How Do I Calculate the Average Force Exerted on Bicycle Pedals?

[Liatana]

What do i need to know to solve this:(please help me, thanks!)

First they ask me:
a-) A cyclist intends to cycle up a 7.90° hill whose vertical height is 118 m. Assuming the mass of bicycle plus person is 72.0 kg, calculate how much work must be done against gravity.

Which i found was m*g*h(height)= 83345.76 J


What i can't solve is:

b-) If each complete revolution of the pedals moves the bike 5.03 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 35.6 cm.

 

[tim_lou]

use energy conservation:

how much energy did the bicycle gain after one revolution of the pedals?

if this energy all comes from the work the cyclist does, what would be the distance the feet of the cyclist travel? according to the definition of work, what would be the average force then?

 

[Liatana]

i still don't get it!

 

[OlderDan]

i still don't get it!

All the work done by the cyclist was converted to potential energy. The mgh result you found can be computed as mgh, or it can be computed as the component of force acting parallel to the incline times the distance moved parallel to the incline. Each revolution of the pedal wheel corresponds to the given distance up the incline. That raises the bicycle to a new height and changes its PE by an amount you can calculate given the distance and the angle. The cyclist must do work equal to that change in PE by forcing the pedals to move. Since you know the amount of work, and are given the invormation needed to figure out how far a pedal has to be moved, you can calculate the average force that must be applied to move the pedals.