Alternative theoretical method for motion of a sand-filled funnel experiment

In “Motion of a Sand-Filled Funnel,” Peter Sullivan and Anna McLoon described how to use numerical methods and a Microsoft Excel spreadsheet to predict the motion of a variant of Atwood’s machine with variable mass. They wrote for noncalculus-based physics classes, but we solve the same problem using the methods of calculus. Our method highlights the less-familiar but more accurate version of Newton’s second law, $∑F =dpdt$⁠. This can help introductory physics students understand a broader definition of Newton’s second law and enhance their calculus skills. It also teaches students how to solve a variable-mass problem.