A 73kg sprinter, starting from rest, reaches a speed of 7.0 m/s in 1.8s, with a negliable effect due to air resistance. The sprinter then runs with the remained of the race at a steady speed of 7.0 m/s under the influence of a 35-N force due to air resistance. What is the average power needed (a) to accelerate the runner and (b) to sustain the steady speed at which most of the race is run? Express the answer in watts and horsepower.
I dont know how to do
To find the average power needed to accelerate the sprinter (part a), we can use the formula for power:
Power = Work / Time
Since the sprinter starts from rest and reaches a speed of 7.0 m/s in 1.8s, we can calculate the work done using the formula:
Work = (1/2) * mass * velocity^2
Substituting the given values:
Work = (1/2) * 73 kg * (7.0 m/s)^2
Work = 0.5 * 73 kg * 49 m^2/s^2
Work = 1764 kg⋅m^2/s^2
Now we can calculate the average power:
Power = Work / Time
Power = 1764 kg⋅m^2/s^2 / 1.8 s
Power ≈ 980.01 watts
To express the average power in horsepower, we can use the conversion factor:
1 horsepower (hp) = 746 watts
So, the average power to accelerate the sprinter is approximately 1.31 horsepower.
For part b, to find the average power needed to sustain the steady speed, we can use the formula:
Power = Force * Velocity
Since the air resistance force is given as 35 N and the velocity is 7.0 m/s:
Power = 35 N * 7.0 m/s
Power = 245 watts
To convert power in watts to horsepower, we can use the same conversion factor as before:
Power in horsepower = 245 watts / 746
Power ≈ 0.328 horsepower
Therefore, the average power needed to sustain the steady speed is approximately 0.33 horsepower.