Determine the length of the third segment

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To determine the length of the third segment of a bent metal rod, two segments of length L = 4.67 m are horizontal, and the system must be in equilibrium. The center of mass must be directly below the support point, which requires calculating the moments around that point. The equation for the center of mass involves the lengths and masses of the segments, leading to a need to solve for the unknown length of the third segment. Proper application of equilibrium principles and moment calculations will yield the required length for stability.
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Homework Statement



A thin uniform metal rod is bent into three perpendicular segments, two of which have length L = 4.67 m. Determine the length of the third segment such that the unit will hang with two segments horizontal when it is supported by a hook as shown in the figure.
Fig1-20.jpg


Homework Equations


sum T=0
sum F=0
mgr=T
mg=F

The Attempt at a Solution


i tried a number of different ways to solve the problem but it seems like nothing has a chance of working

PS this is the first time I've posted on here, i looked through some other posts and read the rules to figure out the etiquette but if i still did anything wrong please just let me know it wasn't on purpose.
 
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I have the same problem as you, I did a google search for this question and got this thread. I have no idea how to solve it though. Good Luck!
 


I can't see the image try uploading it to imageshack or something then posting the link, thanks.
 


If it is in equilibrium then the center of mass lies directly below the point of support.

Find the point that it balances right?

x = 1/M*∑ xi*mi

Since this x is located at L from the right ... you need to solve for the unknown length of the bottom piece (it appears in the sum of the moments) that you don't know.
 

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