Give the definitions of conservative force .

Explanation

(1) A force F(x) is conservative if it can be derived from a scalar quantity V(x) by the relation `DeltaV =-F(x)Deltax` .The three dimensional generalization requires the use of a vector derivative which is outside the scope of the topic .
(2) The work done by the conservative force depends only on the end points . This can be seen from the relation .
`W = K_(f) -K_(i) = V(x_(i))-V(x_(f))`
(3) Work done by this force in a closed path is zero . This can be seen from the `K_(i)+V(x_(i))= K_(f)+V(x_(f))`
For a closed path `x_(i) = x_(f)`