Final answer:
In an isolated system, the sum of kinetic and potential energies always remains the same, which is a consequence of the Law of Conservation of Mechanical Energy. The mechanical energy, a sum of kinetic and potential energy, does not change when there are no external dissipative forces acting on the system.
Step-by-step explanation:
For an isolated system, the correct answer to the sum of the kinetic and potential energies is C. always remains the same. This principle is due to the Law of Conservation of Mechanical Energy, which states that in a closed system where there are no external dissipative forces such as friction, the mechanical energy of the system remains constant. Mechanical energy is the sum of kinetic energy and potential energy, where kinetic energy is the sum of the kinetic energies of a system's atoms and molecules, and potential energy is the sum of the potential energies of a system's atoms and molecules.
An example to help illustrate this concept is a child swinging on a swing. As the child swings upward, the kinetic energy of the child decreases while the potential energy increases due to height gain. Conversely, as the child swings downward, the kinetic energy increases due to speed gain while the potential energy decreases. Despite these transformations between kinetic and potential energies, the total mechanical energy (kinetic plus potential) of the system remains the same if we ignore air resistance and friction.