mechanical energy

According to the work-energy theorem, \[W_{\text{net}}=\Delta K\], and since net work is made up of conservative and non-conservative forces, \[W_{\text{net}}=W_{C}+W_{N}=\Delta K\]. As defined, conservative work is equal to the loss in potential energy, \[W_{C}=-\Delta U\], then \[W_{\text{net}}=-\Delta U+W_{N}=\Delta K\implies W_{N}=\Delta K+\Delta U\]. Thus, the total non-conservative work done on a system is equal to the gain in mechanical energy of the system.

If there is no non-conservative force, \[W_{N}=0\], \[\Delta K+\Delta U=0\]. This is known as the conservation of mechanical energy. This is slightly different compared to the law of conservation of energy, which tells us that \[\Delta K+\Delta U+\text{[change in all other forms of energy]}=0\], as in this case mechanical energy is not conserved, but turned into other forms of energy like heat, but the total energy is still conserved.