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Introductory Physics Homework Help
Three hanging balls of uniformly distributed charge
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[QUOTE="derravaragh, post: 4493189, member: 458047"] [h2]Homework Statement [/h2] Three identical small balls of mass m with uniformly distributed charge Q each hang from a string of length L. The strings are all tethered at the opposite end at the same point. (a) Find the general equation for the angle θ of each string from vertical. [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] I started off by drawing a free body diagram, obtaining a Tension in both the x and y directions, a downward force (m*g) and a horizontal force away in the x-direction (the force due to the other charges). I then collected the Forces for the x and y directions: F[SUB]y[/SUB] = Tcos(θ) - mg = 0 F[SUB]x[/SUB] = Tsin(θ) - Q[SUP]2[/SUP]/(3*L[SUP]2[/SUP]*sin[SUP]2[/SUP](θ)) Using F[SUB]y[/SUB] I solve for T to be mg/cos(θ) and plug it in for T in F[SUB]x[/SUB]. However, a problem arises when I try to solve for θ, I end up with: tan(θ)sin[SUP]2[/SUP](θ) = Q[SUP]2[/SUP]/(3L[SUP]2[/SUP]mg) I do not know how to solve this for θ, and when re-evaluating my work, I feel my value for the distance between balls in the force due to a charge is incorrect. The balls make a triangle, and with the invisible line down the center, you can divide that triangle into three even 30-30-120 triangles. I determined the distance between one ball and the center to be Lsin(θ), and using the Law of Sines, determined r (the distance between two balls) to be: r = √(3)*L*sin(θ) If this is correct, I'm not sure where I went wrong. Any hints would be appreciated. Thanks. [/QUOTE]
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Three hanging balls of uniformly distributed charge
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