- #1
maverick280857
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Hello everyone
First off, a very happy new year to all my PF friends. I need some help with a mathematical analysis of the following situation:
One end of a metallic rod of length [itex]L_{1}[/itex] measured at temperature [itex]T_{1}[/itex] is fixed to a rigid wall and the other end is connected to a spring with force constant [itex]k[/itex] (the other end of the spring is anchored to a parallel rigid wall). The coefficient of linear expansion of the rod is [itex]\alpha[/itex]. We have to find the compression of the spring when the temperature is raised to [itex]T_{2}[/itex].
I've worked out the details...
If we add the strains algebraically,
[tex]\epsilon = \epsilon_{thermal} + \epsilon_{spring}[/tex]
with [itex]\epsilon_{thermal} = \alpha\Delta T[/itex], [itex]\epsilon_{spring} = -\frac{k\Delta L}{YA}[/itex] and [itex]\epsilon = \frac{\Delta L}{L_{1}}[/itex], we do get an expression for [itex]\Delta L[/itex] under the combined action of these forces. This does yield the correct answer but I want to be sure about it. Is it correct?
Thanks and cheers
Vivek
First off, a very happy new year to all my PF friends. I need some help with a mathematical analysis of the following situation:
One end of a metallic rod of length [itex]L_{1}[/itex] measured at temperature [itex]T_{1}[/itex] is fixed to a rigid wall and the other end is connected to a spring with force constant [itex]k[/itex] (the other end of the spring is anchored to a parallel rigid wall). The coefficient of linear expansion of the rod is [itex]\alpha[/itex]. We have to find the compression of the spring when the temperature is raised to [itex]T_{2}[/itex].
I've worked out the details...
If we add the strains algebraically,
[tex]\epsilon = \epsilon_{thermal} + \epsilon_{spring}[/tex]
with [itex]\epsilon_{thermal} = \alpha\Delta T[/itex], [itex]\epsilon_{spring} = -\frac{k\Delta L}{YA}[/itex] and [itex]\epsilon = \frac{\Delta L}{L_{1}}[/itex], we do get an expression for [itex]\Delta L[/itex] under the combined action of these forces. This does yield the correct answer but I want to be sure about it. Is it correct?
Thanks and cheers
Vivek
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