Force-vs-Position Diagrams to distinguish Conservative and Non-conservative forces

A force-vs-position diagram allows us to determine work done by calculating the area under the curve. This feature is commonly used to analyze spring forces and derive potential energy functions. In this poster, we extend this analysis to gravity and to sliding friction acting along closed paths in one dimension. Our analysis allows us to reveal a key distinction: mechanical cycles associated with conservative forces enclose zero area on these diagrams, while those associated with non-conservative forces enclose a nonzero area. This enclosed-area property provides a preview of the work done in thermodynamic cycles in pressure-vs-volume (PV) diagrams.