Final answer:
The law of conservation of energy dictates that the total mechanical energy of an isolated system (kinetic plus potential) remains constant, even as energy transitions from one form to another. This fundamental principle applies to all systems and is a cornerstone of physics and thermodynamics.
Step-by-step explanation:
One of the fundamental principles of physics is that mechanical energy in an isolated system remains constant—this principle is known as the law of conservation of energy. Mechanical energy, which comprises kinetic energy and potential energy, can transform from one form to another within a closed system, but the total mechanical energy is always conserved. When objects in a system move or interact with each other under conservative forces, kinetic energy may be converted to potential energy and vice versa, without the loss or gain of mechanical energy.
The concept of energy conservation applies universally and has been confirmed by numerous experiments. Noteworthy is Einstein's theory encapsulated in the equation E = mc², aligning mass with energy, thus underscoring the comprehensive nature of energy conservation. In physics, we understand that while the forms of energy in a system might change, the system's total energy remains constant, so long as no energy is transferred into or out of the system.
Understanding energy transfer is crucial, as mechanical energy is transferred into or out of a system via work, carried out when an external force has a component parallel to the displacement of the system. Thus, while energy can change in form through various processes, it can neither be created nor destroyed—a concept also echoed in the first law of thermodynamics.