1. Jan 13, 2008

### 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???

2. Jan 13, 2008

### Staff: Mentor

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

3. Jan 13, 2008

### 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?

4. Jan 13, 2008

### Staff: Mentor

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

5. Jan 13, 2008

### BuBbLeS01

Tension

6. Jan 13, 2008

### Staff: Mentor

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

7. Jan 13, 2008

### BuBbLeS01

Tension and weight are the forces

8. Jan 13, 2008

### BuBbLeS01

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

9. Jan 13, 2008

### Staff: Mentor

Don't forget the electrostatic force!

10. Jan 13, 2008

### BuBbLeS01

Isn't that Fel?

11. Jan 13, 2008

### Staff: Mentor

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.

12. Jan 13, 2008

### BuBbLeS01

X.) TSINθ + qE = 0
y.) TCOSθ - mg = 0

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

13. Jan 13, 2008

### Staff: Mentor

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.

14. Jan 13, 2008

### 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)

15. Jan 13, 2008

### Staff: Mentor

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