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 70 kg , what was his average power output during the climb? Give your answer in both watts and horsepower.
p=w
P=hp
Work done by runner
= F *d
= mg * d
= 70 kg * 9.8 m/s2 * (1576 steps * 0.2 m/step)
Divide your answer by time in seconds to get power output in Watts.
Look up conversion to horsepower.
i did divide the answer in sec but the answer still wrong can you pls do it maybe I'm doing something wrong
Well, let's see if I can stair you in the right direction with this answer!
To calculate average power, we need to first calculate the total work done by the runner. The work done is equal to the force exerted multiplied by the distance covered. In this case, the force exerted is equal to the mass of the runner multiplied by the acceleration due to gravity, which is approximately 9.8 m/s^2. The distance covered is equal to the height gain of each step multiplied by the total number of steps.
So, let's calculate the total work done:
Work = (70 kg) x (9.8 m/s^2) x (0.20 m/step) x (1576 steps)
Next, we need to calculate the time it took the runner to complete the climb in seconds:
Time = 9 minutes x 60 seconds + 33 seconds
Now, we can calculate the average power using the formula:
Power = Work / Time
Finally, converting the power from watts to horsepower, we can use the conversion factor:
1 horsepower = 746 watts
Now, let's crunch those numbers! But be careful not to trip on them...
Calculating the total work done:
Work = (70 kg) x (9.8 m/s^2) x (0.20 m/step) x (1576 steps)
Work ≈ 216,371.2 joules
Calculating the time in seconds:
Time = 9 minutes x 60 seconds + 33 seconds
Time ≈ 573 seconds
Calculating the average power in watts:
Power = Work / Time
Power ≈ 216,371.2 joules / 573 seconds
Power ≈ 377.70 watts
Converting the power to horsepower:
Power (in horsepower) = Power (in watts) / 746
Power (in horsepower) ≈ 377.70 watts / 746
Power (in horsepower) ≈ 0.51 horsepower
So, the runner's average power output during the climb was approximately 377.70 watts or 0.51 horsepower.
I hope this answer lifted your spirits like a stair-tening joke!
To calculate the average power output during the climb, we need to use the formula:
Power (P) = Work done (W) / Time taken (t)
To calculate the work done, we need to know the gravitational potential energy gained by climbing the stairs. This can be calculated using the formula:
Gravitational Potential Energy (PE) = Mass (m) x Gravity (g) x Height (h)
Where:
Mass (m) = 70 kg (given)
Gravity (g) = 9.8 m/s^2 (acceleration due to gravity)
Height (h) = Number of steps x Height gain per step
Number of steps = 86 (given)
Height gain per step = 0.20 m (given)
Let's calculate the gravitational potential energy gained:
Height = Number of steps x Height gain per step
Height = 86 x 0.20
Height = 17.2 meters
Now we can calculate the work done:
Work (W) = Gravitational Potential Energy (PE)
Work (W) = Mass (m) x Gravity (g) x Height (h)
Work (W) = 70 kg x 9.8 m/s^2 x 17.2 m
Next, we convert the time taken to seconds:
Time taken (t) = 9 minutes + 33 seconds
Time taken (t) = 9 x 60 + 33
Time taken (t) = 573 seconds
Now we can calculate the average power output:
Power (P) = Work (W) / Time taken (t)
To get the answer in watts and horsepower, we'll need to convert the units:
1 watt = 1 joule/second
1 horsepower (hp) = 745.7 watts
Let's calculate the average power output:
Power (P) = Work (W) / Time taken (t)
Power (P) = (70 kg x 9.8 m/s^2 x 17.2 m) / 573 seconds
To get the answer in watts:
P = (70 x 9.8 x 17.2) / 573
To get the answer in horsepower:
P (hp) = (70 x 9.8 x 17.2) / (573 x 745.7)
Now we can calculate the average power output.
Answer to question #10
The Empire State Building would have been impressive if it were built at any time. What about the time period in which it was built made it even more impressive? Use information from the passage to support your answer.