Spring and electrostatic forces

[Krique]

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

The Attempt at a Solution

When the spring is hanging from the ceiling, it has no acceleration. And since it is lightweight, I assume that the mass of the spring does not matter. The only forces acting on the spring while hanging are the weight of the block and the force of the spring, which should cancel out. So (mass)(gravity) = -kx. We are given that the unstretched length is 4 cm, so we know that x = .01 m. The mass is 1g, and gravity is always -9.81 m/s^2. We can then solve for k. I got 981 N/m.

Now that I have the spring constant, I solved for the charges. When it is on the table, the only forces acting on the spring in the horizontal direction are the charges and the spring, which cancel each other out. So K (Q1*Q2)/r^2 = -kx. In this case, x is .005 m and r is .045 m. k is the same as before, 981. Q1 is equal to Q2 because they have the same charge. I assume K to be 8.99*10^9 because that is what all of our homework assignments have been using.

Solving for Q1^2, I got -1.105*10^-12. This makes Q1 and Q2 non real answers. If I drop the negative, they are 1.05*10^-6 C, which is also incorrect. Any ideas where I am going wrong?

 

[nvn]

Krique: The mass is 0.001 kg, not 1. Try it again and see if this makes your answer correct. In both of your equations, change -k*x to k*x. And change g = -9.81 m/s^2 to 9.81 m/s^2. Your ke value in Coulomb's law is correct; ke = 8.9876e9 (N*m^2)/C^2.

 

[Krique]

Oh man, I feel dumb for missing that. Thanks :)