Charge on two suspended metal balls

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SUMMARY

The discussion centers on calculating the charge on two suspended metal-coated foam spheres, each with a mass of 2.80x10^-6 kg, that are hung from nylon threads 45 cm long and given equal negative charges. The spheres create an angle of 15 degrees with the vertical, leading to a misunderstanding of the geometry involved, as the configuration is an isosceles triangle rather than an equilateral triangle. The correct approach involves resolving forces in both x and y directions and utilizing the formula Q=√((Fr^2)/k) with k=9x10^9 N m²/C². The final charge calculated should be 6.66x10^-9 C, highlighting the importance of accurate geometric interpretation and force resolution in electrostatic problems.

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Homework Statement


Two very small metal coated foam spheres, each of mass 2.80x10^-6kg, are attached to nylon threads 45cm long and hung from a common point. When the spheres are given equal quantities of negative charge, each supporting thread makes an angle of 15 degrees with the vertical. Find the charge on each sphere.


Homework Equations


F=(kQ1Q2)/r^2 in the form of Q=√((Fr^2)/k) as Q1 and Q2 will be the same.
F=ma
probably Pythagoras and sine/tangent/cosine ratios


The Attempt at a Solution


ok, so r or the distance between the charges was pretty obvious. If the strings are 0.45m long and the angle at the point where the strings combine is 30° (2x15°), then its going to be an equilateral triangle so r=0.45m (I think). I suppose we are assuming k=9X10^9. Noe for the force. The force of gravity will be 2.80x10^-6x9.8 (F=ma), which equals approximately 2.7x10^-7. I then did (2.7x10^-7)/tan(90-15), which equals about 7.4x10^-8. I thought that equaled half the force of repulsion of the sphere, but I'm not sure. If that's right then the total force of repulsion is 1.5x10^-7. So then
Q=√((1.5X10^-7x0.45^2)/9x10^9). That equaled 1.8X10^-9. But the actual answer is 6.66X10^-9. I know my rounding is having quite and effect on it, so i did it again, using as many decimals as I could but I was still quite a bit off. What am I doing wrong?
 
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An equilateral triangle has angles of 60° - this one has a top angle of 30°.
 
oh wow, oopsies!
 
I don't really understand your solution attempt here.
Start by drawing a free-body diagram for one of the charges and resolve the forces along the x and y directions.
You should be able to eliminate the tension leaving only 1 unknown ( the charge ).
 
crowdedscience said:

Homework Statement


... angle at the point where the strings combine is 30° (2x15°), then its going to be an equilateral triangle so r=0.45m
First and foremost, when did you learn that an equilateral triangle has an angle 30°? It's not an equilateral triangle!
This one will be isosceles!
Next why are you taking the weight as it is? Take its horizontal components!
Then I don't get why you are dividing by tan75°. Could you explain that?
 
Rookie mistake. You are unworthy of this forum. Next time go to yahoo answers...
 

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