How to find a charge on a sphere in equilibrium?

[sphys4]

Homework Statement

A small, plastic sphere of mass m = 126 g is attached to a string as shown in the figure.

There is an electric field of 151 N/C directed along the + x axis. If the string makes an angle 30 with the y-axis when the sphere is in equilibrium, what is the charge on the sphere?

Homework Equations

The Attempt at a Solution

mg = 0.126kg * 9.81m/s^2 = 1.24 N

To make an angle of 30 degrees, the horizontal force must be 1.24 N * sin30 = 0.62 N

So then i did .62 N/151N/C = .0041 C or 4.1 mC which is the units they want, i entered it but this isn't correct.

Can someone tell me where i went wrong?

 

[vela]

The Attempt at a Solution

mg = 0.126kg * 9.81m/s^2 = 1.24 N

To make an angle of 30 degrees, the horizontal force must be 1.24 N * sin30 = 0.62 N

That's not correct.

So then i did .62 N/151N/C = .0041 C or 4.1 mC which is the units they want, i entered it but this isn't correct.

Can someone tell me where i went wrong?

Start by drawing the free-body diagram for the sphere.

 

[gdbb]

Don't forget about the string!

 

[sphys4]

How do i incorporate the string in?!

 

[vela]

The tension in the string exerts a force on the sphere, so it's another force in the free-body diagram.