The two small spheres each with mass m= 25g are hung by silk threads length L=.65m from a common point. When the spheres are given positive charge such that q1=2q2, each thread hangs stationary at theta=15 degrees from the vertical. Using Newton's first law and coulomb's law, find the values of q1 and q2. I know how to use newtons first law but I'm confused on how to put that into coulomb's law.

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  1. no change in momentum on system means no net force on system. Force on left charge same as on right charge but opposite direction so total on system is zero.
    Horizontal electrical force on each
    Fe= k Q1 Q2 / d^2
    let x = d/2 = distance from center line
    sin 15 = x/.65
    x = .168 meters from center line
    d = .336 meters apart

    now gravity
    T = Tension in string
    T cos 15 = m g
    T = .025*9.81/cos15 = .254 Newtons
    horizontal force component = T sin 15 = .0657 Newtons
    .0675 = k Q1Q2 /.336^2
    calculate Q1Q2
    q2 * 2 q2 = Q1Q2
    2 q2^2= Q1Q2
    q2 = sqrt (Q1Q2/2)
    and of course
    q1 = 2 q2

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