non-conservative
Summary
A non-conservative force is one whose work depends on the path taken, so the work over a closed loop is not zero and no potential energy can be defined for it. Friction and air resistance are the standard examples, and they usually drain mechanical energy as thermal energy.
Detail
Meaning: A non-conservative force does work that depends on the path, not just on the start and end points. Over a round trip the net work is not zero, so no potential energy function exists for it. Friction and drag (air resistance) are the standard examples. They typically convert mechanical energy into thermal energy. Gravity, ideal springs and electrostatic forces are conservative by contrast. A motor or a person pushing can also be a non-conservative source that adds mechanical energy.
Equation: Wnc = ΔK + ΔU = ΔEmech, where Wnc is the work done by non-conservative forces (J), ΔK is the change in kinetic energy (J), ΔU is the change in potential energy (J), and ΔEmech is the change in total mechanical energy (J). For kinetic friction, Wfriction = −μk N d, with μk the coefficient of kinetic friction (unitless), N the normal force (N) and d the distance slid along the path (m).
On the MCAT: A block slides down a ramp or a cart rolls along a track with friction. You compare its final speed with the frictionless case (it is lower) or find the energy lost to heat. A longer path means more friction work, which shows the path dependence.
Common confusion: Students say energy is destroyed. Total energy, including thermal energy, is still conserved. Only mechanical energy (K + U) changes, which is why Wnc is not zero in the equation above.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- University Physics (Young and Freedman)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.