Randall D. Knight — Work and Kinetic Energy: Problem 62

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 \( 0.45 \text{ m}^2 \) and, because the human body is not aerodynamically shaped, a drag coefficient of \( 0.90 \). Use \( 1.2 \text{ kg/m}^3 \) as the density of air at room temperature. (a) What is the cyclist's power output while riding at a steady \( 7.3 \text{ m/s} \) (\( 16 \text{ mph} \))? (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 \( 7.3 \text{ m/s} \)? (c) The food calorie is equivalent to \( 4190 \text{ J} \). How many calories does the cyclist burn if he rides over level ground at \( 7.3 \text{ m/s} \) for \( 1 \text{ h} \)?