The mechanical energy change of a system in an inertial frame of reference equals work done by the total nonconservative force in the same frame. This relation is covariant under the Galilean transformations from inertial frame S to S', where S' moves with constant velocity relative to S. In the presence of nonconservative forces, such as normal and tension forces, the mechanical energy of a system can be conserved in S and not be conserved in S'. In this paper we find useful relations between the mechanical energy changes in two inertial frames of reference.