New Grapes from Old Vineyards: Challenging Problems for Creative Students

Mechanics problems for undergraduates and graduate students tend to be exercises rather than fresh new fields for the student to conquer. These exercises are valuable, but are a far cry from theoretical physics. They focus the student's attention on techniques rather than ideas, and the techniques are merely the same ones they have been given in the lecture and the textbook, and have used over and over again. Here are presented several problems in classical physics that are designed to shake the student out of his torpor and make him think about what he wants to do and can do, rather than what he should do according to the rules. These problems break the rules. Some solutions are partially sketched. The problems are (1) wrong-way dynamics; (2) mechanics in the molasses; (3) the radical charges; (4) the vicious-viscous force; (5) Newton and the Appell function.