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:

     K_i + U_i = K_f + U_f + O_f.

If there is no conversion of mechanical energy to other forms, then O_f = 0, and energy conservation becomes:

     K_i + U_i = K_f + U_f,   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).