Free body diagram of a person sitting on a wheeled chair

[InquilineKea]

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

[Sisyphus]

I'm not quite clear on what you're describing, but I'm pretty sure all mystery will disappear once you take friction into account.

[InquilineKea]

Hm, but if i myself do not move, then the force pairs that I exert on the chair (both of them) must cancel, must they not? If so, then there should be no acceleration. But I can accelerate the chair by pushing against it (and nothing else)

[Sisyphus]

What I mean is this. You push the chair quickly and move it by moving your own center of mass in the opposite direction (by pushing off the chair). Then, you move your center of mass back again (by pushing in the opposite direction), but that part of the motion is slow, meaning the force on the chair is less (but over a longer period of time), meaning that force cannot overcome the static friction between chair and floor.

 

In a frictionless world, the chair would just wobble back and forth, and the whole system of you and the chair would not change it's center of mass.

[InquilineKea]

Hm okay. But how would this shift in the COM affect the free body diagram?

[Sisyphus]

Well, there would be two stages.

 

First, you exert a force (pushing) on the chair, and the chair exerts a force on you. You both move, in opposite directions. This is where the chair moves along the floor. The center of mass for you/chair, however, has not yet moved.

 

Next, you exert force in the opposite direction, pulling the chair towards you. (You probably do not even notice that you are doing this part, because it is just an automatic response for keeping your balance.) However, this time, the chair does not move relative to the floor, because the lateral force between chair and floor is less than the static friction of same. Hence you move but the chair does not, and the overall center of mass shifts in the direction that the chair moved.

 

The end result of these two motions taken together is that you end up sitting in the same position in the chair, but the whole you/chair system has moved relative to the floor.

[InquilineKea]

Ah, I see. thanks!

 

So a strict free body diagram analysis would not work, since there are two times for the free body diagram, and the time lag causes the naive interpretation of the free body diagram (the interpretation I made above) to fail.

 

because the lateral force between chair and floor is less than the static friction of same.

 

And the reason would be that I am a biological agent and I can adjust myself after I push against the chair, such that part of the "equal and opposite reaction" would be canceled, right?