First the principle of the Conservation of Mechanical Energy was stated:
The total mechanical energy (defined as the sum of its potential and kinetic energies) of a particle being acted on by only conservative forces is constant.
See also: Conservation of Mechanical Energy
An isolated system is one in which no external force causes energy changes. If only conservative forces act on an object and U is the potential energy function for the total conservative force, then
Emech = U + K
The potential energy, U, depends on the position of an object subjected to a conservative force.
It is defined as the object’s ability to do work and is increased as the object is moved in the opposite direction of the direction of the force.
The potential energy associated with a system consisting of Earth and a nearby particle is gravitational potential energy.
The kinetic energy, K, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them.
K = ½ mv2
The above mentioned definition (Emech = U + K) assumes that the system is free of friction and other non-conservative forces. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path.
In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. For example the frictional force is a non-conservative force, because it acts to reduce the mechanical energy in a system.
Note that non-conservative forces do not always reduce the mechanical energy. A non-conservative force changes the mechanical energy, there are forces that increase the total mechanical energy, like the force provided by a motor or engine, is also a non-conservative force.