5.3 Conservation of Energy
The study of various forms of energy and the transformation of one kind of energy into another has led to a very important principle known as the principle of conservation of energy. It is stated as:
lightbulbEnergy cannot be created or destroyed. It may be transformed from one form to another, but the total amount of energy never changes.
During an energy transfer process, some energy seems to be lost and not accounted for in calculations. This loss of energy is due to work done against friction of the moving parts in the process. This energy appears as heat and is dissipated in the environment. This energy does not remain available for doing useful work and may be called waste energy.
A process of energy conversion and conservation can be described with the given example.
Let a body of mass m be at rest at a point A above the height h from the ground. Its total energy is P.E. = mgh, and E_k = 0.
Then the body is allowed to drop to point B at a height x from the ground. The body loses potential energy and gains kinetic energy as it gets speed while falling. Assuming air resistance is negligible:
E_p = mg(h - x)
The loss of potential energy will appear as the gain in kinetic energy. Hence, at point B:
E_k = mgx
Total energy at B:
E = mg(h - x) + mgx = mgh
Just before hitting the ground at point C, the whole of potential energy is changed into kinetic energy. Thus:
E_p = 0 and E_k = mgh
Thus, total energy remains the same as mgh. On hitting the ground, this energy is dissipated as heat and sound in the environment.