8.3: Conservation of Mechanical Energy
The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this mechanical energy when only conservative forces cause energy transfers within the system—that is, when frictional and drag forces do not act on the objects in the system? Also assume that the system is isolated from its environment; in other words no external force from an object outside the system causes energy changes inside the system.
When a conservative force does work W on an object within a system, that force transfers energy between kinetic energy K of the object and potential energy U of the system. In an isolated system, where only conservative forces cause energy changes, the kinetic energy and potential energy can change; however, their sum, the mechanical energy E of the system, cannot change. This result is called the principle of conservation of mechanical energy.
The principle of conservation of mechanical energy allows us to solve problems that would be difficult to solve using only Newton's laws. When the mechanical energy of a system is conserved, the sum of the kinetic energy and potential energy at one instant can be related to their sum at another instant without finding the work done by the forces involved. A great advantage of using the conservation of energy instead of Newton's laws of motion is that it is possible to go from the initial state to the final state without considering all the intermediate motion.