Conservative and Non-Conservative Forces

A force is called conservative if the work it does on a body moving from one point to another depends only on those two points -- the starting point and the ending point -- and not at all on the particular path taken to get from one to the other. An immediate and equivalent way to state the same property: the work done by a conservative force around any closed path (one that starts and ends at the same point) is always exactly zero, since the "start" and "end" points then coincide.

Gravity (near the Earth's surface, treated as uniform) is a familiar conservative force: the work it does on a body moving between two heights depends only on the vertical drop or rise between those heights, never on whether the body moved straight down, along a slanted ramp, or by some winding path -- lift a body up by any route at all, then lower it back to its starting height by any other route, and gravity does exactly zero net work over the whole round trip. The spring force obeying Hooke's law is likewise conservative: the work needed to stretch (or compress) an ideal spring by a given amount depends only on its initial and final extension, never on the details of how the stretching was carried out.

A force for which this path-independence fails is called non-conservative. Friction is the most important everyday example: sliding a body from point $A$ to point $B$ along a short, direct path involves less work done against friction than sliding the same body from $A$ to $B$ along a long, winding path, because friction opposes motion along whatever path is actually travelled and the total distance travelled, not merely the net displacement, governs how much energy it dissipates. Air resistance and other forms of viscous drag behave the same way, for the same underlying reason. …