you have a lightweight spring whose unstretched length is 4.0 . you\'re curious

Question

you have a lightweight spring whose unstretched length is 4.0 . you're curious to see if you can use this spring to measure charge. first, you attach one end of the spring to the ceiling and hang a 3.0 mass from it. this stretches the spring to a length of 5.0 . you then attach two small plastic beads to the opposite ends of the spring, lay the spring on a frictionless table, and give each plastic bead the same charge. this stretches the spring to a length of 4.5 .what is the magnitude of the charge (in ) on each bead:

Explanation / Answer

The initial hanging from the ceiling part is used to find the spring constant. Since the weight equals the force, its simple to solve for the spring constant. F (spring) = k*x, where k is a constant (usually N/m) and x is the distance the spring is stretched from equilibrium. Since F = m*g = k*x, 3*9.8=1.5*k, k =19.6. You didnt give units, so that is needs to be in the units given. Now, just use the electrostatic force equation on the beads. F = ke*q*q/ r^2. r = distance between the two, 4.5cm q = the charge to solve for. ke= 9e9 (a constant) Set this equal to k*x=F x=1cm (4.5 from 3.5) ke*q*q/ r^2 = ks*x, note that these are two different k values (ke for electro, ks for spring). q = sqrt( 1cm*ks*r^2/ke)

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