Cycling. For a touring bicyclist the drag coefficient is 1.00, the frontal area ?A? is 0.463 m2, and the coefficient of rolling friction is 0.0045. The rider has mass 50.0 kg, and her bike has mass 12.0 kg. (a) To maintain a speed of 12.0 m/s (about 27 mi/h) on a level road, what must the rider’s power output to the rear wheel be? (b) For racing, the same rider uses a different bike with coefficient of rolling friction 0.0030 and mass 9.00 kg. She also crouches down, reducing her drag coefficient to 0.88 and reducing her frontal area to 0.366 m2. What must her power output to the rear wheel be then to maintain a speed of 12.0 m/s? (c) For the situation in part (b), what power output is required to maintain a speed of 6.0 m/s? Note the great drop in Power requirement when the speed is only halved. (For more on aerodynamic speed limitations for a wide variety of human-powered vehicles, see “The Aerodynamics of Human-Powered Land Vehicles,” Scientific American?, December 1983.)

Solution 99P Step 1: Data given Drag coefficient C = 1 d C(fair = 1/2CAv ) 2 2 Frontal area A = 0.463 m Coefficient of rolling friction Cf= 0.0045 Mass of rider = m = 50.0 kg 1 Mass of cycle = m = 12.0 kg 2 Velocity of the rider v = 12.0 m/s