Conservation of energy states that the total energy of an isolated system remains constant irrespective of whatever internal changes may take place with energy disappearing in one form reappearing in another.

It may be shown that in the absence of externalfrictional force the total mechanicalenergy of a body remains constant.Let a body of mass m falls from a point A,which is at a height h from the ground as shown in fig.

At A,

Kinetic energykE = 0Potential energyEp = mghTotal energyE = Ep + Ek= mgh + 0= mgh

During the fall, the body is at a position B. Thebody has moved a distance x from A.

At B,

velocityv2= u2+ 2as

applying,v2= 0 + 2ax = 2ax

Kinetic energy Ek=1/2 mv2= 1/2m x 2gx= mgxPotential energyEp = mg (h – x)Total energy E= Ep + Ek =mg (h-x) + mgx= mgh – mgx + mgx= mgh

If the body reaches the position C.

At C,

Potential energyEp = 0Velocity of the body C isv2= u2+ 2asu = 0, a = g, s = happlyingv2= 0 + 2gh = 2gh

kinetic energyEk =1/2mv2=1/2m x 2gh= mgh

Total energy at C E = Ep + Ek E = 0 + mgh E = mghThus we have seen that sum ofpotential and kinetic energy of freelyfalling body at all points remains same.Under the force of gravity, themechanical energy of a body remainsconstant.