Hanging Charges Homework: Finding Charge on Suspended Spheres

[ninetyfour]

Homework Statement

There are two of the exact same masses with mass 2.0g and are attached to the ends of an insulating thread that is 0.6m in length. The two spheres are suspended by a hook in the ceiling from the centre of the thread, and the spheres are given identical electric charges and hang in static equilibreum, with an angle of 30 degrees between the string halves. What is the magnitude of the charge on each sphere.

Homework Equations

Fe = K(q1)(q2) / d^2
K = 9.0 E 9 N(m^2) / C^2

The Attempt at a Solution

Alright, so it tried the question, and my answer was 2.4 E -7 C...that is double the value of the actual answer which is 1.2 E -7 C. Where did I go wrong? D:

Here's my work:
(I took one sphere and drew an FBD).
(T is tension in the rope)

Fe = Tsin15
mg = Tcos15
T = mg / cos15
T = (0.0020)(9.8) / cos15
T = 0.020291413 N

Fe = 0.005251804 N = (9.0 E 9) (q^2) / (0.6sin15(2))^2
q = 2.4 E -7 C

:S

 

[collinsmark]

Here's my work:
(I took one sphere and drew an FBD).
(T is tension in the rope)

Fe = Tsin15
mg = Tcos15
T = mg / cos15
T = (0.0020)(9.8) / cos15
T = 0.020291413 N

Fe = 0.005251804 N = (9.0 E 9) (q^2) / (0.6sin15(2))^2

It seems that you either accidentally took the factor of 2 twice (in the distance between the spheres), or forgot that the distance from each ball to the hook on the ceiling is only half the total length of the thread.

In other words, the total length of the string is 0.6 m. So the length from each ball to the hook on the ceiling is half that, which is 0.3 m.