Static equilibrium and tension problem

[Puchinita5]

Homework Statement

In Figure 12-36, horizontal scaffold 2, with uniform mass m2 = 35 kg and length L2 = 2.0 m, hangs from horizontal scaffold 1, with uniform mass m1 = 45 kg. A 17 kg box of nails lies on scaffold 2, centered at distance d = 0.50 m from the left end.
What is the tension T in the cable indicated?

Homework Equations

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c12/q05f.jpg

The Attempt at a Solution

do i have to set the forces equal to zero for the WHOLE system? or the bottom system first? do I have to do anything with rotational? I think what is confusing me is how the tensions act in the system, specifically the tensions in the rods between the two scaffolds. I know there should be a tension force uppard in reaction to the weight of the bottom scaffold, so would the forces of the top scaffold include these tension forces? I'm confused. This is supposed to be a simple problem, perhaps I'm over thinking it.

 

[LowlyPion]

You might consider resolving the system into a single effective mass, and determine the center of mass and then use that to determine the final distribution of Tension between the 2 primary support cables.

Because to answer your question, yes. The system is static, and the sum of the Torques about any point are 0.

 

[Puchinita5]

so i should find a center of mass, but the center of mass of both scaffolds? so i should do

(35)(1.5)+(45)(1.5)+(17)(1) all divided by 97? kind of as if i were to superimpose the top scaffold over the bottom scaffold?

 

[LowlyPion]

so i should find a center of mass, but the center of mass of both scaffolds? so i should do

(35)(1.5)+(45)(1.5)+(17)(1) all divided by 97? kind of as if i were to superimpose the top scaffold over the bottom scaffold?

Yes. That's what I'd do.

Then use the total weight acting through the center of mass for it all.

 

[Puchinita5]

and the tensions? would they all be the same magnitude?

 

[LowlyPion]

and the tensions? would they all be the same magnitude?

The tensions must add to 97 if that's what you're asking. But they will be distributed unequally which is where you take your sum of the torques to figure it.