A new record for running the stairs of the Empire State Building was set on February 3, 2003. The 86 flights, with a total of 1576 steps, was run in 9 minutes and 33 seconds.
If the height gain of each step was 0.20 m, and the mass of the runner was 68 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.
Never mind, i figured it out.
THANKS A LOT ALAN
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To calculate the average power output during the climb, we can use the formula for power:
Power (P) = Work (W) / Time (t)
First, we need to calculate the work done during the climb. The work is equal to the force multiplied by the distance:
Work (W) = Force (F) * Distance (d)
To calculate force, we need to know the weight of the runner. Weight is equal to mass multiplied by the acceleration due to gravity:
Weight (F) = mass (m) * acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
Now, let's calculate the necessary values step by step:
1. Calculate the weight of the runner:
Weight (F) = mass (m) * acceleration due to gravity (g)
Weight (F) = 68 kg * 9.8 m/s^2
2. Calculate the distance climbed:
Distance (d) = height gain per step (h) * number of steps (n)
Distance (d) = 0.20 m/step * 1576 steps
3. Calculate the work done:
Work (W) = Force (F) * Distance (d)
4. Calculate the time taken for the climb:
Time (t) = 9 minutes * 60 seconds/minute + 33 seconds
Now, let's plug in the values into the power formula to find the average power output:
Power (P) = Work (W) / Time (t)
Finally, let's convert the power from watts to horsepower:
1 horsepower (hp) is equal to 745.7 watts.
Now, you can perform the calculations and get the average power output in both watts and horsepower.