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Non-conservative forces like friction, air resistance, and viscosity convert mechanical energy into heat and internal energy. Their work is path-dependent, and mechanical energy decreases over time.
From your prerequisite on conservative vector fields, you know the defining property of conservative forces: the work they do is path-independent, and there exists a potential energy function V such that F = −∇V. Gravity and the spring force are conservative — any energy you "spend" lifting an object or compressing a spring is stored as potential energy and is fully recoverable. Total mechanical energy KE + PE stays constant. Non-conservative forces break this symmetry: the work they do depends on the path taken, not just the endpoints, and the "spent" energy does not return as mechanical energy.
Friction is the canonical example. When you slide a block across a floor, kinetic friction opposes motion at every instant along the path. Take the block on a round trip — push it forward 1 m, then pull it back 1 m — and friction does negative work in *both* legs of the journey. The work done going forward is −f·d; the work done going back is also −f·d. You end where you started, but you have lost 2f·d of mechanical energy. There is no potential energy function for friction because energy is not stored and recovered — it is genuinely lost to heat and sound. This is the precise meaning of path-dependence: the total work done by friction between two points depends on how you travel between them, not just the endpoints.
The energy accounting equation for systems with non-conservative forces is ΔKE + ΔPE = W_nc, where W_nc is the work done by all non-conservative forces. Because friction and drag always oppose motion, W_nc is negative, and total mechanical energy decreases. This "missing" mechanical energy does not vanish — it converts into thermal energy (heat) and internal energy of the materials. The first law of thermodynamics ensures total energy is conserved across all forms, but the mechanical portion steadily shrinks. In any real-world system — a pendulum in air, a car slowing to a stop, a ball bouncing — dissipation is always present.
The deepest consequence is irreversibility. A conservative system — a frictionless pendulum, an ideal spring — is time-reversible: play the motion backward and it obeys the same physical laws as forward motion. Add friction, and reversal becomes impossible: the reversed motion would require friction to spontaneously *add* energy to the system, which never happens. Dissipation gives physical processes a direction in time: the forward slide and the backward slide are distinguishable by the heat generated. This asymmetry is the mechanical foundation of the second law of thermodynamics — the tendency of isolated systems toward greater disorder and energy dispersal — which you will explore in the topic on energy dissipation and irreversibility. Non-conservative forces are the bridge between Newton's reversible equations of motion and the irreversible thermal world we actually inhabit.