A record was set for stair climbing when a man ran up the 2100 steps of the Empire State Building in 15 minutes and 10 seconds. If the height gain of each step was 0.2 m, and the man's mass was 73.0 kg, what was his average power output during the climb
I'm not sure which equation to use to solve.
energy = m g h = 73.0 * 9.81 * 420
time = 60 * 15 + 10
power = energy / time
To find the average power output during the climb, you can use the equation:
Power (P) = Work (W) / Time (t) ...(equation 1)
To find the work done, you can use the equation:
Work (W) = Force (F) x Distance (d) ...(equation 2)
In this case, the force can be calculated using the equation:
Force (F) = Mass (m) x Acceleration (a) ...(equation 3)
Now, let's break down the calculation step by step:
1. Calculate the distance (d):
Given that there are 2100 steps, and each step has a height gain of 0.2 m, the total distance climbed can be calculated as:
Distance (d) = 2100 steps x 0.2 m = 420 m
2. Calculate the time (t):
Given that the time taken to climb was 15 minutes and 10 seconds, convert it to seconds:
Time (t) = 15 minutes x 60 seconds/minute + 10 seconds = 910 seconds
3. Calculate the force (F):
Using equation 3, we can calculate the force exerted by the man:
Force (F) = Mass (m) x Acceleration (a)
Since no acceleration is mentioned, we can assume that the man is climbing at a constant velocity. Thus, the net force acting on him is zero (since he is not accelerating). Therefore, the force can be calculated as:
Force (F) = Mass (m) x Acceleration (a) = 73.0 kg x 0 m/s^2 = 0 N
4. Calculate the work done (W):
Using equation 2, we can calculate the work done by the man:
Work (W) = Force (F) x Distance (d) = 0 N x 420 m = 0 J
5. Finally, calculate the average power (P):
Using equation 1, we can calculate the average power output during the climb:
Power (P) = Work (W) / Time (t) = 0 J / 910 s = 0 W
Therefore, the average power output during the climb is 0 Watts (W).