REVISITING THE DEFINITION OF ELASTIC COLLISION:A PEDAGOGICAL ANALYSIS OF KINETIC ENERGY CONSERVATION

Abstract

The definition of an elastic collision is typically introduced early in undergraduate mechanics. Although the underlying physics is universally agreed upon, introductory mechanics textbooks employ different linguistic formulations to express the conservation of kinetic energy. Some texts use concise statements such as “the total kinetic energy is unchanged” or “kinetic energy is conserved,” whereas others explicitly state that the kinetic energy before the collision is equal to that after the collision or clarify that kinetic energy need not remain constant during the collision. For novice learners, the distinction between these formulations may be pedagogically significant. During a finite-duration collision between deformable bodies, translational kinetic energy can be temporarily converted into elastic potential energy and subsequently restored. Thus, equality of the initial and final kinetic energies should not be interpreted as instantaneous constancy throughout the collision interval. This study examines the physical and pedagogical implications of these alternative formulations and argues that explicitly identifying the initial and final states can provide greater clarity for novice learners. The study further proposes such wording as a pedagogical baseline for introducing elastic collisions, while recognizing that similar clarifications are already present in some existing textbooks.