Another classic mechanics problem involves a type of roller coaster problem. When you have a loop-the-loop, what is the minimum height on a hill the roller coaster, or in this case a block, have to start to just make it around the loop, without falling off?
This is a good problem primarily because it has some engineering overtones, but also because it combines circular motion with energy and a force diagram. It gives some decent insights of how mechanics principles are related and how to combine them. Check it out, and see if it makes sense.