Posted by Rachel on Thursday, October 16, 2008 at 3:04pm.
Suppose you press a book against the wall with your hand. The book is not moving and you are pushing horizontally. Now suppose you decrease your push, but not enough for the book to slip. What happens to each of the following forces? DO they increase in magnitude, decrease, or not change?
F(push)
Weight
Normal
Friction Force

Physics  Damon, Thursday, October 16, 2008 at 3:16pm
F(push) of course decreases
The weight, m g, does not change
Now the normal force against the wall is exactly your push force.
The maximum friction force is mu, the coefficient of friction, times the normal force. Until the book slips, it is equal to mg, the weight. When mu * F decreases to equal the weight, mg, then the book will start to slip. 
Physics  Damon, Thursday, October 16, 2008 at 3:30pm
Here is a way to think about this:
Think of the book attached to the wall by a frictional hook.
Until the hook breaks, the hook(friction)holds the book up and the hook (friction) force is exactly equal to the weight because the friction and the weight are the only vertical forces on the book and the book is not accelerating.
However when the normal force decreases so that mu F = mg, the frictional hook breaks and the book slides down.