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When we calculate the energy stored in the rod after elongation by an external force, we only consider longitudinal expansion. My question is that according to Poisson, there is also a sideways/transverse contraction in the rod. If any, how significant is the error in calculating the potential energy of the rod(if we consider it also)?

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The contraction occurs with zero transverse force. So the transverse force times the transverse displacement is zero. No work is done and, thus, this contributes nothing to the stored elastic energy.

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  • $\begingroup$ How does the contraction occur without any transverse force ? $\endgroup$ – Jitushek-Kumar May 7 at 3:10
  • $\begingroup$ By conservation of mass, if it gets longer in one direction, it must contract in the perpendicular direction. What make you think that this requires a transverse force? $\endgroup$ – Chet Miller May 7 at 3:15
  • $\begingroup$ Although mass is conserved, what I am looking for is the mechanism behind the transverse contraction. $\endgroup$ – Jitushek-Kumar May 7 at 16:25
  • $\begingroup$ Without any transverse force, it seems rather unreasonable as to why the diameter of the rod would contract. $\endgroup$ – Jitushek-Kumar May 7 at 16:26
  • $\begingroup$ On what fundamental basis is this unreasonable. Isn't this just your intuition (which, in this case, is wrong)? If you think you are right, please identify which physical law has been violated? In particular, please identify what external force is doing work on the sample in the transverse direction. $\endgroup$ – Chet Miller May 8 at 23:01

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