"In addition to the previous answer, here is a stratagem that allows you to /construct/ (rather than select) calculus problems.
Executive summary: Turn a cut-and-dried calculation into an optimization."
I think this is a good idea. I tried the suggested example sliding block problem and found it to be both fun and informative. In fact, the difference in the angles which produced minimum tension and minimum work surprised me at first until I thought about it (I don't teach mechanics on a regular basis). This seems like the type of calculus problem the students can relate to in practical terms and also find interesting and informative. Much better for learning physics than simply plugging numbers in to find the tension at 40 deg, and it's fun!
Don
Dr. Donald Polvani
Retired
Adjunct Faculty, Physics
Anne Arundel Community College
Arnold, MD 21012