**Lance Armstrong's Power**

The instantaneous power generated by a force that does work is the rate *P* = d*W*/d*t* 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 d**x** is d*W* =** ***F* . d**x**, then the
instantaneous power is *P* = *F* . *v*.

## At his
training peak, Lance Armstrong was capable of generating 350 Watts with his
aerobic metabolism, meaning that he could sustain this level of power output for
extended periods of time.

## (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 ) *v*^{2},
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?