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John Darby
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A little more information.

In basic physics tests, a conservative force is defined as one where the work done by the force in moving from point a to b is independent of the path taken in going from a to b. For a conservative force, the change in potential energy is defined as the negative of the work done by the force. The use of potential energy instead of evaluating the work for the conservative force simplifies many problems. For example, for the gravitational force near the earth the change in potential energy is simply $mgh$ where $m$ is mass $g$ is the acceleration of gravity and $h$ is the change in height, regardless of how complicated the actual physical path is in changing the height. $mgh$ is easy to evaluate and equals the negative of the work done by gravity $-\int_{r_1}^{r_2} \vec F_g \cdot d\vec r$ which is not always not easy to evaluate. $\vec F_g$ is the force of gravity and $\vec r$ describes the path taken in changing the height by $h$.

In classical mechanics texts it is shown that a conservative force has zero curl, as @jensen paull says. Also, it is shown that a potential energy function $V$ can be defined for a conservative force, and $\vec F = -\nabla V$. See the text Mechanics by Symon for details.

John Darby
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