Understanding the conservation of total energy is crucial in physics, particularly when analyzing isolated systems. Total energy encompasses all forms of energy within a system, including mechanical energy (kinetic and potential) and non-mechanical energy (thermal and others). For a system to maintain energy conservation, it must be isolated, meaning no external forces are acting on it. An isolated system only experiences internal forces, which are forces that occur between objects within the system.

To illustrate this concept, consider a scenario involving a box and a spring. If we define the system as just the box, the spring force acting on it is external, as it originates from outside the defined system. Consequently, the system is not isolated, leading to a situation where energy is not conserved. For example, if the initial kinetic energy of the box is 20 joules and the final kinetic energy after being launched by the spring is 30 joules, the total energy has changed, indicating that energy conservation does not hold.

Now, if we expand our system to include both the box and the spring, the forces acting between them become internal. The spring exerts a force on the box, and by Newton's third law, the box exerts an equal and opposite force on the spring. In this case, since all forces are internal, the system is isolated, allowing for energy conservation. Here, if the initial total energy (kinetic plus potential) is 30 joules and the final total energy remains 30 joules, energy conservation is upheld.

In summary, for energy to be conserved in a system, it must be isolated with only internal forces at play. This principle is fundamental in solving problems related to mechanical energy and understanding the dynamics of systems in physics.