Pushing an incline so mass on ramp accelerates upward

This seems to be a slight variation of a pretty standard problem, however I didn't have any luck finding any seemingly helpful information. I am mainly wondering if I am not getting the FBDs correct?



1. The problem statement, all variables and given/known data



A block of mass [itex]m[/itex] is sitting on a movable ramp of mass [itex]M[/itex] with an incline of [itex]\theta[/itex] degrees to the horizontal. The system is initially held at rest. Once released, a force, [itex]F[/itex], pushes the vertical side of the ramp such that the block accelerates upward along the incline. There is no friction anywhere; Write an expression for the force.



2. Relevant equations



[itex]\sum \text{F} = ma[/itex]



3. The attempt at a solution



The FBD's are in the attached image.



I seem to be arriving at a system with one more variable than equations, so I am definitely not understanding something, and I believe it has to do with the FBD? Here is what I come up with:



As the inclines acceleration ([itex]a_{\text{I}}[/itex]) is purely on the horizontal plane, then the components of the blocks acceleration ([itex]a_B[/itex]) are:



[itex]a_x = a_{\text{B}}\cos \theta - a_{\text{I}}[/itex] and [itex]a_y = a_{\text{B}}\sin \theta[/itex].



for the little mass, m:



[itex]\sum \text{F}_x = N_1 \sin \theta = m(a_{\text{B}} \cos \theta - a_{\text{I}}) [/itex]



[itex]\sum \text{F}_y = N_1 \cos \theta - mg = ma_{\text{B}}\sin \theta[/itex]



and for the incline:



[itex]\sum \text{F}_x = \text{F} - N_1\cos \theta = a_{\text{I}}M[/itex]







I'm pretty stuck and have no idea what it is that I'm missing, so I would really appreciate it if someone could give me a hint.