Energy equations for projectiles with linear and quadratic drag

Although linear and quadratic drag are treated early in upper-level undergraduate mechanics courses, energy dissipation due to drag is not. In this paper, energy equations with exact analytic formulas for dissipation due to air resistance are developed for projectiles using linear and quadratic drag models, based on the work–energy theorem. Examples with analytic results for specific cases are presented for quadratic drag in one dimension, and linear drag in one and two dimensions suggested as student assignments. Similarly, three numerical examples of energy dissipation showing kinetic, potential, and/or dissipated energy versus either time or distance are presented, suggested as assignments that students could code and graph in a spreadsheet application.