Finding the Center of Mass of a Suspended Scaffold and Paint Cans System

[bravoman]

Homework Statement

A horizontal scaffold, of length 2.00 m and uniform mass 50.0 kg, is suspended from a building by two cables. The scaffold has dozens of paint cans stacked on it at various points. The total mass of the paint cans is 80.0 kg. The tension in the cable at the right is 830 N. How far horizontally from that cable is the center of mass of the system of paint cans?

I can't seem to get the right answer, I believe I may be missing a force. I set the rotational axis to the left side

Homework Equations

Sigma F = 0

The Attempt at a Solution

I have tried to create a balance of torque equation:

(L/2)* MassScaffold * g + x*MassPaint*g - 830L = 0

 

[BvU]

Hello Bravo, welcome to PF :)

Your relevant equation doesn't show up in your attempt at solution. What's the tension in the cable at the left ? When you know that, it's a piece of cake to establish where mg should be located (i.e. where the c.o.m. is) ! Then you still have to go to the c.o.m. of the paint cans only .

 

[mfb]

Your relevant equation doesn't show up in your attempt at solution.

I don't think you need it with the approach bravoman used. The attempt gives a linear equation which can be solved for x as everything else is known.

 

[BvU]

mfb is right and Bravo should continue on the path he (she?) started on.

 

[willem2]

This should work. You didn't forget that x is the the distance from the left side, while the distance from the right side is needed for the answer?