^Work by a conservative force
Work done by a conservative force in moving a body from one point say ‘A’ to other point say ‘B’ is always equal to
loss of potential energy between same points i.e.,
Here the negative sign implies that a conservative force is always directed in the direction of decreasing
potential energy (i.e. increasing stability).Dropping the integral sign & the dot product in the LCF, we can write,
i.e. a conservative force is equal to the negative of potential energy gradient.
In vector form the above result can be expresses as
For one dimensional force we can write