The power rating of the student is approximately 800 Watts.

Step-by-step explanation:

To calculate the power output, we need to use the work-energy principle, which states that the work done is equal to the change in kinetic energy (KE) plus the change in potential energy (PE). The work done is given as 1200 Joules, and the vertical height of the stairs is 2.0 meters. We can calculate the change in potential energy using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height. The initial kinetic energy is zero, as the student starts from rest. So, we have:

W = KEƒ + PEg

1200 J = 0 + (60 kg × 9.8 m/s² × 2.0 m)

Simplifying, we have:

1200 J = 1176 J

To calculate the power, we divide the work done by the time taken. The time taken is given as 1.5 seconds. So, we have:

Power (P) = Work (W) / Time (t)

P = 1200 J / 1.5 s = 800 W

Answer 2

The student's power rating is approximately 800W.

Power is the rate of doing work. Its SI unit is Watt. 1 W = 1J/sec

Given: The work done to get to the top is 1200 Joules

Time = 1.5 seconds.

Power =
`(work done)/(time) = (1200J)/(1.5 sec) = 800J/sec = 800W`