Action and Reaction Forces

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I have a 2 questions regarding Newton’s third law and I will explain them using examples:

1. Body A is pushing against Body B with a force F(AB), Now body B will push against body A with a reaction force F(BA) equal but opposite to F(AB). Now shouldn’t be another reaction force F2(AB) due to the action of the reaction force F(BA) and another reaction force F2(BA) as a reaction to that reaction !!!

2. Three bodies A, B and C setting on a frictionless surface in the order A, B and C. A is pushing on B with F(AB)
First, is it true that B will also push on C with the same force F(AB) and if that is true shouldn’t C also exert a reaction force on B with the magnitude F(AB).

I think I am misunderstanding the concept and how are forces transmitted through the bodies and how does Newton’s third law apply here.

I need some help here.

Thanks in advance.
 

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Doc Al
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I1. Body A is pushing against Body B with a force F(AB), Now body B will push against body A with a reaction force F(BA) equal but opposite to F(AB). Now shouldn’t be another reaction force F2(AB) due to the action of the reaction force F(BA) and another reaction force F2(BA) as a reaction to that reaction !!!
There are just two bodies and thus two forces involved: F(AB) and F(BA). Those forces are equal and opposite. (Using your notation, F2(BA) is the same force F(BA).)

2. Three bodies A, B and C setting on a frictionless surface in the order A, B and C. A is pushing on B with F(AB)
First, is it true that B will also push on C with the same force F(AB) and if that is true shouldn’t C also exert a reaction force on B with the magnitude F(AB).
No, it is not true. At least it's not necessarily true. If those blocks are held in place so they have no acceleration, then the force that A exerts on B must equal the force that C exerts on B. Nonetheless, they are not 'action-reaction' pairs.

I think I am misunderstanding the concept and how are forces transmitted through the bodies and how does Newton’s third law apply here.
Using your three bodies (let's assume blocks on a frictionless surface) as an example. The Newton 3rd law pairs are:
(1) A pushes on B and B pushes on A
(2) B pushes on C and C pushes on B

The force between A and B does not necessarily equal the force between B and C. To fully analyze the forces exerted, you'll need Newton's 2nd law as well as the 3rd.
 

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