This is a standard block on wedge problem - we have an incline of angle [tex]\alpha[/tex], a block of mass m on wedge of mass M. The block is released from the inclined surface. The wedge is not fixed and can accelerate. The question is typical - find the horizontal accelerations of the block and wedge a1 and a2 respectively, and the normal foces N1 and N2 (in terms of the masses the angles and g and stuff). I know this is a standard problem and I in fact know how to solve it using the constraint invoking the geometry of the incline.
However, I really want to do this problem using fictious forces. I want to use a reference frame in which the wedge is fixed.
Let inertial frame be S, accelerated one be S' (not rotated).
ma = F + Ffictitious
The Attempt at a Solution
I thought the above equation wold make this problem fall out very quickly using the above equation, because the acceleration of the wedge with respect to the inertial frame (and hence the fictitious force) is easy to calculate once we know the normal force N1.
Now, in the frame fixed with respect to the wedge, I thought we would have N1=mgcos[tex]\alpha[/tex] (and consequently an acceleration of the block down the incline of gsin[tex]\alpha[/tex]). But this isn't the case, right? Why not, though? And how would we solve for N1 using our fictitious force framework?