Equilibrium Formula Derivation for Torque and Lever Systems

[pinky2468]

I have this homework question that I an having a lot of trouble with. I am not sure if anyone could help, but here it is:

Using the definitions of torque and lever arm and the fact that the system is in equilibrium, derive this formula-
Xo= m1x1 + m2x2 + m3x3
... m1 + m2+ m3

So, I know all the different formulas for torque and the levers etc... but I can't figure out how to turn them into this formula?

 

[Galileo]

Mind telling what $x_0,x_1,x_2,x_3$ are?
All I can tell is that the equation can be written as such:
$$m_1(x_1-x_0)+m_2(x_2-x_0)+m_3(x_3-x_0)=0$$

Maybe that helps...

 

[pinky2468]

That does help, here are some of the given equations in the chapter before the problem:

T1=m1gl1 T2=m2gl2 l1=Xo-X1 l2=Xo-X2 l3=Xo-X3

The numbers in the equation:
Xo= 121.8(.3000) + 71.40(6500) + 145.4(.5005)/ 121.8 + 71.40 + 145.4


121.8=m1(hanging mass from bar on the left) 71.40=m2(hanging mass on the right)
145.4=m3(mass from the center of gravity) and we are looking for Xo-the balance point in between m1X1 and m3X3 wih m2X2 on the right of m3X3

Does that help or make it more confusing?