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Charges please help

  1. Jan 13, 2008 #1
    Charges...please help!!

    1. The problem statement, all variables and given/known data

    [​IMG]

    Two 3.52 g point charges on 7.49-m-long threads repel each other after being equally charged. What is the charge q? (θ=31°.)


    2. Relevant equations
    F = KQQ/R^2


    3. The attempt at a solution
    How do I find Q without having a distance r???
     
  2. jcsd
  3. Jan 13, 2008 #2

    Doc Al

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    You are given the thread length and the angle--use that to figure out the distance.
     
  4. Jan 13, 2008 #3
    Oh yea...so the length from the center to one of the masses is 3.858 m.
    So I can do...
    F = K*Q*Q/r^2
    F = K*Q^2/ r^2
    An wouldn't F = 0 since they cancel each other out?
     
  5. Jan 13, 2008 #4

    Doc Al

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    Since the masses are in equilibrium, the net force on each is zero. What forces act on each mass?
     
  6. Jan 13, 2008 #5
    Tension
     
  7. Jan 13, 2008 #6

    Doc Al

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    That's one force. List them all. (And draw yourself a free body diagram showing how the force act on each mass.)
     
  8. Jan 13, 2008 #7
    Tension and weight are the forces
     
  9. Jan 13, 2008 #8
    So do I include the electric force? Like...
    T - W + Fel = 0
     
  10. Jan 13, 2008 #9

    Doc Al

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    Don't forget the electrostatic force!
     
  11. Jan 13, 2008 #10
    Isn't that Fel?
     
  12. Jan 13, 2008 #11

    Doc Al

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    Yes, but realize that forces are vectors--direction counts. Set up two equations: One for the horizontal components, one for the vertical components. Combine these to solve for the charge.
     
  13. Jan 13, 2008 #12
    X.) TSINθ + qE = 0
    y.) TCOSθ - mg = 0

    T = mg/COSθ
    mg/COSθ * SINθ + qE
    q = -mg*TANθ/E
     
  14. Jan 13, 2008 #13

    Doc Al

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    I'd write that first equation as:
    Tsinθ - qE = 0 (since the force components are in opposite directions)

    Realize that E is also a function of q, so rewrite that in terms of k, q, and r (which you figured out).

    Otherwise, you are on the right track.
     
  15. Jan 13, 2008 #14
    Okay so I end up with...
    -q = -(mg*tanθ) / (kq/r^2)
    q = (mg*tanθ) / (kq/r^2)
    and the q's cancel?
    = (mg*tanθ) / (k/r^2)
     
  16. Jan 13, 2008 #15

    Doc Al

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    The q's don't cancel. And when you divide by a fraction, simplify the result. (Invert and multiply.)
     
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