Bike gears and work
Q. How do the concepts of work and energy relate to the gears on a bicycle?
A. Remember the question in your homework (#2) concerning “jacking” up the corner of a car? Well, the physics involved is the similar to what we use to understand pedals on a bike.
The work you do on the handle of the jack is equal to the work that the jack does on the car (neglecting the effects of friction). Work equals the force applied times the distance over which that force is exerted. Pedals are a method for transferring work from you to the bike (just like the jack transfers work from you to the car). The product of the force (F) you exert on the pedals and the distance (D) the pedals move equals the force exerted on the rim of the wheel times the distance it moves. That is, Fpedal * Dpedal = Ftire * Dtire.
For the freestanding bike that we used in DR, one can vary the force applied to the tire over a large range (by changing gears) while keeping the force one applies to the pedals constant.