A record was set for stair climbing when a man ran up the 2300 steps of the Empire State Building in 10 minutes and 20 seconds. If the height gain of each step was 0.2 m, and the man's mass was 63.0 kg, what was his average power output during the climb?
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0-9
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To determine the average power output of the man during the climb, we need to calculate the work done and divide it by the time taken.
First, let's calculate the height the man has climbed:
Height of each step = 0.2 m
Total height = Height of each step * Number of steps = 0.2 m/step * 2300 steps = 460 m
Next, let's calculate the work done:
Work = Mass * Gravity * Height
Mass = 63.0 kg
Gravity = 9.8 m/s^2 (acceleration due to gravity)
Height = 460 m
Work = 63.0 kg * 9.8 m/s^2 * 460 m = 280,548 J
Now, let's convert the time taken to seconds:
Time taken = 10 minutes * 60 seconds/minute + 20 seconds = 620 seconds
Finally, let's calculate the average power output:
Average power = Work / Time taken
Average power = 280,548 J / 620 s
Using a calculator, divide 280,548 by 620 to get the average power output. The answer will be in watts (W).