You have a lightweight spring whose unstretched length is 4.8 cm. You\'re curiou

Question

You have a lightweight spring whose unstretched length is 4.8 cm. 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 1.0 g mass from it. This stretches the spring to a length of 7.0 cm. 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 5.9 cm. What is the magnitude of the charge (in nC) on each bead?

__ nC

Thanks

Explanation / Answer

spring constant from 1st experiment

F = -kx

k = F/x = mg/x = 1*10^-3*9.81/((7 - 4.8)*10^-2)

k = 0.446 N/m

Now in the second experiment

F = kx = 0.446*(5.9 - 4.8)*10^-2 = 4.91*10^-3 N

Now at equilibrium

Fs = Fe

Fs = K*q1*q2/r^2

q1 = q2 = q

q^2 = Fs*r^2/k

q = sqrt(Fs*r^2/K) = r*sqrt(Fs/K)

q = 5.9*10^-2*sqrt(4.91*10^-3/(9*10^9))

q = 0.436*10^-9 C
q = 0.436 nC

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