The following concept map for the work-energy theorem illustrates the power of cognitive condensation.

This map clearly shows that one can learn a tremendous amount of science, mathematics, and technology by judiciously organizing knowledge using causal, logical, and functional relationships and by making only statements that are correct in their generalities or contain specifications of the limits of their applicability.

Please see how the work-energy theorem, correctly stated in terms of the work done by non-conservative forces (Wnc), directly leads to the law of conservation of the total mechanical energy (i.e. if Wnc=0 then ET= constant).

And then,

Also note the various ways in which a potential (Ep) and a kinetic (Ek) energy can be expressed, depending on the problem. Further, note the general and always correct statement for the element of work done by a force (constant or variable). This map will completely avoid someone writing mgh for the potential energy associated with a spring! Such errors occur if the teaching and learning (reading) processes only mentioned mgh; in such cases, the learner may get the "impression" that this is always the expression for the potential energy.

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