🧄Work Done by a Non-Conservative Force and Conservative Force

The app illustrates that the work done by a non-conservative force field, such as the one described, is path-dependent, meaning the calculated work varies along different trajectories (circular vs. straight line) despite identical starting and ending points, unlike the path-independent work associated with conservative forces. This path dependence of work performed by non-conservative forces like friction, air resistance, etc., implies that mechanical energy within the system is not conserved but can be transformed into other forms, such as heat. The calculation employs line integrals and path parametrization to determine the work done, emphasizing the necessity of these mathematical tools when analyzing force fields and trajectories.

🎬The work Done Along a Circular Path and a Straight Line under non-conservative force and conservative force

The work done by a non-conservative force depends on the specific path taken between two points, as seen in the different results for Path A and Path B. In contrast, the work done by a conservative force is completely independent of the path. It only depends on the starting and ending points. For this particular demo, since the starting and ending points are at the same distance from the origin, the work done is exactly zero for both paths.

🖊️Mathematical Proof

Work Done by a Non-Conservative Force and Conservative Force | Proof and Derivationviadean on Notion