Calculating Total Charge in a Charged Block and Spring System

[Punchlinegirl]

Two identical metal blocks resting on a frictionless horizontal surface are connected by a light metal spring having constant of 148 N/m and unstretched length of 0.3 m. A total charge of Q is slowly placed on the system causing the spring to stretch to an equilibrium length of 0.7 m. Determine the value of Q, assuming that all the charge resides on the blocks and the blocks can be treated as point charges. Answer in units of C.
I drew a free body diagram, but I have no idea where to go from there.. can someone please help me?

 

[Doc Al]

The charge distributes itself equally on the two blocks (how much on each?), thus there is a repulsive electrostatic force between the blocks (Coulomb's law). That force is balanced by the stretched spring, which pulls the blocks together. (What's the spring force?)

Since there's equilibrium, the net force on each block must be zero.

 

[Punchlinegirl]

so -kx= k*q_1*q_2 /r^2 since it has to equal 0.
(-148)(.3)=9 x 10^9 *q_1*q_2 /(.7)^2
-21.756 = 9 x 10^-9 * q_1 *q_2
-2.42 x 10^-9 = q_1 * q_2
-242 x 10^-9 / 2 = -1.21 x 10^-9 since the charges are equal.
am I doing this right?

 

[Doc Al]

(1) "x" is the amount the spring stretches. How much is that? (Compare stretched to unstretched length.)

(2) q_1 = q_2. But q_1 doesn't equal (q_1 * q_2)/2 ! (You'll need to take a square root at some point.)

 

[Punchlinegirl]

ok, so the length that the spring stretches is .4 m.
So -(148)(.4)= 9 x 10^9 *q_1*q_2 / .7^2
-29.01 = 9 x 10^9 * q_1 *q_2
-3.22 x 10^-9 = q_1 * q_2
-3.22 x 10-9 = (q_1)^2
But how can I take the square root of a negative?

 

[Doc Al]

That negative sign doesn't belong there.

 

[Punchlinegirl]

Ok so $$\sqrt 3.22 x 10^-9$$ = 5.68 x 10^-5.
This isn't right.. am I doing something else wrong?

 

[Doc Al]

You solved for q_1, but you are asked to solve for total charge Q. (I didn't check your arithmetic.)