Electrostatic Equillibrium Question

vg19

Hey,

Here is my question:
Three identical small Styrofoam balls (m = 2.05 g) are suspended from a fixed point by three nonconducting threads, each with a length of 45.5 cm and with negligible mass. At equilibrium the three balls form an equilateral triangle with sides of 28.4 cm. What is the common charge q carried by each ball?

This is what I have done.

I made my diagram 3d and did a FBD for 1 ball (Tension up and at an angle, mg going down, and Fe going to the left) As a result, solving for the Forces in the x-direction I had
Ftcos60 = Fe
and solving in the y direction
Ftsin60 = mg

I divided EFy by EFx to get rid of the tension force and then solved for Fe. I then put that into the coulomb law equation and made both q charges the same so it was q^2 and solved for q. I am not getting the right answer though. I think my assumption of the angles being 60 may be wrong. Can anybody help out?

Thanks

Tide

The angle that the strings make with the vertical is not 60 degrees (nor is it 30 degrees!).

You're going to have to do some geometry to figure out the angle but it is simplified by noting the triangle with vertices at each of the charges is equilateral and the triangles with the vertices at the support and pairs of points is isosceles. It may also help to note that the center of the equilateral triangles is located 1/3 of the way from the base to the opposite vertex.

vg19

I tried using the cosine law, and for the isosoleces triangle I am getting a top angle of 36.4degrees and the two bottom ones as 71.8degrees, but I am still not getting the right answer...Am I still doing something wrong?

Tide

What you are looking for is not the angle between a pair of strings but the angle between the vertical and a string.

vg19

So would I just divide the 36.4 by 2?

Tide

The easiest way to do the geometry is to first find the radius of a circle in which the equilateral triangle can be inscribed. Then you can find the angle the string makes with the vertical using the ratio of that radius to the length of the string.