Question

Work done by or against a conservative force in a round trip is ________.

Answer 1

Conservative force:

1. A force is said to be conservative if the work done by the force depends only on the initial and final positions of the body and not on the path taken.
2. The work done by a conservative force during a round trip of a system is always zero. For example, spring force, gravitational force, etc.

For conservative force work done over a closed loop is zero,

1. The work done by a conservative force is independent of the path, that is, the work only depends upon the initial and final state.
2. Work done $\left(\mathrm{W}\right)$ is the dot product of force $\left(\mathrm{F}\right)$ and displacement $\left(\mathrm{d}\right)$.
3. Mathematically, it can be given as, $\mathrm{W}=\mathrm{Fdcos}\theta$. As the dispalcement $\left(\mathrm{d}\right)$ in closed path is zero implies $\mathrm{W}=\mathrm{F}\left(0\right)\mathrm{cos\theta }=0$.
4. Thus, work done over a closed-loop for conservative force is zero.

Hence, for conservative force work done over a closed loop is zero.