# B Why do conservative forces try to reduce potential energy?

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1. Mar 30, 2016

### Soren4

I do not understand the reason why a conservative force always "tries" to reduce the potential energy of a system at its minimum (forgive me if I said it in a wrong way).

The explanation I gave me is: since for a conservative force, from the definition of potential energy, $W=-\Delta U$ that means that if the work is positive, the potential energy decreases. Now, saying "the work is positive" means that the force is not opposing the displacement (more precisely $\vec{F} \cdot \vec{ds}>0$) or equivalently that the kinetic energy is increasing. Nevertheless I do not see why a (conservative) force should "naturally" do positive work (since this depends also on $\vec{ds}>0$). This is surely a wrong explanation.

So what is the correct reason for this? And how to interpret this fact?

2. Mar 30, 2016

Staff Emeritus
What would happen if the direction of the force were reversed?

3. Mar 30, 2016

### andrewkirk

I don't like the work explanation either. If we throw a rock up in the air then gravity does negative work on the rock while it is moving up.

An explanation I like better is that a conservative force defines a potential field, and the force is the negative gradient of that field, which means that the force points in the direction of the greatest decrease of the field (like how a ball on a hill will roll down in the direction of the steepest gradient). So the force is always pushing a particle in the direction of maximum decrease of potential.

4. Mar 31, 2016

### Soren4

Thanks a lot for the answer! It is more clear now! If I may ask, how to interpret "physically" (less then mathematically) the fact that the force is the negative gradient of the potential field (and so it is directed towards the greatest decrease of it)? Of course it is a consequence of how the potential field has been defined but is there something more (from the point of view of physics) in this?