Two initially uncharged identical metal spheres, 1 and 2, are connected by an in

Question

Two initially uncharged identical metal spheres, 1 and 2, are connected by an insulating spring (unstretched length L0 = 2.00 m, spring constant k = 20.0 N/m), as shown in the figure.

Charges +q and q are then placed on the spheres, and the spring contracts to length L = 1.630 m. Recall that the force exerted by a spring is Fs = kx, where x is the change in the spring's length from its equilibrium length.

Determine the charge q.


If the spring is coated with metal to make it conducting, what is the new length of the spring?

Explanation / Answer

q = 4.677 * 10-5 C

and if the spring is conducting, the charges cancel out and the new length is 2.0 m

To see the first part, consider that the spring has compressed 0.37 m, so the force = kx = (20 N/m)(0.37m) = 7.4 N.

That must equal the Coulomb force of kq2/r2. Solving for q, we get

q = (Fr2/k)½

= ((7.4 N)(1.63 m)2/(8.99 * 109 Nm2/C2))½ = 4.677 * 10-5 C

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