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Classical Mechanics Level 4

The above system comprises of three ideal springs, and two thick rods (they don't look like a rod!).The Temperature of the above system is increased by \(\displaystyle\Delta T\). The coefficient of linear expansion of the material of the rods is \(\displaystyle \alpha\).

Calculate the energy stored in the spring with spring constant \(\displaystyle 2K\).

Details and Assumptions:
\(\bullet\) The springs are initially relaxed.
\(\bullet\) The rods expand only in the horizontal direction.
\(\bullet\) Neglect the expansion of the springs due to the increase in temperature
\(\bullet\) \(\displaystyle L = 1m\)
\(\bullet\) \(\displaystyle K = 200 N/m\)
\(\bullet\) \(\displaystyle \alpha = 2\times 10^{-5} K^{-1}\)
\(\bullet\) \(\displaystyle \Delta T = 20^o C\)


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