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

[senior]

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?

 

[grzz]

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.