Newton's Law of Motion: Surface Force Unaffected by Acceleration?

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SUMMARY

The discussion centers on the interpretation of Newton's Law of Motion concerning surface forces and acceleration in a system. Specifically, it addresses the question of whether the normal forces, FN1 and FN2, acting on masses m1 and m2 are influenced by the system's acceleration, a3. The conclusion drawn is that since FN1 and FN2 are internal forces, they do not affect the overall acceleration of the system and should not be included in calculations for a3, aligning with Newton's Third Law of Motion.

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What I want to ask is the (b) part (It's one of our old MTs). In the solution given, it talks about an acceleration,a3, on the horizontal axis. However, in the equation, the surface forces acting on m1 and m2, FN1 and FN2, are not affected by this acceleration, a3. Isn't that wrong?
 

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If a3 is the acceleration of the whole system, then FN1 and FN2 will be internal forces for the whole system and will have their corresponding equal and opposite forces by Newton's 3rd law. Hence FN1 and FN2 must not be considered to find a3.
 

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