The coefficient of kinetic friction between the inclined face of a wedge of mass M and a block of mass m sitting on its inclined face is μk (see figure below). The vertical face of the wedge is pushed with a horizontal force such that m slides up the inclined surface with an acceleration a with respect to the inclined surface. Derive an expression for the magnitude of the force. (Assume the angle of inclination is some angle θ. Use any variable or symbol stated above along with the following as necessary: g. Assume SI units.)
2. Homework Equations (my thought process; equations are further down the post)
Since m is accelerating up the incline, the force of friction on m is down the incline. The normal would be perpendicular to the incline and the gravity would be straight down.
Also, since the m is accelerating up the incline at an angle of θ with an acceleration of a, we can say that the horizontal acceleration of the m (with respect to the ground) would be ax - acosθ and the vertical acceleration of m would be asinθ, where ax is the acceleration of the system. Using this, I just added the horizontal components and set them equal to m(ax - acosθ). I also added up the vertical components and set them equal to m(asinθ).
But the answer I'm getting is wrong... apparently. Any thoughts?
The Attempt at a Solution
My most recent attempt at the problem:Attempt #... I have no clue.