How to Find the Electric Force Between Two Charged Spheres?

[germx3]

Homework Statement

Two small spheres with mass m = 14.3 are hung by silk threads of length L = 1.26 from a common point. When the spheres are given equal charges, so that , each thread hangs at an angle $$\theta$$ = 22.0 from the vertical.

A. Draw a diagram showing forces on the left sphere.
B. Find the magnitude of q.

Homework Equations

F_e = k |q₁||q₂| / r²

The Attempt at a Solution

Part A.
I drew three forces on the left sphere. I have the force of gravity, pointing straight down from the shpere. The tension force point along the length of the thread, away from the shpere. And the Electron force pointing directly to the left. I drew the F_e pointing away because I figured both spheres have the same charge since they are being repelled apart. This answer is wrong but I am not sure why.

Part B.
I used the sum of forces.

F_x = T_x - mg = 0
T_x = mg = 0.140

F_y = T_y - F_e = 0
T_y = F_e

I calculated T_y = 1.17
Using that I found q

1.17 = kq² / (0.944)²
q = 1.08 * 10^-5

This was also wrong.

Any help will be appreciated. Thank You.

 

[rock.freak667]

Split the tension into its vertical and horizontal components.

T_y-mg=0 ! not T_x

Just remember how to split the tension,T, into its vertical and horizontal components.

also how did you get 0.994 as the distance between the spheres?

 

[germx3]

Sorry about that. I meant T_y but it got lost in translation from paper to computer.

I found r by using 1.26 * sin(22) = .0472. That was half the distance to one sphere so I mutliplied by 2.