Physics

The key insight is that mechanical energy isn't always conserved—it changes whenever non-conservative forces (like friction or air resistance) do work on a system. Rather than energy disappearing, these forces either dissipate it or add it to the system. The relation you're looking for directly links the work done by non-conservative forces to how much the total mechanical energy ($E_{\text{mech}} = KE + PE$) actually changes, giving you a powerful way to track energy flow in real, non-ideal situations.

The key insight is that mechanical energy isn't always conserved—it changes whenever non-conservative forces (like friction or air resistance) do work on a system. Rather than energy disappearing, these forces either dissipate it or add it to the system. The relation you're looking for directly links the work done by non-conservative forces to how much the total mechanical energy ($E_{\text{mech}} = KE + PE$) actually changes, giving you a powerful way to track energy flow in real, non-ideal situations.