When you ride a bicycle at constant speed, nearly all the energy you expend goes
ID: 1660732 • Letter: W
Question
When you ride a bicycle at constant speed, nearly all the energy you expend goes into the work you do against the drag force of the air. Model a cyclist as having cross-section area 0.42 m2 and, because the human body is not aerodynamically shaped, a drag coefficient of 0.90.
a)What is the cyclist's power output while riding at a steady 7.3 m/s (16 mph)?
b)Metabolic power is the rate at which your body "burns" fuel to power your activities. For many activities, your body is roughly 25% efficient at converting the chemical energy of food into mechanical energy. What is the cyclist's metabolic power while cycling at 7.3 m/s?
c) The food calorie is equivalent to 4190 J. How many calories does the cyclist burn if he rides over level ground at 7.3 m/s for 1.1 h ?
Please show your work and thank you !
Explanation / Answer
a). Take density of air = 1.2 kg/m3
Drag Force = Cd * 1/2 * AV^2
D = 0.9 * 0.5 * 1.2 * 0.42 * 7.3^2
D = 12.086 N
Power = D * V
= 12.086 * 7.3
= 88.23 W
b). Metabolic power = 88.23 / 0.25
= 352.92 W
c). Work done W = Metabolic power*time
= 352.92 * (1.1 * 60 * 60)
= 352.92 * 3960
= 1397563.2 J
Food calorie = 1397563.2 J / 4190 J
= 333.547 calories
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