I am trying to understand how mechanical advantage works in a bicycle but I am still a little confused. I understand that the force applied to the pedal goes first to the crank sprocket which then applies a force to the chain at its radius which is the then applied to the gear at the wheel. While the force applied is same in either case, the torque is not. Because the big gear has a larger radius, it would receive a greater torque. What I don't understand, however, is why is that there is a greater output force with the larger gear? And also I don't quite understand why a greater output force is beneficial.