Question

A force is conservative if

Answer 1

Step 1: Conservative force

1. Conservative forces are forces that act on a body and the mechanical energy associated with the system are conserved.
2. But in actual definition, conservative forces are forces that do work on a body that only depends only on the endpoints and not the path taken.
3. So the work done depends only on the initial point and final point of the path taken by the body.
4. Since the initial and final positions are the same, the work done by a conservative force in a circular route is zero.
5. Conservative forces include electrical and gravitational forces.

Step 2: Condition for the conservative force

1. If a force can be represented as the gradient of a scalar potential, it is called a conservative force.
2. For example, in the case of an electric field, the gradient of electrical potential, which is a scalar potential, can be stated.$E=-\nabla V[E=electricfield,V=scalarpotential]$

Hence, a force is conservative if the work done over a closed path is zero, as it depends only on the initial and final positions.