Law of Conservation of Energy states that, if a body or system of bodies is in motion under a conservative system of forces, the sum of its kinetic energy and potential energy is constant.
From the principle of work and energy;
Work done = change in the kinetic energy
W1→2 = EK2 – EK1 … … (i)
If a body moves under the action of a conservative force, work done is stored as potential energy.
W1→2 = – (EP2 – EP1) … … (ii)
Work done is equal to negative change of potential energy. Combining the equation (i) and (ii),
EK2 – EK1 = – (EP2 – EP1)
Or, (EP1 + EK1 = EP2 + EK2
Which means that the sum of the potential energy and kinetic energy of a system of particles remains constant during the motion under the action of the conservative forces.