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Newton's third law of motion is essential to our understanding of forces and interactions between objects. It states that for every action, there is an equal and opposite reaction. This means whenever one object exerts a force on a second object, the second object simultaneously exerts a force equal in magnitude and opposite in direction on the first object.

To illustrate, consider two skaters pushing against each other on an ice rink. As they exert force on one another, both skaters move in opposite directions with forces that are equal in size but directed oppositely. This concept is the cornerstone for analyzing the interaction of bodies in a system, and it lays the foundation for the conservation of mechanical energy in systems where only internal forces act, like the two bodies mentioned in the exercise interacting with a conservative force.

A conservative force is fundamental to energy conservation. The characteristic of a conservative force is that the work it does on an object moving between two points is independent of the path taken. This is crucial because it implies that the total mechanical energy (kinetic plus potential) of an object influenced solely by conservative forces remains constant as the object moves.

Gravitational and elastic spring forces are examples of conservative forces. If a ball is thrown into the air, gravity will do work on it during its ascent and descent, yet the total mechanical energy at any point in its trajectory will remain the same (discounting air resistance). Understanding conservative forces explains why, in the given problem, the work done by such forces on the two-body system relates directly to changes in potential energy, hence reinforcing the concept of energy conservation within an isolated system.

The work-energy theorem is a powerful concept within physics that connects the work done by forces to the change in kinetic energy of an object. It states that the net work done by forces on an object is equal to the change in that object's kinetic energy. Mathematically, it can be expressed as: \[ \text{Work} = \text{Change in Kinetic Energy} \[\Delta K = W\]\]

For instance, when a person pushes a stationary block, the work done by the person leads to an increase in the block's kinetic energy, causing it to move. Conversely, when a block sliding on a rough surface comes to a halt, the work done by friction (a non-conservative force) is equal to the reduction in the block's kinetic energy. This principle helps us predict the new velocities of objects after forces have done work on them and is directly applied in the exercise solution to relate the conservative force’s work to changes in kinetic energy.

The concept of an isolated system in physics is crucial when studying conservation laws. An isolated system is one where no energy or matter is exchanged with the surroundings. This isolation creates a closed environment in which we can confidently apply conservation laws, such as the conservation of mechanical energy.

In the context of the problem given, comparing two bodies as an isolated system and assuming that there are no external forces means that the total mechanical energy within the system is conserved. The assumption of no external work allows us to consider only the internal interactions, making the analysis and application of energy conservation feasible. In real-world scenarios, perfectly isolated systems don't exist, as there are always some external interactions, be it friction with the environment or gravitational effects from other bodies. However, assuming a system is isolated is a practical abstraction that simplifies calculations and helps us understand the fundamental principles governing physical interactions.