As significant as the law of conservation of energy is, it’s critical to notice that the law does not say “Energy is always conserved.” The law of conservation of energy refers to the energy of a system—hence our emphasis on systems in Chapters 9 and 10. Energy is conserved for some choices of system, but not others. For example, mechanical energy is conserved for a ball sailing through the air (ignoring air resistance) if we define the system to be ball earth but not if we define the system to be only the ball.
In addition, the law of conservation of energy comes with an important qualification: Is the system isolated? Energy is certainly not conserved if an external force does work on the system. Thus the answer to the question “Is energy conserved?” is “It depends on the system.”