What does the conservation of mechanical energy in a closed system imply?

The conservation of mechanical energy in a closed system implies that the total mechanical energy, which is the sum of kinetic and potential energy, remains constant when only conservative forces are doing work. This principle holds true because, in an ideal closed system devoid of external forces and friction, energy can transform from kinetic to potential and vice versa, but the overall total of these forms of energy does not change.

For example, when an object falls freely under the influence of gravity, its potential energy decreases while its kinetic energy increases, but the sum of these energies remains the same, illustrating the conservation of mechanical energy. Therefore, the correct understanding is that in a closed system, as energy shifts between forms, the total remains constant, demonstrating the essential nature of energy conservation principles in physics.