物理:為什麼這個力N可以被忽略?

You are right that N should be included into the equation in the vertical movement of the left block.

Hence, for vetical motion of the left block, we have,
R.sin(45) + N - mg = ma' where a' is the vertical acceleration of the block
i.e. R.sin(45) - mg = ma' - N

But when the block slides upward, a' is +ve and N =0 (because the block will leave the floor and no longer in touch with it). This gives,
R.sin(45) - mg = ma'
or R.sin(45) - mg > 0 (because ma' >0)
This equation describes the condition for the block to slide upward.

Conversely, the condition for the block NOT to slide upward is when
R.sin(45) - mg <= 0,
hence, R.sin(45) <= mg, which is the equation appears on your model answer.

[ Notice that under that situation, although N is non-zero (i.e. N >=0), the sum (ma' - N) is still -ve due to the -ve sign in front of N]

力N，與Rsin45°方向可以是相同，所以互相抵銷，因此，可以被忽略。