An 80 kg man climbs a 50 m-high hill in 20 minutes. What is the average power in watts he expends climbing the hill?
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To calculate the average power exerted by the man while climbing the hill, we can use the formula:
Power (P) = Work (W) / Time (t)
To find the work done, we need to determine the force required to overcome gravity and move the man upward. The force necessary to counteract gravity is given by the formula:
Force (F) = mass (m) * acceleration due to gravity (g)
Given that the mass of the man is 80 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the formula to calculate the force.
F = 80 kg * 9.8 m/s^2 = 784 N
The work done can be calculated using the formula:
Work (W) = Force (F) * distance (d)
Given that the distance climbed is 50 m, we can substitute this value into the formula to calculate the work done.
W = 784 N * 50 m = 39,200 J
Finally, we can substitute the values for work and time into the power formula:
P = W / t
Since the time is given as 20 minutes, we need to convert it to seconds, as power is measured in watts which is joules per second.
1 minute = 60 seconds
20 minutes = 20 * 60 = 1,200 seconds
P = 39,200 J / 1,200 s ≈ 32.7 W
Therefore, the average power expended by the man while climbing the hill is approximately 32.7 watts.