Has Hooke's Law-force is proportional to extension - got a mathematical proof from quantum mechanics and how atomic bonds behave?
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Like Ohm's law, Hookes law is not really a physics law, but an empirical conjecture that for most materials stress dependence on strain (i.e., the force dependence on displacement of a spring) has a linear part:
In other words, this "law" does not follow from the laws of quantum mechanics, but from the fact that a function allows linearization near zero displacement, i.e., its expansion in Taylor series has a non-zero second coefficient: $$ F(\Delta x)\approx F(0) + F'(0)\Delta x + ... $$
On a more general level, the elasticity arises from the fact that molecules are bound together and one needs to apply a force to break them apart.
Related:
Don’t understand how nonlinear resistors violate Ohm’s law
Please provide me with a proof for the formula : $R(T)=\rho(1+\alpha T)$
which relates the change of resistivity with temperature
Roger V.
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