1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Electrostatic equilibrium between 3 styrofoam balls

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Three identical small Styrofoam balls (m = 1.95 g) are suspended from a fixed point by three nonconducting threads, each with a length of 52.1 cm and with negligible mass. At equilibrium the three balls form an equilateral triangle with sides of 28.3 cm. What is the common charge q carried by each ball?

    2. Relevant equations
    F = (k q1 q2) / r^2
    F = mg
    k = 9 * 10^9

    3. The attempt at a solution
    First I need to find the angle the string makes with the vertical, I start from one of the vertices and imagine a right triangle that connects with the midpoint of the equilateral triangle connecting the 3 balls. Given that I know from the corner of this right triangle will be 30 degrees, and that the adjacent side will be (28.3/2) cm, I calculate the hypotenuse to be 16.339 cm then I use this value to find the angle I want.

    θ = sin^-1 ( 16.339 / 52.1 )
    = 18.2768 degrees with vertical

    Now I can find F tension in the same plane as the electrostatic forces.

    Ft = mg tan 18.2768
    = 6.3179 * 10 ^(-3)

    This is equal in magnitude to the resultant vector of the two opposing electrostatic charges. I take the components of each electrostatic force with 30 degree angles to the resultant.

    resultant = kq^2 cos 30 /r^2 + kq^2 cos 30 / r^2

    6.3179 * 10^(-3) = kq^2 ( cos 30 + cos 30 ) / r^2
    q = 3.3168 * 10^(-7)

    CAPA says this is wrong, and I have no idea where I'm going wrong.


    EDIT: I solved it, it seems I was making a mistake somewhere with the vector part.
     
    Last edited: Feb 6, 2012
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted