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Homework Statement
Three identical wires Lo, diameter d, are arranged like a Y letter (please see attachment)
Each end of the wires is secured to a wall. Initial tension is approximately zero. If the wires are cooled ΔT, find the distance the knot moves to the right and the final tension in each wire. (assume θ does not change when the knot moves.)
Homework Equations
ΔL = Lo[itex]\alpha[/itex]ΔT
ΔL/Lo = -F/AY = [itex]\alpha[/itex]ΔT
The Attempt at a Solution
Tensions in wires: Fwire1 = 2 * Fwire2 * cos(θ/2)
Here is where I'm stuck. I think that the total expansion is zero, so the equation is something like this
ΔLtotal = ΔLwire1 + ΔLwire2 cos(θ/2)
= (Lo[itex]\alpha[/itex]ΔT - Lo Fwire1/AY) + ( Lo[itex]\alpha[/itex]ΔT - Lo Fwire2/AY) cos(θ/2) = 0
But I got the wrong answers. It is hard for me to visualize how the system changes with the assumption that θ is still the same. It doesn't make sense. Please help me.
Thank you very much.