forcesnewtonian-mechanics
If I sit on a chair, the first action and reaction pair force is my weight and the force acting on the earth by me. And the 2nd pair is the force acting on the chair by me and the opposite force.
According to newton third law, the action and reaction force must be equalI. 'm confused because how come the force acting on the chair by me is equal to normal force?
F=gmm/r2
Action/reaction pairs are describing momentum flow. Momentum is a vector, so it is more difficult to explain intuitively, so you should start with money, which is a scalar. Let me call a "payment" money that enters your posession. A payment can be negative, in which case you lose money, like when you buy a hat.
Newton's third law of finance says: for any payment, there is a negative equal payment associated to it on somone else (if you aren't a central bank!). So if you have a payment of -100 dollars, someone else got 100 dollars. This should be completely intuitive, because, outside of banking, on the personal level, money is a conserved quantity.
Newton's law is the same: the conserved quantity is momentum, and the momentum is flowing between objects. The flow is called the force, and the force is the "payment", it tells you how many units of momentum are incoming per unit time. The third law says that every payment is associated with a reverse payment going the other way (just like money, except the quantity is a vector).
So when the Earth pulls on you, it is paying you downward momentum, which means that you are paying the Earth upward momentum. That's the action reaction pair. If you are on a scale, the scale pays you up momentum (it pushes you up), and you pay the scale down-momentum (you push the scale down). The end result is that the force from the Earth and the scale cancel out, and the gravitational force on the Earth from you plus the downward force you exert on the Earth through the scale cancel out, and nothing ends up moving.
This is like a closed circuit of momentum, and elucidating the way in which momentum is flowing, even though the objects don't move, is the subject of statics. Newton's laws add to this the interpretation of momentum as a dynamical quantity, mass times velocity, so when an object accumulates momentum, you know how fast it is going.
This point of view is very useful, but it is not often explicitly taught.
This page has a helpful summary of the history--it seems he initially accepted the Aristotelian idea that objects could only continue to move if some "force" inside them was moving them (keep in mind this is before his technical definition of 'force'), and it took him a while to switch to the idea that bodies naturally tend to keep moving unless acted on by a force, i.e. inertia (it seems he got this idea from Galileo and Descartes). After this he developed the concept that "force" must be acting whenever there is a change in motion, i.e. an acceleration. From there, the article suggests he got the idea for the third law from various mechanical experiments in which it could be observed that the total momentum always remained constant (and if you define force as mass*acceleration, conservation of momentum implies that forces must always be equal and opposite):
Continuing his investigation of impact, he analyzed a collision between two bodies of unequal mass in the center of gravity frame of reference. He stated that they had “equal motions” in this frame, both before and after the collision. This could only mean mass×speed, or momentum (equal and opposite, of course)—the Third Law. (He realized and stated that during such a collision, the center of mass itself would move at a steady speed.)
A Third Law Experiment with Pendulums
In fact, there is a Third Law experiment in the Principia, in the second Scholium, right after the Laws of Motion and their Corollaries. He collided together two pendulums (about ten feet long) with different masses, to establish that the impacts (i.e. forces) felt by them were equal and opposite, as measured by how far they rebounded.
He went to considerable trouble to account properly for air resistance and imperfect elasticity.
Best Answer
Where does the 'pairing' in your first pair come into place? I.e. what is the force counteracting the earth's gravity pull on you (in your theory)?
The relevant force pair in your example is the attractive force between your body and the earth (gravitational pull) and the repulsive force between your body and the chair's surface (its lack of compressability).
You can either see the chair as part of the earth in this scenario OR you can use a force chain in which the repulsive force the earth has on the bottom of the chair transfers via the chair to your body.
It's getting more complicated by the fact that thereby the force the earth has on you is mostly translated into the deformation of your body.
The application of Newton's laws is very much about abstraction and simplification or in other words macroscopic effects, that are in fact the result of a LOT of microscopic effects. (Electromagnetic repulsion vs. attraction on atomic level vs. gravity making up the bulk but not all of the forces ar work here.)