non-conservative force
Summary
A non-conservative force does work that depends on the path taken, so no potential energy can be defined for it. Friction and air drag are the standard examples; they typically convert mechanical energy to thermal energy, so mechanical energy is not conserved.
Detail
Meaning: A force is non-conservative when the work it does between two points depends on the path, or equivalently when its work around a closed loop is not zero. No potential energy can be assigned to it. Kinetic friction and air resistance are the standard examples; they are dissipative, turning mechanical energy into thermal energy. A motor or a person pushing an object is also non-conservative and can add mechanical energy. Gravity, the spring force and the electrostatic force are conservative.
Equation: Wnc = ΔKE + ΔPE, where Wnc is the work done by non-conservative forces (J), ΔKE is the change in kinetic energy (J) and ΔPE is the change in potential energy (J). For kinetic friction, Wf = −fk d, where fk is the friction force (N) and d is the distance traveled along the path (m).
On the MCAT: A block slides down a rough incline, or a cart coasts to a stop. You find that the final speed is lower than in the frictionless case, or you calculate the mechanical energy lost as heat.
Common confusion: Students use displacement for friction's work. Friction depends on path length, so a round trip returns an object to its start while friction still removes energy; gravity's net work over that loop is zero. Total energy is still conserved. Only mechanical energy is not.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- College Physics (Serway and Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.