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Conservative forces
Intermediate
Work done is path independent and zero over a closed loop.
A force is conservative if the work it does between two points is independent of path, or zero around a closed loop. Gravity, springs and electrostatic forces qualify and have potential energies.
Gravity does the same work whichever ramp you lift a block along.
Friction depends on path length, so it's not conservative.
In more detail
A conservative force does work that depends only on initial and final positions, not on the path. Gravity and spring forces are conservative, and they allow mechanical energy to be conserved.
Real-world uses
- A roller coaster's energy depends only on its height, not the route taken.
- Electric forces in electronics are conservative, so energy stays well-defined.
- Gravity and the electric force in a static field are conservative, so the energy you put in lifting a box is returned when it falls.
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Frequently asked questions
How can I tell if a force is conservative?
If the work around any closed path is zero, the force is conservative.
Is friction conservative?
No. Friction depends on the path, since the total distance travelled matters.
How can I tell a force is conservative?
If the work done round any closed path is zero, the force is conservative and has a potential energy function.
Related topics in Work, Energy & Power
Potential energy · Gravitational potential energy · Elastic potential energy · Non-conservative forces · Force from potential energy · Potential energy curves