A 62 kg hiker climbs to the top of a 3700 m-high mountain. The climb is made in 5.0 h starting at an elevation of 2600 m. Calculate the average power output in watts. Calculate the average power output in horsepower.
First you need to calculate the PE needed to make the climb.
U=mgh U=(62*(2600-3700)*9.8)
This value is energy or work denoted as a Joule. A Watt= Joule/Seconds
So simply take your joules and divide it by the time the trip took. Convert your 5hr to seconds so...
W=(62*(2600-3700)*9.8)/(5*3600)
easy way to find HP is 1W=0.00134102209HP or
HP=(62*(2600-3700)*9.8)/(5*3600)*0.00134102209
To calculate the average power output in watts, we can use the formula:
Power (in watts) = Work / Time
First, let's calculate the work done by the hiker. The work done is equal to the change in potential energy:
Work = m * g * Δh
Where:
m = mass of the hiker (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Δh = change in height (in meters)
Given:
m = 62 kg
g = 9.8 m/s^2
Δh = 3700 m - 2600 m = 1100 m
Using the equation, we have:
Work = 62 kg * 9.8 m/s^2 * 1100 m
Work = 67,236 J (joules)
Now, we can substitute the values into the power formula:
Power (in watts) = 67236 J / 5.0 h
However, since the given time is in hours, we need to convert it to seconds:
1 hour = 3600 seconds
So, the time in seconds would be:
5.0 h * 3600 s/h = 18,000 s
Now, substituting the values:
Power (in watts) = 67236 J / 18000 s
Power ≈ 3.736 watts
Therefore, the average power output in watts is approximately 3.736 watts.
To calculate the average power output in horsepower, we can use the conversion factor:
1 horsepower (hp) = 745.7 watts
So, to convert the power from watts to horsepower:
Power (in horsepower) = Power (in watts) / 745.7
Substituting the values:
Power (in horsepower) = 3.736 watts / 745.7
Power ≈ 0.005 hp
Therefore, the average power output in horsepower is approximately 0.005 horsepower.