# Conservation Of Mechanical Energy

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This principle state that if only the conservative force are doing work on a body, then its total mechanical energy (kinetic energy + potential energy) remains constant.

Let a body undergoes displacement ∆x under the action of conservative force F(x), then from work energy theorem, the change in Kinetic Energy is

∆K = F(x).∆x (I)

As the force is conservative the change in Potential energy is given by

∆U = Negative of work done = – F(x).∆x (II)

Combining the above two equations, We get

Although, individually the Kinetic Energy K and Potential Energy U may change from one state of the system to another, but their sum of the total Mechanical Energy of the system remains constant under the conservative force.

### Mechanical Energy Of A Stretched Spring

If the block of mass m is extended to position Xm and released from rest, then it’s total Mechanical Energy at any arbitrary point X, where X is lies between – Xm and Xm.

At any intermediate position X between -Xm and Xm, the energy is partially Kinetic Energy and Potential Energy.