 |
| Conservation of Mechanical Energy |
|
| We can see many situations in which energy is transferred to or from objects and systems, similar to money being transferred between accounts. In each situation, we assume that the energy that was involved can be accounted for, that is, energy cannot appear or disappear. Energy obeys the law of conservation of energy, which is concerned with the total energy of the system. |
| |
| The total energy 'E' of a system can change only by amounts of energy that are transferred to or from the system. |
| |
| If a system is isolated from its environment, there can be no transfer of energy to or from it. In this case, the law of conservation of energy states that “The total energy 'E' of an isolated system cannot change". |
| |
| Energy transformation may be going on within an isolated system, say, between kinetic energy and potential energy or kinetic energy and thermal energy. However, the sum total of all the forms of energy in the system remains unchanged. |
| |
|
| We define the change in the potential energy of the system, corresponding to a conservative internal force, as |
| |
 |
| |
| Where 'W' is the work done by the internal forces on the system as the system passes from the initial configuration 'i' to the final configuration 'f' . |
| |
| We cannot define potential energy corresponding to non-conservative forces. Suppose only conservative internal forces operate within the system and the potential energy U is defined, corresponding to these forces. There are no external forces or the work done by them is zero. |
| |
 Uf - Ui = -W = - (Kf - Ki) |
| |
| or Uf + Kf = Ui + Ki |
| |
| The sum of the kinetic energy and the potential energy is called the total mechanical energy. The above equation shows that the total mechanical energy of the system remains constant if the internal forces are conservative and the external forces do not do any work. This is called the principle of conservation of energy. |
| |
| The total mechanical energy is not constant for non-conservative forces such as frictional forces. |
| |
