Lance Armstrong's Power

The instantaneous power generated by a force that does work is the rate P = dW/dt at which it does work. The SI unit of power is the Watt, equal to 1 Joule per second. The average power is the work done by the force, divided by the time over which it was applied.  If the work done by a force F through a small displacement dx is dW = F . dx, then the instantaneous power is P = F . v.

## (A) If we make the assumption that the rolling friction forces on the bicycle and air friction forces are negligible while climbing, how long would it take Lance Armstrong to climb a mountain in the Alps (Alpe d'Huez) with an elevation change of 1,000 m? Assume Lance has a mass of 66 kg and that his climbing bicycle has a mass of 7.5 kg.

(B) (Bonus question; your group will get an extra whiteboard point for today if you can show me by next class a solution that gives the right answer to the following:) There is a friction force on a rolling object (due to deformation of the object and the surface on which it rolls) called rolling friction. To a good approximation this is a constant force; for a good road bike this is 3.5 N. The air friction force on a bicyclist is proportional to the square of the square of the riders velocity, and has the value (0.26 kg/m ) v2, where v is in m/s. Using Armstrong's sustained power output, with what speed (in miles per hour) could he ride on level ground?