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We can argue all day about where the energy does or does not reside. But
the Modeling program finds that using the idea of energy as merely being
transferred from one place to another helps students understand conservation
of energy. When you use the word potential, the student thinks that is
somehow different from other types of energy. But when it is labeled
according to where it resides, they get a more unified view. Students tend
to treat mgh as a magic incantation. But if they understand it is
expressing how much energy is available in the Earth-object system then they
will not make as many mistakes.