# Homework Help: Equilibrium Reasoning

1. Sep 30, 2009

### camino

1. The problem statement, all variables and given/known data

http://img121.imageshack.us/img121/9765/equilibrium.jpg [Broken]

2. Relevant equations

Equation of Equilibrium: Sum of all forces = 0

3. The attempt at a solution

I'm just wondering how you guys would go about this question. I just need to answer this as a reasoning answer and have an idea of what to say but I'm just looking for your input.

Last edited by a moderator: May 4, 2017
2. Sep 30, 2009

### willem2

That equation of Equilibrium you gave isn't the only thing you need. The question asks for a
stable equilibrium, so you have to show that the potential energy of the truss has a minimum if you place the truss in a tipped position.

I'd compute the potential energy of the truss as a function of the angle that the truss makes, or maybe as a function of the length AB, and show that there is a minimum if the angle is 0 or AB=BC.
you have to show this for all possible lengths of the truss and distances AC

3. Sep 30, 2009

### willem2

It appears that the equilibrium is actually unstable if the truss doesn't have any thickness, so the center of mass is in the middle of the line segment AC. (call this point M)
Only if the center of mass of the truss is somewhat below M can the equilibrium be stable. The computation gets really hard if the center of mass isn't between A and C anymore, because this means that M need not be on the same vertical line as B.

If the center of mass is in the middle of the line segment at the point M, this means M will be exactly below B and a minimum of the potential energy of the truss is a maximum of m.
it isn't too hard to find BM as a function of x, if the lengths of AB and BC are l+x and l-x
(the length of the string is 2l). I hope you know the cosine rule.