Chapter 5, Problem 12PE

If an object is to rest on an incline without slipping, then friction must equal the component of the weight of the object parallel to the incline. This requires greater and greater friction for steeper slopes. Show that the maximum angle of an incline above the horizontal for which an object will not slide down is $\theta ={\tan }^{-1}\text{μs}$. You may use the result of the previous problem. Assume that $a=0$ and that static friction has reached its maximum value.