The work-energy theorem: the effect of varying mass

Abstract

This paper examines the work-energy theorem ofclassical physics and applies it to two situations withnon-constant mass. The first is that of a rocket burning fuel. The second is that of a proton in a particle acceleratorreaching relativistic speeds. The analysis leads to areformulation of the work-energy relation in terms of momentumand velocity rather than force and displacement. This allowsgraphical determinations of kinetic energy that are both simpleto make and clear even to beginning students. The use of graphical integration obviates the necessity of using calculusfor the non-constant mass situations. An unexpected result isthe invariance of this reformulation even for the relativistic case.