Charges...please help!!

BuBbLeS01

1. The problem statement, all variables and given/known data



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°.)


2. Relevant equations
F = KQQ/R^2


3. The attempt at a solution
How do I find Q without having a distance r???

Doc Al

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

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

Don't forget the electrostatic force!

BuBbLeS01

Isn't that Fel?

Doc Al

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

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

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