Conservative Force
When the total work done by a force F acting as an object moves over any closed path is zero, the force is conservative. Mathematically.
`ointvecF.dvecr=0` (conservative force)
Suppose we move an object along the straight path between point A and B shown in figure, along which a conservative force acts; Jet the work done by the conservative force be `W_(AB)`. Since the work done over any closed path is zero, the work `W_(BA)` done in moving back from B to A must be `-W_(AB)` whether we return along the straight path or the curved path or any other path. So, going from A to B involves work `W_(AB)` regardless of the path taken.
The work done by a conservative force in moving between two points is independent of the path taken:
mathematically, `int_A^BvecF.dvecr` depends only on the A end points A and B, not on the path between them.
These include force due to gravity(mg), spring force, electrostatic force etc.
`ointvecF.dvecr=0` (conservative force)
Suppose we move an object along the straight path between point A and B shown in figure, along which a conservative force acts; Jet the work done by the conservative force be `W_(AB)`. Since the work done over any closed path is zero, the work `W_(BA)` done in moving back from B to A must be `-W_(AB)` whether we return along the straight path or the curved path or any other path. So, going from A to B involves work `W_(AB)` regardless of the path taken.
The work done by a conservative force in moving between two points is independent of the path taken:
mathematically, `int_A^BvecF.dvecr` depends only on the A end points A and B, not on the path between them.
These include force due to gravity(mg), spring force, electrostatic force etc.