Law of conservation of mechanical energy

The statement of conservation of energy for the ideal mechanical process is known as conservation of mechanical energy". The equation for the mechanical process is WE + WF = ΔK + ΔU Here,

WE = 0

WF = 0

Hence, for the isolated system,

ΔK + ΔU = 0 ΔE_mech = 0

This is what is known as conservation of mechanical energy. We can interpret this equation in many ways and in different words :

When only conservative forces interact within an isolated system, sum of the change in kinetic and potential energy between two states is equal to zero.

ΔK + ΔU = 0

When only conservative forces interact within an isolated system, sum of the kinetic and potential energy of an isolated system can not change.

ΔK = -ΔU

K_f - K_i = - (U_f - U _i) K_i + U_i = K_f + U_f

When only conservative forces interact with in an isolated system, the change in mechanical energy of an isolated system is zero. ΔE_mech = 0

When only conservative forces interact within an isolated system, the mechanical energy of an isolated system can not change. E_mech = 0 We should be aware that there are two ways to apply conservation law. We can apply it in terms of energy for initial (subscripted with i) and final (subscripted with "f") states or in terms of change in energy. The internal forces are only conservative force. This ensures that transfer of energy takes place only between kinetic and potential energy of the isolated system. Since potential energy is regained during the process, there is no dissipation of energy.

As there is no dissipation of energy involved, the system represents the most energy efficient reference for the particular process.