Finding Magnitude of a Charge on Sphere

[cheerspens]

Homework Statement

Two small metallic spheres, each of mass 0.20 g, are suspended as pendulums by light strings from a common point as shown in the figure I attached. The spheres are given the same electric charge, and it is found that they come to equilibrium when each string is at an angle of 5.0 degrees with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere?

Homework Equations

Coulomb's Law

The Attempt at a Solution

I've drawn a force diagram for the first ball and I find that it's F_g=.00196, the tension, T, is .00197, and the Force of ball 2 on ball one, F₂₁, is 1.71x10_-4. When I plug into this equation: F=(k_e|q|)/(r²), I get 5.1x10^-9.

However, I know this is wrong because the correct answer is 7.2nC. How do I do this correctly?

 

[Tomer]

Notice that F = K * q * q / r^2...
Your formula lacks one q... Maybe that's where it fell? I'm too tired to make the calculation :)

 

[cheerspens]

Ok I've made sure that I account for both q's.
In order to solve this, do I have to break the vectors into components and set them equal to each other?

 

[Tomer]

Yes. It seems to me you did everything properly.
You get the tension from comparing the y-axis forces: Gravity and T*sin5.
Then by comparing the x-axis forces: T*cos5 = Kq^2 / r^2 you can isolate q.
notice that r = 0.3 * sin5 * 2.
It should work. If you still get the same answer, then the book's wrong...

 

[cheerspens]

I'm not sure if you took the time to actually solve it (I wouldn't blame you if you didn't) but for my final answer I got 6.88nC. If the book's answer is 7.2nC would it be safe to say this is accurate?

 

[Tomer]

I'm getting the book's answer after trying.

You get the equation:

0.00197 * sin5 = 9 * 10^9 * q^2 / (0.3*(sin5)*2)^2)

solving it leads to q = 7.22 nano C.