It is usual in introductory courses of mechanics to develop the work and energy formalism from Newton’s laws. It has been shown how forces transform under a change of reference frame. No analogous study is usually done for the way in which work and energy transform under a change of reference frames. We analyze the behavior of energy and work under such transformations and explicitly show the expected invariance of the formalism under Galilean transformations for one particle and a system of particles. The case of noninertial systems is also analyzed and the fictitious work is characterized. In particular, we showed that the total fictitious work in the center of mass system vanishes even if the center of mass defines a noninertial frame. Some subtleties that arise from the formalism are illustrated by examples.

1.
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6.

If we naively applied the conservation of energy by assigning the traditional potential energies for mg and N (mgh and zero, respectively), we would obtain the mechanical energies EA=mgh+(12)mu2 and EB=(12)mvF2. If we use conservation of mechanical energy and apply Eq. (25), we find that such an equality can hold only for the particular cases u=0 and θ=0. Such a contradiction comes from an incorrect use of the potential energies when changing reference frame. If we recall that the potential energy associated with a constant force F (in Σ) is Fr+constant, and take into account that N and mg are constant (in both frames), then suitable potential energies for both forces in Σ can be constructed by using potential energies of the form Fr+constant.

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