Question #202507

I have a problem where two charged spheres repell each other, and as they do so compress springs. Solving for the k of the springs using force analysis is simple and results in a k value of about 55 N/m. If however you try to solve using conservation of energy you get a very different result at around 439 N/m. I can't see where either solution is incorrect but also can't resolve the difference:

Two spheres 8cm apart are each charged with 2.5 x 10^-6C. They come to rest 16cm apart. Find k.


1
Expert's answer
2021-06-03T09:15:14-0400

kCq2x2=0.5k(xx)9109(2.5106)20.162=0.5k(0.160.08)k=55Nmk_C\frac{q^2}{x'^2}=0.5k(x'-x)\\9\cdot10^9\frac{(2.5\cdot10^{-6})^2}{0.16^2}=0.5k(0.16-0.08)\\k=55\frac{N}{m}

Energy can be dissipated but the forces needs to be equal for equilibrium.


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