8.7:
Conservation of Energy
The law of conservation of energy states that the total energy of an isolated system is always conserved. It signifies that energy can only be converted from one form to another.
For example, the stored potential energy of water at the top of a cliff gets converted to kinetic energy when it falls.
Similarly, when a log of wood is burned, potential energy stored in the wood is converted to kinetic energy in the form of light and heat.
Mathematically, the law of conservation of energy is represented as the sum of the change in kinetic energy, potential energy, and internal energy as equal to zero. In other words, if one form of energy decreases, it is compensated by an increase in other forms of energy.
8.7:
Conservation of Energy
The terms 'conserved quantity' and 'conservation law' have specific scientific meanings in physics, which differ from the meanings associated with their everyday use. For example, in everyday usage, water could be conserved by not using it, by using less of it, or by re-using it. However, in scientific terms, a conserved quantity of a system stays constant, changes by a definite amount that is transferred to other systems, and is converted into other forms of that quantity. In the scientific sense, a conserved quantity can be transformed but not strictly created or destroyed. Thus, there is no physical law of conservation of water.
In conservation of energy, the mechanical energy of a particle stays constant unless forces outside the system or non-conservative forces do work on it. In this case, the change in the mechanical energy is equal to the work done by the non-conservative forces. This statement expresses the concept of energy conservation for a classical particle as long as there is only conservative work. Recall that a classical particle is just a point mass that is non-relativistic and obeys Newton's laws of motion.
This text is adapted from Openstax, University Physics Volume 1, Section 8.3: Conservation of Energy.