# Homework Help: Thermal expansion with set of 3 wires

1. Mar 31, 2013

### awerter

1. The problem statement, all variables and given/known data
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.)

2. Relevant equations
ΔL = Lo$\alpha$ΔT
ΔL/Lo = -F/AY = $\alpha$ΔT

3. 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$\alpha$ΔT - Lo Fwire1/AY) + ( Lo$\alpha$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.

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2. Mar 31, 2013

### Sunil Simha

This question can be solved by assuming a Young's modulus (Y) for the material. It helps to draw the diagram of individual wires before cooling, after cooling (assuming absence of other wires) and the real scenario after cooling. I have attached these in this reply. So just check it out and see whether it works. Here x is the required extension.

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Last edited: Mar 31, 2013
3. Mar 31, 2013

### CWatters

θ would change but the change could be small so they are telling you to assume it's constant.

I reckon for some angles Δx could be -ve, 0 or +ve.

4. Mar 31, 2013

### awerter

Thank you for all your help! I can do it now.