Calculating Power and Force in Cycling: Solving for Force in the Equation P=Fv

[oisdas]

Homework Statement

Professional cyclists typically travel at 40 km/h during races. Air resistance produces a force on a cyclist that obeys a law~F(v) =−bv^2 opposite the direction of motion and proportional the speed squared. The coefficient b differs from person to person. The average power Pave that a well-trained cyclist can maintain for Nh hours is roughly Pave^2= 3(Pftp^2)/Nh, where Pftp is the maximum power she can produce without lactic acid accumulation. Solve for the average speed the cyclist can maintain in terms of Pftp and the distance of the race.

Relevant Equations

P=Fv

OK, so I tried to relate the equation P=Fv to the given equation that Pave^2= 3(Pftp^2)/Nh. I put Nh in terms of distance to satisfy the requirement that the answer should be in terms of Pftp and distance by saying Nh = distance/Vave. I also substituted Pave with Fvage.
(FVage)^2 = 3(P^2ftp)Vave/d ---> Vave = 3(^2Pftp)/Fd

My problem is I don't know what to substitute force with. The force is not only the -bv^2 from air resistance, it is also the force applied by the cyclist. With this, how would I find force?

 

[haruspex]

The force is not only the -bv^2 from air resistance, it is also the force applied by the cyclist.

Taking the speed as constant, what is the net force?

 

[oisdas]

Taking the speed as constant, what is the net force?

If speed was constant, the net force would just be from air resistance. However, how would I assume that speed is constant?

 

[haruspex]

how would I assume that speed is constant?

Because if it varies significantly you do not have enough information.

 

[oisdas]

Because if it varies significantly you do not have enough information.

I see, thank you! With this, I will set the force the bicyclist is applying = Fair since a=0 and get F= -bv^2.