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Homework Help: Hanging charged spheres

  1. Aug 16, 2014 #1
    1. The problem statement, all variables and given/known data[]

    Two spheres each of 5g, tied to 1.0m strings, repel each other after being charged to +91nC of the two spheres . What is the angle θ they form with the vertical after repulsion

    2. Relevant equations

    (1) F = mg....m=5.0g, g= 9.8m/s^2
    (2) F = Kq1q2/r^2 .....q1=q2=q=+91nC, r = distance of separation after repulsion= ?,K = electrostatic constant = 9.0 x10^9 Nm^2/C^2
    (3) sin θ= opp /hyp....opp = r/2, hyp = 1.0m, θ = angle with the vertical axis = ?
    (4) ∑Fx = 0
    (5) ∑Fy = 0
    3. The attempt at a solution
    I need to find the distance of separation (r) after repulsion, so I can solve for θ using the sin θ equation (3).I did the sum of the horizontal and vertical forces, using equation (4 & 5), substituted T =mg/cosθ,(obtained from the summation of vertical forces equation) in the horizontal forces equation (4) to eliminate the unknown T (tension in the string) but I get stuck with two unknowns r and θ
    Last edited: Aug 16, 2014
  2. jcsd
  3. Aug 16, 2014 #2


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    Gold Member

    If I understand the set up correctly, write (3) like r = 2 sin θ and use this in your ∑Fx=0 equation together with T = mg/cosθ to leave only θ.
  4. Aug 18, 2014 #3
    @CAF123....Aaah but yes of course thank you!!!
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