Accelerating Wedges with Friction

[americanforest]

Homework Statement

A block rests on a wedge inclined at an angle $$\theta$$. The coefficient of friction between the block and the plane is $$\mu$$.Let the wedge move with horizontal acceleration a to the right. Assuming
that tan $$tan(\theta) < \mu$$, find the minimum value of a for the block to remain on the wedge without sliding.

Also find the maximum value of a.

Homework Equations

The Attempt at a Solution

$$mgcos(\theta)+masin(\theta)=F_{normal}; \tex{mgcos(\theta)+\mu (F_{normal})=macos(\theta); a=\frac{g(sin+\mu cos}{cos - \mu sin}$$

which gives wacky limiting values and isn't a range at all but just one value.

 

[hikaru1221]

Have a bit correction with this one: $$F_{static friction} \leq \mu F_{normal}$$
Also, there must be a condition for a to be positive, as a acts to the right.