Pushing a Book against the Wall.
You are holding a book against a vertical wall by pushing upwards with your hand. The angle between your force and the vertical is a (< 90?). The mass of the book is m and the coeficient of static friction is µ. If you push too hard, the book will start to slide upwards, if you don't push hard enough, the book will slide down.
a) Draw "free-body" diagrams for these two cases when the book is just about to start sliding.
b) Calculate the magnitude of your force (as a function of a) to just prevent slipping, in both cases.
c) Calculate the force (as a function of a) for which the friction becomes zero. Evaluate your result for a = 0? and 90?.
d) For what values of µ (as a function of a) is it impossible to make the book slide upwards?