Why is work done by a conservative force equal to change in the potential energy only? Why doesn't it account for all mechanical energy, what about kinetic energy?
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Conservative forces can cause changes in kinetic energy. For example, the conservative force of gravity doing work on a falling object gives that object kinetic energy. It's just that conservative forces don't account for the changes in kinetic energy due to work done by non conservative forces.
The thing is, all work done by conservative forces result in either an increase or decrease in potential energy. The work done by gravity on a falling object giving it kinetic energy is at the expense of gravitational potential energy. The work done by gravity on a rising object increases gravitational potential energy. That's why the work done by gravity is always the negative of the change in potential energy, or
$$W_{g}=-\Delta U$$
For the example of a falling object of mass $m$ near the surface of the earth,
$$W_{g}=-\Delta U = -(-mgh)=mgh =\frac{1}{2}mv^2$$
Hope this helpsl.
