So I am a person sitting on a chair that has wheels. Now, the question is - can I push the chair when I am sitting on the chair and have nothing to push against? [other than the chair]? Note that I have no contact whatsoever with the floor. From experience, I know I can. So why? Whenever i try to push against the chair, according to Newton's 3rd Law, each force produces an equal and opposite force. So as I push against the chair, I exert a force, and it exerts an equal and opposite force on me. But I move along with the chair, so I must exert a second force on the chair, which is in the opposite direction as the direction of acceleration of the chair. (a) <--- (man on chair) ---->(chair on man) (b) --->(man's bottom on chair) <---(chair on man) such that man does not move with respect to the chair's reference frame. What about the outside world though? I know that the chair accelerates, so there must be a net force to the left. The guy is in the middle, and he tries to push the chair to the left. I see three forces exerted. (a) is the man pushing chair left, the chair edge pushes the man right. Then the man's bottom and the chair have to push each other (b). Man pushes chair right, chair pushes man left. And what if you replace the man with say, a motor? The difference here would be that the motor would probably be a lot more attached to the bottom of the chair than the man would be. So the question is - is the force in (a) greater than the force in (b) and why? Since if the force in (a) is greater than that in (b), then the chair will experience acceleration to the left, which is apparently what I experienced
Think of it this way. If there was no friction between the wheelchair and the ground, or between your palms and the wheelchair, would you get anywhere? If you like, you can envision all surfaces (ground, wheelchair, and your palms) being slicked with oil. why is that you can't just use your pinky to propel the wheelchair and you need to put in a fair bit of energy (work) to get it moving from rest?
Interesting analogy with the wheelchair (however, I am not talking about a wheelchair here). On the other hand, perhaps a small force change would be enough to propel the wheels forward.
You're just shifting the centre of mass of the chair-person system around. Suppose you sit on the chair, and the chair is on ice. There are no net external forces on the chair-you system, so total momentum is conserved (and is zero if the chair starts off stationary). If you then flail your arms or legs about, you will shift the centre of mass of the system relative to the position of the chair, but (importantly) NOT relative to the ice. So, the most you can achieve is to move the chair a small amount in any direction, and the motion will stop when you stop moving your body. Replace the ice with a surface with friction and things change a little. In that case, when you shift the centre of mass you can apply enough force to the ground in order to start the chair rolling. The static friction force between the ground and the wheels is then reduced, and a larger force will be needed to stop the chair rolling again. So, the chair might roll for a certain distance across the floor. Possibly, you can also interact with the air, by flapping your arms around for example, and generate a net force that way.
But how does friction relate to COM? None of my physics textbooks explain any relation of CoM with friction (perhaps since the friction chapter in those books is before the chapter that explains CoM)
