Conservation of Energy

The law of conservation of energy states that the total energy of an isolated system is always conserved. Energy cannot be created or destroyed; it can only be converted from one form to another. For example, stored potential energy of water at a cliff top converts to kinetic energy as it falls, demonstrating how energy transforms while remaining constant in total amount.

Potential energy stored in objects converts to kinetic energy through motion or transformation. When water falls from a cliff, its gravitational potential energy becomes kinetic energy of motion. Similarly, burning wood releases potential energy stored chemically, converting it into kinetic energy in the form of light and heat energy.

Mathematically, the law of conservation of energy is represented as the sum of changes in kinetic energy, potential energy, and internal energy equaling zero. This equation expresses that if one form of energy decreases, it is compensated by an increase in other forms of energy, maintaining the system's total energy constant.

In scientific terms, a conserved quantity stays constant, changes by a definite amount transferred to other systems, and is converted into other forms without being created or destroyed. In everyday usage, conserved means using less or reusing. Scientifically, energy is a true conserved quantity that transforms but never disappears from the universe.

The mechanical energy of a particle stays constant unless forces outside the system or non-conservative forces do work on it. When only conservative forces act, mechanical energy is conserved. If external or non-conservative forces perform work, the change in mechanical energy equals the work done by those forces.

A classical particle is a point mass that is non-relativistic and obeys Newton's laws of motion. The concept of energy conservation applies to classical particles as long as only conservative forces perform work on the system, ensuring mechanical energy remains constant.

In an isolated system, the total energy is always conserved because no external forces or energy sources interact with it. All energy transformations occur internally, converting between kinetic, potential, and internal energy forms. This principle ensures that the system's total energy remains constant throughout all processes.