|
The principle of conservation of mechanical energy states that, for an isolated system of objects subjected only to conservative forces (e.g. only to a gravitational force), its total mechanical energy remains constant. It can be given as:
If more than one conservative force acts on an object within a system, a potential energy function is associated with each force. In such a case, we can apply the principle of conservation of mechanical energy as:
where the number of terms in the sums equals to the number of conservative forces present. For example, if an object connected to a spring oscillates vertically, two conservative forces act on the object: the spring force and the gravitational force.
Energy conservation in Rotational motion:
For rotational motion, the potential energy and kinetic energy are related to the moment of inertia and the angular velocity. And the same law prevails for the conservation of mechanical energy in the case of rotational motion:
E1 = E2
- [ KE+PE]1 ==[ KE+PE]2
- [ (1/2)mv2 + (1/2)Icmω2 + PE]1 =[ (1/2)mv2 + (1/2)Icmω2 + PE]2
|
