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## Homework Statement

An object with a small mass (m) causes two balloons to float (neither ascending nor descending) in the air at a fixed distance from each other, as shown in the diagram. The balloons, with a volume (V) each carry a positive charge, Q. The balloons are said to be point charges, and their mass is not considered.

1. Create a diagram of all the forces at work.

2. Give a literal expression for the angle θ according to m, g, p, and V (study the condition of flotation, and do not consider Archimede's Principle exercised on the mass (m)).

3. By supposing that m=10g, L=1.5m, and d=30cm, calculate Q.

## Homework Equations

Coulomb's Law: F=[itex]\frac{k|qQ|}{r^{2}}[/itex]

Gravitational Force: F=[itex]\frac{GmM}{r^{2}}[/itex]

Tension Force: F=Fgrav-ma

## The Attempt at a Solution

First off, my knowledge of physics is very elementary. Before this class, I had

**never**taken a physics course and the last math course I had was very basic. As I'm studying in Switzerland, I unfortunately don't have the option of taking an introductory course at university, and was therefore placed directly in this class, which I think is rather advanced physics. It's a lecture style course without step-by-step problem solving, and little to no explanation. Students are expected to already have a solid background and be able to follow along. As you can imagine, I'm rather lost. I need very clear, precise and elementary explications: i.e as you would give to a child, because this is honestly not my strong suit. I don't have a strong mathematical background either, so again, easy, clear explanations (when possible) are best. I apologize if the question is worded rather strangely; it was translated from my homework which is in French, so if something seems unclear, I will do my best to explain it.

1. For the drawing of the diagram, and the figure from the problem, please see the attached photo.

3. I attempted to solve #3 first as I'm really unsure of how to go about solving #2. Considering the diagram, I tried to calculate the gravitational force, and the tension forces. I believe that because the balloons are at equilibrium, one can assume that these two forces cancel each other out, but I'm not sure about that given that the string creates an angle and is not perpendicular to the gravitational force. From that I would assume then that the only force acting upon the sphere is the electric force. But with the angles coming into play, I'm really thrown off. I attempted to calculate the electrical force acting on the balloon and got 1.0x10[itex]^{9}[/itex] N/C[itex]^{2}[/itex], but I'm pretty sure this is a huge number and therefore doesn't seem possible.

I apologize if there's really no sense in my calculations. I'm trying my best to comprehend this, but I seem to be missing quite a lot.

Any help is greatly appreciated! Thank you!