Consider, only conservative forces performs on a system of particles and potential energy U is described corresponding to these forces. There are either no other tension or the work provided by them is zero. Equation has

            U_f - U_i = - W   and      W = K_f - K_i                  (from work energy theorem)

then     U_f - U_i = - (K_f - K_i)     or         U_f + K_f = U_i + K_i          ... (i)

The sum of the kinetic energy and the potential energy is known the total mechanical energy. We look from Eq. (i), that the total mechanical energy of a system have constant if only conservative forces are performing on a system of particles and the work done by all other forces is zero. This is known the conservation of mechanical energy.

The total mechanical energy is not fixed if non-conservative forces such as friction are behaving between the parts of a object. However, the work energy theorem is still valid. Thus, we may apply

                        W_c + W_nc + W_ext = K_f - K_i

Here,               W_c = - (U_f - U_i)

So, we get       W_nc + W_ext = (K_f + U_f) - (K_i + U_i)        or         W_nc + W_ext = E_f - E_i

Here, E = K + U is the total mechanical energy.

Conservation of energy in non-conservative field  

If a object moves from a point a to another point be in a non-conservative field and if K_i and K_f be the starting and final kinetic energies and U_f and U_i are the starting and final potential energies of the body, then

K_i + U_i = K_f + U_f - work done by non-conservative force.

Note: - If only conservative forces are performing on a system of particles and work done by any other external force is zero, then mechanical energy of the object will remain saved. In this case, some fraction of the mechanical power will be decreasing while the other will be increasing.

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