Is the force you exert on the ground greater than the force you can exert with your legs?

Question

I want to know if making a bicycle that is powered by the riders weight would be more efficient than the riders legs. Do you exert more force with your legs or with your weight? I want to have an extremely high gear ratio and I want to know if it could be powered by, well, gravity. Gravity is a force and I know it CAN be converted into motion, but is it a more powerful force than your legs? I would assume it is but i don't know any of the math behind it. That's what I'm here for. The equations. If you don't understand what I'm looking for but think you can help me tell me so I can explain further.

Answer 1

No, your legs are more powerful. Not only can adaviel carry furniture upstairs, but one of the reasons bicycle racers can use such tiny hard saddles is that they're not putting all their weight on them. They push down so hard on the pedals that they are partially lifted off the saddle. At times, they need to pull up on the handlebars because they are pushing down on the pedals with a force greater than their weight, so the pedals are pushing up on them with a force greater than their weight (Newton's Third Law). How hard they can push down on the pedals can be limited by how hard they can pull up on the handlebars.



Check out the picture of Fiorenzo Magni racing in the 1956 Giro d’Italia. He had a broken collar bone in a crash the day before, which reduced how hard he could pull up on the handlebars. So he tied a piece of inner tube to his stem, and pulled up on it with his teeth.



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Edit: Sorry, I was so tickled to be reminded of that photo of Magni, that I didn't really address your question about equations. Let's apply Newton's Second Law to all the vertical forces on a casual cyclist. There is a gravitational force mg downward, and upward forces P from the pedals, S from the saddle, and H from the handlebars, so



Σ F = P + S + H - mg = ma = 0



where the sum is zero, as cyclists don't accelerate their bodies up and down out of the saddle, as it would be a terrific waste of energy. We want P, the upward force by the pedals, to be as big as possible, because we want the Newtwon's Third Law reaction force, downward by the cyclist on the pedals, to be as big as possible. Let's solve the equation for P.



P = mg - S - H



So to make P as big as possible, we could ride no-handed (H = 0), and push on the pedals to the point where we just barely lift off the saddle (S = 0)



P = mg



so at that point, the force P is the same as the force of gravity. Can we do any more? Yes! Instead of riding no-handed and making H = 0, we can pull up on the handlebars instead of resting on them, which changes the sign of H (because if we pull up on the handlebars, the handlebars are pulling down on us). Now we have



P = mg + H



so the force of the pedals on us (and thus the force of us on the pedals) can be greater than our weight by the amount we can pull up on the handlebars with our hands (or, in Magni's case, our teeth!).



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Later Edit: I'm almost saying you can't exert a force greater than your weight unless you have something to pull up on. If you try to exert a force greater than your weight without something to pull up on, the net force on you (weight downward, and, from Newton's Third Law, a force greater than your weight upward) will be upward, so you will accelerate upward yourself. You'd be in a situation where



Σ F = P + S - H - mg = ma



S and H go to zero, and P is greater than mg, so ma is positive, meaning you accelerate upward. Essentially, you'll jump up into the air. So you can exert such a force, but only briefly. If your person could jump suddenly enough (large acceleration) they might be able to break the board without pulling up on something. But that approach isn't going to get you very far on your bicycle.

Answer 2

1. Yes, from a simple perspective, in order to leave the ground during a jump, you must exert more force than is currently holding you to the ground. All actions have an equal and opposite reaction... so if your weight is exerting 100 kg/m/s/s of force on the earth you must exert over 100 in order to jump. However, your legs are a series of levers, so the actual force needed is reduced, this gets very complicated very quickly though, but the way to begin is to consider the type of lever involved in the hips, knees, ankles and toes. 2. Yes, Force = Mass X Acceleration, so in order to generate enough force (as in question 1) to jump, you must accelerate at more than 9.8 m/s/s, since you cannot change your mass.

Answer 3

Personally, I'm a normal guy who can carry furniture upstairs, so I can exert more force with my legs than my weight.



re. the bicycle thing, as the handlbars don't line up with the seat on a normal bicycle, pushing hard on the pedals is not that efficient - some of the force on the handlebars goes to counteracting the resulting turning moment rather than being used directly on the pedals.



but really, with a modern bike you can just use a lower gear. it's only on an old 3-speed where I refused to get off and walk that I would need to do that, and the bike construction isn't really strong enough - it makes creaking noises with 1600N of tension or whatever in the chain and sprocket and 800N off-centre on the handlbars.