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)? Use 1.3 kg/m3 as a value for the density of air.
P=
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?
PM=
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 2.0 h?
c=
When you ride a bicycle at constant speed, almost all of the energy you expend goes into the work you do against the drag force of the air. In this problem, assume that all of the energy expended goes into working against drag. The drag force on an object is approximately proportional to the square of its speed with respect to the air. For this problem, assume that F ∝ ν2 exactly and that the air is motionless with respect to the ground unless noted otherwise. Suppose a cyclist and her bicycle have a combined mass of 60 kg and she is cycling along at a speed of 5 m/s.
Upon reducing her speed back down to 5 m/s, she hits a headwind of 5 m/s. How much power is she expending now?
A. 100 W B. 200 W C. 500 W D. 1000 W
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