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Conservation of Mechanical Energy

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Conservation of Mechanical Energy - Lesson Summary

Law of Conservation of Energy 

Energy can neither be created nor destroyed. If it disappears in one form it reappears in another form. It can be changed from one form into another. The total energy of the system remains constant.

Principle of Conservation of Mechanical Energy states that the energy can neither be created nor destroyed; it can only be transformed from one state to another.  Orthe total mechanical energy of a system is conserved if the forces doing the work on it are conservative.

Consider any two points A and B in the path of a body falling freely from a certain height H as in the following figure.

According to the Principle of Conservation of Mechanical Energy, we can say that for points A and B, the total mechanical energy is constant in the path travelled by a body under the action of a conservative force, i.e., the total mechanical energy at A is equal to the total mechanical energy at B...”work done by a conservative force is path independent. It is equal to the difference between the potential energies of the initial and final positions and is completely recoverable.”

Also, as the work done by a conservative force depends on the initial and final position, we can say that work done by a conservative force in a closed path is zero as the initial and final positions in a closed path are the same.

If a body is thown vertically upwards, we assume that the potential energy is only due to gravitational force and we take the ground level as the reference level.

The body thrown vertically upwards with velocity ‘u’ has only kinetic energy at A and zero potential energy at A.

At point B, the body possesses both potential and kinetic energies.

and

On simplification by substituting the values we get total mechanical energy at B as the following:

As we know that the velocity at C (Maximum height) is zero its kinetic energy is also zero, so

Total mechanical energy at C as the following:

Thus from the above equations of  total energies at the different positions , we can say that according to the Principle of Conservation of mechanical Energy, energy can neither be created nor destroyed, it can only be transformed from one state to another.

Note:

  • Work done by a conservative force will be path independent. It is equal to the difference between the potential energies between the initial and final positions and is completely recoverable.

  • Work done by a conservative force in a closed path is zero.

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