# Energy conservation, and conservative forces?

1. May 23, 2014

### Dash-IQ

What is the relationship of conservative & non-conservative forces to the conservation of energy? What differs with the two? Energy in each case...?

2. May 23, 2014

### BiGyElLoWhAt

I'm not really sure that there is a connection. One is a concept, and the other is a "thing".
Conservation of energy states one of two things, depending on the situation.
$E_{initial} = E_{final}$
If there are external forces:
$E_{initial} \pm \Delta W = E_{final}$

A conservative force is another thing entirely.

A force is conservative if $\vec{∇} \times \vec{F} = 0$ Which basically states that the work done on an object moving through the vector field F is independent of path; meaning if an object moves through the field from point a to point b, the work done on the object by the field is the same no matter what path it chooses to take.

$\vec{∇}$ is defined as: $<\frac{\partial}{\partial x}\hat{i},\frac{\partial}{\partial y}\hat{j},\frac{\partial}{\partial z}\hat{k}>$

3. May 23, 2014

### UltrafastPED

Conversely, for non-conservative forces the amount of work done varies with the path taken.

4. May 23, 2014

### abitslow

Conservative force? Hmmm. Oh yeah, in certain problems it is useful to invoke a force (or a set of forces) which are constant (in the context of the problem). Are you familiar with Kilroy's 1st law? "Force is always conserved." No? Well, there is a reason for that. (there is no such law). A real (general) conservation principle will have an associated Law.

5. May 23, 2014

### AlephZero

For a conservative force, the work done moving between two points depends only on the points, not on the path between them.

So you can define a potential function that describes the work done by the force when moving between any two points in space.

That potential function can be interpreted as "potential energy". A simple example is gravitation, in classical mechanics.

6. May 23, 2014

### Matterwave

A conservative force will have with it an associated potential energy. The total energy, kinetic plus potential, will then be conserved. A non-conservative force, like friction, will not have an associated potential energy function, and thus you cannot say kinetic plus potential energy is constant. There may be sources of energy loss such as heat.

But not all sources of non-conservative forces will lead to energy loss. The magnetic force, for example, will lead instead to no kinetic energy change since it always acts perpendicular to the direction of motion.

EDIT: Whelp, looks like Aleph beat me to it.

7. May 26, 2014

### Dash-IQ

Energy is certainly conserved in BOTH kinds of forces correct?

8. May 26, 2014

### UltrafastPED

Yes, energy is always conserved; for example, friction is non-conservative - the lost work goes to heat & sound. For a conservative force like gravity the work done against gravity becomes potential energy; and the potential energy lost by a falling body goes into kinetic energy.

So all of the energy is converted to other forms of energy in all cases.

9. Jul 1, 2015

### anastasia15

Are hysteretic forces by definition non conservative?

Thanks :)