[Physics] Change in mechanical energy

energy-conservationnewtonian-mechanics

When one pulls an object from A to B with a constant force (so a conservative force), the mechanical energy of the object is modified by the work of this force so why is there a law saying that the change in mechanical energy equals the work of non-conservative forces only ?

EDIT:
In this situation:

sliding a block

is the change of mechanical energy only due to work of friction ? the pull is constant and conservative shouldn't I take its work into account ?

Best Answer

Mechanical energy is a term that covers kinetic energy $K$ and potential energies $U$ (gravitational $U_g$, elastic $U_{el}$ etc.).

A swinging pendulum is an example. When swinging downwards, gravitational potential energy $U_g$ is converted into kinetic energy $K$. When swinging upwards, the opposite takes place. Those energy forms simply transform into one another and never leave the system.

But doesn't gravity do work in this system? Yes, it does. Gravity is a conservative force. The work done by conservative forces is what we call potential energies. So gravity's work is already included in this consideration.

The reason for this "renaming" is that when a conservative force does work, that work is stored. The system can return to its original state again by releasing that energy. In other words, work done by a conservative force doesn't leave the system. Only work done by non-conservative forces disappears and leaves the system, causing the total energy to reduce.

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