Charged sphere hanging from a string-Find the charge?

[Hayliee30]

Charged sphere hanging from a string--Find the charge?

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 degrees with the y-axis when the sphere is in equilibrium, what is the charge on the sphere?


http://s1345.photobucket.com/editor...4-01-19at25516PM_zps9741502d.png.html?filters[media%5Ftype]=image&sort=3&o=0

I figured you could use the equation F=QE ---------> you're given E, and I think you have the information to find F?


I did the following:

Tcos30 = mg

T= mg/cos30--------> (.126 kg x 9.8)/cos30-------> T= 1.4258

So I assume T is the only force to consider..therefore:


F=QE

1.4258 = 151Q


Q= .00944 C

For some reason this answer isn't correct. So what am I doing wrong? I thought about multiplying the force side of the equation(1.4258) by sin30..however I don't see why I would do that. Anyways, can anyone help me?? I've been stuck on this problem all day! I greatly appreciate any help given.

 

[CAF123]

The sphere is in the vicinity of the electric field directed horizontally. This creates an electric force of magnitude qE on the sphere. For the sphere to be in equilibrium at angle θ, this force must be balanced.

 

[Hayliee30]

Right, I'm aware the force must be balanced. However, I believe I'm missing something. I have gravity and tension as forces; gravity acting straight down onto the sphere and Tcos30 in the +y direction. I'm assuming you incorporate the tension in the +x direction, as well, to put it into equilibrium, but I'm not sure how to do this. My guess would be Tsin30---> 1.4258(.5)= .7129. Then would I set up the equation 1.4258(.7129) = 151q? I'm still slightly confused.

 

[CAF123]

Yes, Tsinθ is the horizontal component of tension that would balance the electric force qE. The gravitational force balances the vertical component Tcosθ, as you said. From the analysis of the statics in the vertical direction, you can obtain T. Use this for the analysis in the horizontal direction to then get q.

I think this is what you were trying to do but the final equation you wrote is not correct, which may have been more obvious to you if you had used variables up to the point where you obtain an explicit expression for q.

 

[Hayliee30]

Oh okay, I understand now! Thank you so much for the help!