State and explain the law of conservation of mechanical energy.

Explanation

The total mechanical energy of a system in motion remains a constant at all point From the work energy theorem, `DeltaKE=F(x)Deltax`
where F(x) is a conservative force
For a conservative force, `Delta P.E=-F(x)Deltax`
Hence, the total energy `(1)+(2)DeltaKE+DeltaPE=0`
i.e., `Delta(KE+PE)=0`
i.e., `KE_(f)+PE_(f)=KE_(i)+PE_(i)` = constant.
As K.E. increases, P.E. decreases and as K.E. decreases, P.E. of a body system increases so that their sum always remains a constant.
So as long as the force is conservative force, the total mechanical energy of a system is conserved.