(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two balls, each with a mass of 500 mg, are attached to the same point in the ceiling by strings with the length of 40 cm. The balls have been given equal and opposite charges, which caused them to separate in a way that the strings formed a 60-degree angle. Find the charges and the tension force in the string. Make a sketch.

The answers ought to be

q=~0,2*10^{-6}C

F_{t}=~0,0044 N

2. Relevant equations

F_{g}=mg

F_{C}=kq_{1}q_{2}/d^{2}

3. The attempt at a solution

http://desmond.imageshack.us/Himg513/scaled.php?server=513&filename=fdafdafa.png&res=medium [Broken]

An equilateral triangle is formed with the strings, so the distance between the balls is also

d=40cm=0,4m

Gravitational force on a ball

F_{g}=mg=~5*10^{-3}N (g=9,8 m/s^{2})

In order for equillibrium to be reached, the component vector of gravity, which is at a right angle with the string, must be equal to the component vector of Coulomb's force, which is also at a 90^{o}with the string.

That component vector of gravity is

F_{g1}=F_{g}*cos60^{o}=2,5*10^{-3}

So if F_{C}=kq_{1}q_{2}/d^{2}, then

F_{g1}=F_{C}*cos30^{o}, from which we get that

F_{C}=5*sqrt3*10^{-3}/3 N

and that

q_{1}=q_{2}=~0,2*10^{-6}C

So far it seemed to me that everything went correctly, but I dont get the tension force to be 0,0044 N. Using sines and cosines on F_{g}and F_{C}, or Pythagoran theorem for that matter, I got

F_{t}=F_{t1}+F_{t2}

F_{t1}=cos30^{o}*F_{g}=5*sqrt3*10^{-3}/2

F_{t2}=cos60^{o}*F_{C}=2,5*sqrt3*10^{-3}/3

F_{t}=~0,0058 N

Now I've seen many mistakes in answers in this textbook, but Im not so sure it's the textbook which has a fault in it this time. So please tell me, did I go wrong and where, or is the answer in the textbook once again wrong?

(I didnt mark up all the angles, but they should be pretty easy to figure out. If you dont understand some of my calculations or think they are wrong, be sure to shout out or ask!)

Thanks in advance

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# Homework Help: Coulomb's law problem

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