Train Wheels Problem: Solving for Force and Gravity | Homework Statement

[Jakecp]

I looked here https://en.m.wikipedia.org/wiki/Mechanical_advantage#Speed_ratio but it is just the MA

 

[haruspex]

You are right in that , but i don't get at 100% how does that happen? This : you can arrange to get twice the force if you accept getting half the speed, or you can get twice the speed if you accept only getting half the force.

Consider two of the front gears on a bicycle, one twice the diameter of the other. Uphill, in low gear, I apply a steady torque to the pedals and turn them at some constant rate. That exerts a force F on the chain and and makes it move at speed v. Cresting the hill, I change to the high gear, but find applying the same torque keeps the pedals rotating at the same rate as before. The force on the chain drops to F/2, but the chain moves twice as fast. The power transferred is Fv in both cases.