# Prove a system is at equilibirum?

1. Nov 3, 2012

### flaren5

I am aware of the meaning when "the system is in equilibrium".

What are two ways to prove it?

Any insight would be greatly appreciated...

Thank you.

2. Nov 3, 2012

### rock.freak667

In what context are you referring to? Like in physics, for a system to be in equilibrium, the sum of forces in the x,y,z directions are zero and the sum of moments about any point is zero.

3. Nov 3, 2012

### flaren5

That sounds to be what I am referring to...I'm assuming it has to do with:
ΣFx = 0 and ΣFy = 0...
Is that how I would prove it?...I was wondering what the explanation is for two ways of proving when a system is in equilibrium.

I hope that explains better to what I am looking for.

Thank you.

4. Nov 3, 2012

### rock.freak667

Well that is how you would show a system is in equilibrium. Mechanical equilibrium is defined such that the net forces acting on an object are zero. There are also different kinds of equilibrium such as thermal equilibrium.

5. Nov 4, 2012

### AJ Bentley

In general an equilibrium state is characterised by an energy minimum (or plateau).

Generally you calculate the energy of the system as a function of position, differentiate it and set equal to zero. That gives the position of equilibrium.