The Question: Let’s imagine a bicyclist maintaining a constant acceleration of 2 m/s which results in the subsequent increase in speed proportional to time and consequent quadratic increase in distance covered. (This level of acceleration is doable, but not normal.) Let’s not dwell on it, but we now all know that my mass is 90.7 kg.
a) How much force do I have to apply to the ground through the pedals and the tires in order to keep up that constant acceleration?
b) What fraction of my weight is this force?
The Answer:
a) This is a simple application of the popular form of Newton’s Second law,
b) To compare to my weight, we again can use the same formula with an important difference (we’ll call my weight w) and I’ll approximate the acceleration due to gravity, which is m/s, as m/s.
So the force that my legs would have to continuously apply to the pedals, and in turn to the ground through the friction between the tires and the road is about 20% ( 180/900) of my weight.
How much sustained force is this? Well, suppose we have a stationary bike hooked up to a pulley and a bag with five bowling balls. The force required to keep that bag ‘o balls aloft—forever—is the amount of force that I’d have to sustain — forever— to maintain that acceleration on the road.
Now is any of this sensible? After 10 seconds of this acceleration I’d be traveling at 20 m/s, which is about 45 mph. So obviously, that’s too fast to imagine pedaling a bicycle. Rather, if it were possible for me to exert 181 N, after about a couple of seconds, I’d be moving around 10 mph and surely at that point I’d stop trying to accelerate and apply just enough force to maintain that speed.