Two initially uncharged identical metal spheres, 1 and 2, are connected by an insulating spring (unstretched length L0 = 1.39 m, spring constant ks = 20.7 N/m), as shown in the figure. Charges +q and –q are then placed on the spheres, and the spring contracts to length L = 0.51 m. Recall that the force exerted by a spring is Fs = -ks Δx, where Δx is the change in the spring’s length from its equilibrium length.
a) Determine the charge q.
b) If the spring is coated with metal to make it conducting, what is the new length of the spring?
For a) I got 2.29*10^-5 C which is correct, I just have no idea how to figure out b.
a.
We use the equation $$ F = \frac{kq1q2}{d^2} $$
$$ F = \Delta X spring constant $$ q1 = q2 so it becomes q^2
spring constant = 20.7
d = .51
delta x = 1.39 - .51
k = coulombs constant = 8.99x10^9
so $$ .88 * 20.7= \frac{8.99*10^9q^2}{.51^2}$$ so $$ sqrt(\frac{(.88 * 20.7).51^2}{8.99*10^9}) = q$$
Q = -2.2295x10^-5
b. The net charge = 0 if charges are connected. The answer is the original length of the spring 1.39