Electromagnetism - Infinite plane of charge & Tension

[thejuanestevez]

TL;DR Summary: Ping-pong ball hanging static from infinite plane of charge and a string

Really struggling with this question. I'm not sure if I have set up the free body diagram correctly and don't know how to set up the x and y components

 

[Orodruin]

You setup looks fine. Now solve the system of equations.

There are perhaps ways of setting up the problem that make the solution easier, but we can discuss those once you have solved it.

 

[TSny]

I agree with @Orodruin that your diagrams are correct. Nicely drawn!

However, your two force equations are not correct. Check these.

 

[thejuanestevez]

I agree with @Orodruin that your diagrams are correct. Nicely drawn!

However, your two force equations are not correct. Check these.

Would this be correct:
Fx: T cos(10) = Fe cos(60)
Fy: T sin(10) = Fg + Fe sin(60)

 

[TSny]

Would this be correct:
Fx: T cos(10) = Fe cos(60)
Fy: T sin(10) = Fg + Fe sin(60)

The first equation looks good. The second equation has a sign error.

 

[thejuanestevez]

The first equation looks good. The second equation has a sign error.

Is it T sin(10) = Fe sin(60) - Fg ?

 

[TSny]

Is it T sin(10) = Fe sin(60) - Fg ?

No. What is your reasoning behind setting up the two equations?

 

[thejuanestevez]

No. What is your reasoning behind setting up the two equations?

I need to find Fe so that I can use it to find the charge of the of the ping pong ball. Fe is the force pushing the ball away, Fg and T are holding it static. So that should mean that T + Fg = Fe?

 

[TSny]

I need to find Fe so that I can use it to find the charge of the of the ping pong ball. Fe is the force pushing the ball away, Fg and T are holding it static. So that should mean that T + Fg = Fe?

You are working with vectors. For static equilibrium, the net force must equal zero. So, the vector sum of the forces must equal zero. This means that the x-components of all the forces must add to zero and the y-components of the forces must add to zero:

$T_x + Fe_x + Fg_x= 0$
$T_y + Fe_y + Fg_y = 0$

You just need to fill in the correct expressions for each of the terms being careful with signs.

 

[Orodruin]

Let me just add that splitting into components is not the way I would handle this particular problem. Even if I chose that route I would have chosen different directions to study the components in.