Calculating Angle and Distance of Separation for Repelling Charged Spheres

[madonset@eskom]

1. Homework Statement []

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

Homework 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

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

 

[CAF123]

If I understand the set up correctly, write (3) like r = 2 sin θ and use this in your ∑F_x=0 equation together with T = mg/cosθ to leave only θ.

 

[madonset@eskom]

@CAF123...Aaah but yes of course thank you!