Two Insulated Balls: What is the length of each string?

[purduegirl]

Homework Statement

Two insulated balls of mass 0.1 g hang from the same support point by massless insulating threads of length l (as shown in the diagram below. A total positive charge of 8.25 × 10-7 C is added to the system. Half this charge is taken up by each ball, distributed uniformly, and the balls spread apart to a new equilibrium position.

If θ=39.5°, what is the length, l, of each string?

Homework Equations

Pythagorean theroem
Sine

The Attempt at a Solution

With this problem, I know that I need the x components to find l. I think this would be - Force + Tension(sin 39.5)

 

[dotman]

Yeah, you know a couple of things here; you know you have some balls with some mass that then of course having a gravitational force act on them; and you have some balls with some charge that will have an electrostatic force on each other.

Can you write some equations down describing the gravitational force and the electrostatic force? Where does the quantity l end up in these equations? Can you solve for it?

Can you describe in words what's going on here?

 

[Moetasim]

= 0.

However, I am not sure how to proceed from there without knowing the force or tension values.

As a scientist, my response would be that in order to accurately determine the length of each string, we need to know the values for force and tension in the system. Without this information, it is not possible to calculate the length of the strings using the given angle and charge values. I would suggest conducting further experiments or providing more information in order to solve the problem accurately.