Is the Normal Force on m2 Affected by Vertical Acceleration in Different Cases?

[Like Tony Stark]

Homework Statement

Suppose two cases:
1) The room shown in the picture is static, and so are the blocks in it.
2) The room is being accelerated to the right, and the blocks are static with respect to each other

Relevant Equations

Newton's equations

I want you to tell me if I'm right

For 1), does $m_2$ feel a normal force? Because I don't think so, since it isn't pushing the wall.

For 2), $m_2$ suffers a normal force because it feels a pseudo-force to the left and so it pushes the wall

 

[berkeman]

I think you are correct about the normal force on m2 for both cases. The vertical acceleration is different for case 1 & 2, but I don't think that affects the normal force between m2 and the wall.