Average force exerted on pedalf tangent to their circular path of a bike

[thulling]

Homework Statement

A cyclist intends to cycle up a 8.2^\circ hill whose vertical height is 180 m. The mass of the bike and the cyclist is 95kg.

If each complete revolution of the pedals moves the bike 4.7 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 39 cm.

Homework Equations

Work of person=Work of gravity
Work of gravity=mgsintheta(d)
Force of person(2pi(r))=mgsintheta(d)
Force of person= mgsintheta(d)/(2pi(r))

The Attempt at a Solution

I plugged the numbers into this final equation and it keeps saying try again. I converted 39cm to meters and took half of that as the radius.

(95*9.8*sin(8.2)*4.7)/(2pi(.0195)

I got 5100 (rounded sig figs) This is wrong.
Please help.

 

[Inferior89]

The work that needs to be done will be mgh where m is the mass of the bike + cycle, g is the gravitational acceleration and h is the vertical height of the hill.

The total length that the wheels will need to turn will be 180/sin(8.2 degrees).

Now you can calculate how many times the wheel will need to turn which you can convert to how many times the pedals must turn.

When you know the number of times the pedals must turn you can calculate the total distance the pedals must turn.

The answer will be mgh/(total distance the pedals must turn).