Answer:
the percentage of power output that keeps the man moving on the treadmill is approximately 2093%.
To calculate the percentage of power output that keeps the man moving on the treadmill, we need to determine the total amount of energy required to keep him running on the treadmill and compare it to his power output.
First, let's calculate the gravitational potential energy lost by the man while running on the treadmill:
ΔPE = m * g * h
Where m is the mass of the man (85.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height he ascends (determined by the incline angle of the treadmill):
h = d * tan(θ)
Where d is the horizontal distance traveled and θ is the incline angle (2.40°).
The horizontal distance traveled can be calculated based on the time spent running on the treadmill:
d = v * t
Where v is the velocity of the man (2.90 m/s) and t is the time spent running (35.0 min, converted to seconds).
Substituting the expression for d into the expression for h:
h = (v * t) * tan(θ)
Substituting the values for m, g, v, t, and θ:
h = (2.90 m/s * 35.0 min * 60 s/min) * tan(2.40°)
h = (1029 m) * tan(2.40°)
h = (1029 m) * 0.0424
h = 43.98 m
Substituting the values for m, g, and h into the expression for ΔPE:
ΔPE = 85.0 kg * 9.8 m/s^2 * 43.98 m
ΔPE = 35,734 J
The man also does work against air resistance and friction, but for simplicity, we will assume those are negligible. The total energy required to keep him running on the treadmill is thus equal to the change in gravitational potential energy, or 35,734 J.
Next, let's calculate the man's power output:
Power = Work / Time
Where Work is the amount of energy expended and Time is the time spent running.
Substituting the values for Work and Time:
Power = 35,734 J / (35.0 min * 60 s/min)
Power = 35,734 J / 2100 s
Power = 16.95 W
Finally, we can calculate the percentage of power output that keeps the man moving on the treadmill:
Percentage Moving = (Power Required / Power Output) * 100%
Substituting the values for Power Required and Power Output:
Percentage Moving = (35,734 J / 16.95 W) * 100%
Percentage Moving = 2092.71%
So the percentage of power output that keeps the man moving on the treadmill is approximately 2093%. This is because the man's power output of 300 W is not sufficient to sustain his running on the treadmill and he must rely on stored energy in his body to make up the difference.
Step-by-step explanation: