How do I find Q without having a distance r?

[BuBbLeS01]

Charges...please help!

Homework Statement

Two 3.52 g point charges on 7.49-m-long threads repel each other after being equally charged. What is the charge q? (θ=31°.)

Homework Equations

F = KQQ/R^2

The Attempt at a Solution

How do I find Q without having a distance r?

 

[Doc Al]

How do I find Q without having a distance r?

You are given the thread length and the angle--use that to figure out the distance.

 

[BuBbLeS01]

Oh yea...so the length from the center to one of the masses is 3.858 m.
So I can do...
F = K*Q*Q/r^2
F = K*Q^2/ r^2
An wouldn't F = 0 since they cancel each other out?

 

[Doc Al]

Since the masses are in equilibrium, the net force on each is zero. What forces act on each mass?

 

[BuBbLeS01]

Tension

 

[Doc Al]

Tension

That's one force. List them all. (And draw yourself a free body diagram showing how the force act on each mass.)

 

[BuBbLeS01]

Tension and weight are the forces

 

[BuBbLeS01]

So do I include the electric force? Like...
T - W + Fel = 0

 

[Doc Al]

Tension and weight are the forces

Don't forget the electrostatic force!

 

[BuBbLeS01]

Isn't that Fel?

 

[Doc Al]

So do I include the electric force? Like...
T - W + Fel = 0

Yes, but realize that forces are vectors--direction counts. Set up two equations: One for the horizontal components, one for the vertical components. Combine these to solve for the charge.

 

[BuBbLeS01]

X.) TSINθ + qE = 0
y.) TCOSθ - mg = 0

T = mg/COSθ
mg/COSθ * SINθ + qE
q = -mg*TANθ/E

 

[Doc Al]

X.) TSINθ + qE = 0
y.) TCOSθ - mg = 0

I'd write that first equation as:
Tsinθ - qE = 0 (since the force components are in opposite directions)

Realize that E is also a function of q, so rewrite that in terms of k, q, and r (which you figured out).

Otherwise, you are on the right track.

 

[BuBbLeS01]

Okay so I end up with...
-q = -(mg*tanθ) / (kq/r^2)
q = (mg*tanθ) / (kq/r^2)
and the q's cancel?
= (mg*tanθ) / (k/r^2)

 

[Doc Al]

Okay so I end up with...
-q = -(mg*tanθ) / (kq/r^2)
q = (mg*tanθ) / (kq/r^2)
and the q's cancel?

The q's don't cancel. And when you divide by a fraction, simplify the result. (Invert and multiply.)