# Help with conservative/non-conservative forces

1. Oct 19, 2006

I'm confused about conservative and non-conservative forces from a note I took in class. This is basically the note:

Conservative (force of gravity, effort force)

-is the force that does work on an object
-amount of work is independant of the path taken
-it takes the same amount of work to lift a mass to height 'h' regardless of the path

Non-Conservative (force of friction, normal force)

-the work done against the force of friction when a crate pushed on a rough surface depends on the path

(Work done conservative) results in energy changes that are independant of the path, and therefore reversible.
Time1 = total mechanical energy initial
Time2 = total mechanical energy

(Work done non-conservative) results in energy charges that are dependant on the path, and therefore may not be reversed.

I don't really get the note, and I don't think my teacher explained it well enough. Can somebody please translate this for me into something easier to understand?

2. Oct 19, 2006

### Staff: Mentor

The path concept is a good way to think about it. Lift a weight from the floor to 2m and let it back down to 1m. The total work is the same as if you just lifted it from 0m straight to 1m, because you can extract the extra PE out of the object in the drop from 2m to 1m (the same as you put in to lift it that extra meter from 1m to 2m in the beginning). The same kind of thing holds true for an electron in an Electric field, etc., and for any conservative field and related forces.

However, with friction and other non-conservative forces, the path does make a difference. Push a crate 1m forward, or push it 100m forward and 99m back. It takes positive work input all along that path to move the crate, and you can't extract any energy back out anywhere along that path.

Makes more sense?

3. Oct 19, 2006

Yeah, that helps me understand it more.

4. Oct 19, 2006

### PhanthomJay

Primarily in mechanics, weight (gravity) forces and spring forces are conservative; everything else (friction, drag, normal force, applied forces, etc.) are non-conservative. If there are only conservative forces acting, then mechanical energy is conserved:
Initial Kinetic plus initial potential energy equals final kinetic plus final potential energy. Note that work done by conservative forces is the change in potential energy (gravitational potential energy (mgh) or spring potential energy, (1/2kx^2)).
If there are non conservative forces acting that do work, then
Initial Kinetic plus initial potential energy equals final kinetic plus final potential energy plus the work done by the non-conservative forces.

Note that work done by non conservative forces is the change in potential energy (gravitational potential energy (mgh) or spring potential energy, (1/2kx^2).
The work done by non-conservative forces is equal to the change in mechanical energy.