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Physics homework charges

Hi ^^! I was doing my physics homework and had a little trouble doing this one, so I was wondering if anyone could help me out if they had time. It would mean alot, but thanks anyway just for reading this ^_^!! I appreciate it =)

1. Homework Statement

Two spheres, each having a mass of 50 mg, are suspended from a common point by massless threads 50 cm long. One of the spheres has been given a charge twice that of the other. The strings make an angle of 6 degrees.

What are the charges on each of the spheres?
What kind of charge is on each sphere (+ or -)? Explain

2. Homework Equations
F = kq1q2/r^2
Q = Ne
F = ma
q_1 = 2q_2

3. The Attempt at a Solution

Well, assuming that the charges are not coming close together, they must be repelling each other. As such, I thought there must be some kind of acceleration... F = 2ma = 2(50 x 10^-6 kg)(9.8 m/s^2) = 9.8 x 10^-4 N
In addition, if I use sin6 = x/.5m, I can tell the distance separating the charges is .0523 m.
Now that I found the F, I plugged it into the first equation
9.8 x 10^-4 N = (9x10^9)(q_1)(q_2)/(.0523 m^2)
(q_1)(q_2) = 2.978 x 10^-16 C
2q_2^2 = 2.978 x 10^-16 C
q_2 = 1.22 x 10^-8 C
q_1 = 2q_2
q_1 = 2.44 x 10^-8 C

As for the kind of charge, I said that it is impossible to tell except that the must both be either positive or negative, not one and the other, because otherwise there would not be a 6* angle separating them.
 
Last edited:

Answers and Replies

^^;; Does anyone agree/disagree? I'm just a bit worried, because I usually dont understand how to do these kinds of problems even though I understand the equations individually.. I guess I have trouble combining two or more topics? At any rate, if possible,any direction on where I went wrong would be very helpful :). Thank you (even just for reading this!)
 
BobG
Science Advisor
Homework Helper
110
80
Force of gravity pulls the spheres straight down. The force on each sphere is its mass times gravity (i.e. - look at each sphere separately). The force from the charge pushes the spheres apart horizontally. The vector sum of the forces is enough to deflect each string 3 degrees - i.e - This statement is not true: 9.8 x 10^-4 N = (9x10^9)(q_1)(q_2)/(.0523 m^2)

By the way, you got lucky on the small angle. You don't have a right triangle with a 6 degree angle; you have two right triangles with a 3 degree angle. With angles that small, the difference is negligle, especially since you're using a rounded off value for k.
 
Oh, I see, I can set up a diagram with mg pointing down and F as the horizontal component. As such,
tan 3* = x / (50 x 10^-6)(9.8)

I solve for x as the force, and then the other equation I had before was right.. I just used the wrong force.

Thanks! :D
 

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