Finding Charge Using Coulomb's Law

[Canadian]

Ahhh, just typed out a big long post and I did something wrong and now it's gone. Oh well. This problem was given on a practice problem sheet in my first year university physics class.

Homework Statement

You have a lightweight spring whose unstretched length is 4.0 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 5.0 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 4.5 cm.

Homework Equations

F = kx, F = K((q1)(q2))/r^2

K = 8.988×109 N m^2 C^-2

The Attempt at a Solution

I will call the two beads q1 and q2.

First: I calculated the spring constant using the information from the hanging mass part of the question.

F = kx
(0.001 kg)(9.81 m/s^2)= k (0.01 m)
0.981 kg/s^2 = k

Second: Using the spring constant from the previous part I calculated the force needed to push the spring apart when the beads are on either end.

F = kx
F = (0.981 kg/s^2)(0.005 m)
F = 0.004905 kgm/s^2

Third: Using the force from above, and using coulombs law calculate the charges. I know that q1 and q2 are equal, q1 =q2 = q

F = K((q1)(q2))/r^2
0.004905 kgm/s^2 = ((8.988×109 Nm^2/C^2)(q1)(q2))/(0.045 m)^2

I am unsure of how to proceed from here, should I treat q1 and q2 as 2*q and solve from there? or not?

Thanks.

 

[mjsd]

nice solution, looks good to me. as u mentioned $$q_1=q_2 =q$$, so $$q_1 q_2 = q^2$$... what more do u need eh ?

 

[Canadian]

Thanks so much, sometimes I amaze myself at my stupidity . I was trying to treat q*q as 2q instead of q^2.