A cyclist intends to cycle up a 7.00o hill whose vertical height is 104 m. Assuming the mass of bicycle?

plus person is 71.2 kg, calculate how much work must be done against gravity. ( I already found this part of the question to be 72,567 J. But now i must figure out:
**If each complete revolution of the pedals moves the bike 5.04 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 33.8 cm.

First, recognize that the only work your bicyclist needs to do is the work to raise that combined mass (bike and rider) to a height H = 104 m. This results because we are neglecting friction and other losses.

Thus, find the average work (we = work per d = 5.04 m along the path). we =mgh = mg(d sin(theta)); where theta = 7 deg slope, g = 9.81 m/sec^2, and m = 71.2 kg. Then, from the work function, we have we = Fs and F = we/s = we/(2pi D/2); where D = .338 m the diameter of the pedal path. s is the circumference of the pedal path, which is the pedal distance traveled for each 5.04 advance along the slope.

F = 2f; where f is the force on each of two pedals to give us the average total force F for each 5.04 m of advance. Therefore F = 2f = we/(2pi D/2) = mg(d sin(theta))/(2pi D/2); so that f = mg(d sin(theta))/(2pi D) = (71.2*9.81*5.04*sin(7))/(2*3.14159*.338) = 202 N per pedal on average. For total force F = 2f, just double the answer.

PS: There's another way to work this. Use your answer WE = 72,567 kg-(m/sec)^2 (aka Joules), find the number of increments N = S/d = H/sin(theta)//d of distance d = 5.04 to travel the slope distance S = H/sin(theta) = 104/sin(7).

Then the average work per d covered is we = WE/N = WEd/S = WEd//H/sin(theta) = WEd sin(theta)/H = mgH d sin(theta)/H = mgd sin(theta). And this is a good thing because earlier, through the earlier approach we also got we =mgh = mgd sin(theta). From then on, find F or f in the same manner as before.