Finding acceleration on an incline plane with static friction

[Arclite Cham]

Hello everyone I am a newbie as well as in physics. I am having a problem in a question as in the attachment. I have learned that the equation of the static friction (Fs) of an object is equals to the product of the coefficient to the normal force of the object.

In this question, let mass of A be M(a) and mass of B be M(b) and the total mass of A and B be M.
Assume g is the gravitational acceleration with 9.81ms^-2.

However, in this question, what is the reaction force for the Fs between A and B? Is it M times cos θ or just 0.4gM(a)? And after finding the Fs, how does it affect the total acceleration of the objects? Does the kinetic friction have anything to do with the result? I tried to find the Fs by assuming the weight of A times 0.4. Then I consider the force to be horizontal to the plane and hence the force opposing the motion (Fb) would be Fs cos θ. After that the resultant force will equals to Mg sin θ - Fb. But that gave me a negative answer. So where is the error?

 

[TSny]

Hello, Arclite Cham. Welcome to PF.

This is one of those problems where you don't know ahead of time whether there's enough static friction to prevent A from slipping on B. One approach is to assume there is no slipping and then calculate under this assumption what the normal force and friction force would be between A and B. You will then be able to see if the coefficient of static friction given in the problem is sufficient to provide the necessary friction force. If so, then the problem is essentially solved. If not, you will have to then assume that A slips on B and re-do the analysis for slipping.

In any case, you're going to need carefully drawn free-body diagrams for A and B so that you can apply Newton's laws to each body.