No values are given, so analytically I suppose. But I get the feeling this spits out a very ugly equation if I do it exactly..
So maybe the answer to this question just is "For a θ which satisfies this equation, the distance is given by r = d + 2Lsinθ"?
Or, maybe, if I assume θ is small, I can...
What I assume is L,d,q and m are given. (d being the distance between the fixpoints of the two ropes). I then have to solve for the distance r between the centers of the spheres (which can be found by finding θ.)
Using this diagram, I get the conditions:
|Fel|= q²/(4π*ε*r²) = |T|sin(θ)
|Fg| = mg = |T|cos(θ)
And I'm stuck here: how do I find r (or θ?) from this?
Edit : Dividing top by bottom I get : tanθ = q²/(4π*ε*r²*m*g)
I can write r = d + 2Lsin(θ) -> r² = d²+4dLsinθ + 4L²sin²(θ)
If I denote...
The charges are equal, so the electrical forces act 'outwards', right?
I got that last equation by fiddling a bit, I'm not too sure how to find the rope tension force..
First of all, hey everyone.
I was wondering if any of you could help me solve this. I've tried but i keep getting insane equations so I might be doing something wrong.
Two equal spheres with a mass of m have equal charges q. They're suspended by two ropes with length L in points distanced d...