Need Conceptual Framework for Reaction vs. Net Force

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Main Question or Discussion Point

I find the common physics problem of accelerating boxes that are touching very confusing. (To be clear, boxes are on surface, force comes from one side and all boxes accelerate. Questions typically ask about magnitude of force between particular boxes).
Once the boxes are accelerating, why is the net force on each different? I understand mathematically that it needs to be different if their masses are different (due to F=MA), but I can't get my head around it conceptually--what "happens" to the force as it gets transferred from box to box. Why does it vary?
Related, if the force from box 1 on box 2 is equivalent to the force from box 2 on box 1, why are they moving? Again, I get the idea that the reaction forces are different than the net forces, but conceptually, how can box 2 be accelerating if it's pushing just as hard back on box 1? (I.e., wouldn't the force coming from box 1 be "neutralized" by the reaction force?)
I know how to solve these problems to get the right answer in a textbook but any insights at the conceptual level to help develop a more intuitive understanding of the situation would be appreciated.
Jon
 

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jbriggs444
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Related, if the force from box 1 on box 2 is equivalent to the force from box 2 on box 1, why are they moving? Again, I get the idea that the reaction forces are different than the net forces, but conceptually, how can box 2 be accelerating if it's pushing just as hard back on box 1? (I.e., wouldn't the force coming from box 1 be "neutralized" by the reaction force?)
https://www.lhup.edu/~dsimanek/physics/horsecart.htm
 

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