Physics Problem Involving Power?

Question

At his training peak, Lance Armstrong was capable of generating 395 Watts with his aerobic metabolism, meaning that he could sustain this level of power output for extended periods of time. He uses crank arms of length 175 mm (this is the distance from the bottom bracket axle to the axle on which the pedals rotate), and pedals at the optimum cadence of 90 revolutions per minute while climbing.

1) What is the average force with which he pushes down on the pedals? You may assume the force is applied at 90 degrees to the crank arms.

If we make the assumption that the rolling friction forces on the bicycle and air friction forces are negligible while climbing,

2) How long did it take Lance Armstrong to climb L'Alpe d'Huez in the French Alps, a 15.5 km (10 mile) time trial with an elevation change of 1,110 m? You can assume that Lance's racing mass was 75 kg and his climbing bike had a mass of 7 kg.

Answer 1

Good old lance.  He could probably blow 6.0 - 6.5 l/min O2 which would be phenomenal for a guy his size.  OK

1.

E/t = Watts

E = F*d

F=E/d

= 395 W * 2 pi 0.175m * 90 rev/min * 1 min/60 s

= 651 N

2. PE = mgh

= (75+7)kg * 9.81m/s^2 * 1,100 m

= 884,862 J

PE/t = Power (Watts)

t = PE/Power

= 884,862 J/ 395 W

=2240 sec

= 37 min 20 secs