The total energy of any system is always constant. It neither increases nor decreases and it remains constant.

The mechanical energy of the system is of two forms and they are potential and kinetic energies.

Let that a body undergoes displacement Δx under the action of a conservative force F. Then from the WE theorem we have, ΔK = F(x) Δx .

If the force is conservative, the potential energy function V(x) can be defined such that

− ΔV = F(x) Δx

The above equations imply that

ΔK + ΔV = 0

Δ(K + V ) = 0

which means that K + V, the sum of the kinetic and potential energies of the body is a constant. Over the whole path, xi to xf, this means that Ki + V(xi) = Kf + V(xf ) .

The quantity K +V(x), is called the total mechanical energy of the system. Individually the kinetic energy K and the potential energy V(x) may vary from point to point, but the sum is a constant.

The total mechanical energy of a system is conserved if the forces, doing work on it, are conservative.

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If the work done is independent of path then it is called conservative and vice verse.