Basic Fact: Total Energy K+U+O is conserved! Energy can neither be created nor destroyed. It can only be converted from one form to another.
General form of the energy conservation statement:
Ki + Ui = Kf + Uf + Of.
If there is no conversion of mechanical energy to other forms, then
Of = 0, and energy conservation becomes:
Ki + Ui = Kf + Uf, or ΔK + ΔU = 0.
Energy conservation provides an important tool to analyze mechanics
problems that is complementary to Newton's second law (endpoint information vs. complete trajectory).