Optimal Length for Triple-Segment Metal Rod Hanging | Torque Equations

[chriskaplan]

Homework Statement

thin uniform metal rod is bent into three perpendicular segments, two of which have length L . You want to determine what the length of the third segment should be so that the unit will hang with two segments horizontal when it is supported by a hook

u <--hook
L
---------
| L
|
----------------
x

Homework Equations

Torque = 0

The Attempt at a Solution

I tried to do three separate torques, T1 = L T2= L2 and T3 = X but i don't know how to solve

 

[Bill Foster]

I'm having trouble visualizing this.

 

[chriskaplan]

its a backward C

the top and perpendicular part is length L and the bottom length X which is what we are looking for in terms of L

It looks like ______ <--- L
......|
......| <--- L
......|
________________|
...x...