Energy from Nothing?

Abstract

When reading “Galilean Relativity and the Work—Kinetic Energy Theorem” by Brandon and James Tefft (TPT 45, 218–220, April 2007), one might ask a question, “What is the source of the kinetic energy the ball is obtaining?” The natural answer would be that this source is the muscles of the man throwing it (i.e., electrochemical processes in the arm). This answer is described mathematically by Eq. (7), where F is the force acting on the ball from the arm of the man, and d is the displacement provided by the arm. If we mention that this is right only for the system resting relative to the train, the answer, provided by Eq. (8), would sound like this, “The source of the energy is the muscles of the man throwing the ball and .” Here we would have to stop, because the last term in Eq. (8), has, according to the authors, a purely kinematical (i.e., geometrical) origin. Without giving to this term a dynamical explanation, one can get an impression that the work done on the system can be the result of purely geometrical transformations.