The principle you're referring to is the conservation of energy and mass, as stated in the law of conservation of mass-energy. According to this principle, the total mass-energy of a closed system remains constant. However, the concept of mass increasing as an object approaches the speed of light is a consequence of special relativity, which provides a more comprehensive understanding of the behavior of objects moving at high speeds.
In special relativity, Einstein's famous equation, E=mc², relates energy (E) and mass (m). This equation shows that energy and mass are interchangeable. When an object accelerates to speeds approaching the speed of light (c), its energy increases, and correspondingly, its mass appears to increase. This increase in mass is referred to as relativistic mass.
It's important to note that relativistic mass is a concept used within the framework of special relativity to describe the behavior of objects in motion. It does not imply that the object is gaining physical matter. Instead, it reflects the change in energy content and the associated effects on the object's behavior.
As an object's velocity increases towards the speed of light, its kinetic energy increases, and so does its relativistic mass. However, this effect is only noticeable at velocities close to the speed of light. For everyday objects and velocities much lower than the speed of light, the increase in mass due to relativistic effects is negligible and can be disregarded for practical purposes.
In summary, the conservation of mass-energy still holds true according to the law of thermodynamics. The apparent increase in mass as an object approaches the speed of light is a consequence of special relativity, where energy and mass are interconnected through the famous equation E=mc².