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The situation is, my colleague and I are sitting on wheeled office chairs. He weighs more than me. When I push him, he remains at rest and I move backwards. Is this because he has more inertia than me?

If it was just due to inertia, then if I got off the chair and was just standing on the floor, then I would still move. But as I now have more friction with the floor than him, he now moves.

Would the amount of force I apply effect the outcome? Or is it the length of time of the application of force that matters?

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  • $\begingroup$ Do you think that the friction in the wheels of the chairs might affect what is happening? If so, do you think that the friction in the wheels is the same for both chairs? $\endgroup$ – Bill N Sep 21 '17 at 16:03
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The reason you move is because of Newton's third law of motion, when you push him, the same force is pushed back at you. The reason he doesn't move is because the static friction between his chair and wheels on the chair is higher than the friction of your chair, this friction is generally proportional to the weight of the object in situations like this. When you stand on the floor, your feet's contact with the floor has more friction than the wheels in his chair, this overcomes his chair's static friction and thus he moves.

In both cases you mentioned, if you apply an instantaneous force that is a lot stronger that overcomes both static friction forces on both of you (whether you are in a chair or not), you will both move. This might be more than you can apply by hand depending on how much friction is there.

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Yes, the amount of force applied affects the outcome. What's happening is that any force that you apply comes in a force-pair by Newton's third law, so if you push on him with a force $\vec F$ then the force $-\vec F$ is imposed on you to impose a property called "conservation of momentum," which in a very deep sense comes from the fact that the laws of physics are the same if you move one millimeter over from where you presently are. If you perform this experiment in a frictionless setting you will both move inversely proportional to your masses.

There is a force of friction, however, due to the chair on the ground: when rolling this force is relatively negligible but when stopped it can be comparatively stronger. This force scales like the normal force which in this case is going to be proportional to your weights, as well.

When you move your arms to push your colleague there is generally some springy interface which responds to some of this force. Try to push yourself from your desk softly, then firmer and firmer, until you finally start moving: you will notice that you "move" at first but it is only you pushing yourself "into the back of your seat." If you apply the force too gently, then this springy force will build up between two people in chairs until one of the chairs (with lower friction) starts moving, and then it will relax that compression and the force will suddenly drop a little on your colleague's wheels. This is the basic reason why "when I'm standing he moves, when I'm in my chair I move." If you give a really good shove you should be able to impart momentum to the both of you before this force relaxes -- if your upper body is not strong enough you can probably do it with your feet against the back of their chair and giving a very sharp kick.

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