balls hanging from strings

Two positively charged pith balls hang from a nail at the end of equal-length strings in Earth’s surface gravitational field. The problem consists in finding each of the hanging angles when the balls do not necessarily have the same mass or charge. The solution is an excellent exercise in developing two skills: wisely choosing the coordinate axes in a free-body diagram, and correctly interpreting the roots and limits of a numerical solution. The treatment is accessible to undergraduate physics majors in their first or second year of physics courses. (Some figures in this article are in colour only in the electronic version) 1