Law of Conservation of Energy - QS Study
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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.