We noticed that the total system energy does not change if no work is done by external forces. It’s time to expand on that idea. One of the most powerful statements in physics is the law of conservation of energy:

The key is that energy is conserved for an isolated system, a system that does not exchange energy with its environment either because it has no interactions with the environment or because those interactions do no work. FIGURE 10.15 shows our basic energy model for an isolated system.

FIGURE 10.15 The basic energy model for an isolated system.

The total macroscopic kinetic and potential energy $K+U$ is often called the mechanical energy $E_{\text{mech}}$. Mechanical energy is transformed into thermal energy by any dissipative forces such as friction or drag. The real world always has dissipative forces, but we’ll often find it useful to model processes as being nondissipative, in which case the mechanical energy is conserved.