How Do You Calculate the Charges on Two Spheres in Electrostatic Equilibrium?

[krnaudio]

Electrostatic forces helpp!

Homework Statement

Two spheres, each having a mass of 50.0 mg, are suspended from a common point by massless threads 50.0 cm long. One of the spheres have been given a charge twice that of the other. The strings make an angle of 6.00 degrees.
What are the charges on each of the spheres?

Homework Equations

F = k ((q1)(q2))/r^2

The Attempt at a Solution

Since the lengths of the strings on both sides are 50 cm, I drew an imaginary line between the two spheres. I found out that the other two angles had to be 87 degrees because both of the sides were equal. Then, I used law of cosines to find that the length between the spheres is 27.4 cm, which would be r in the equation. I also know that either q1 = 2q2 or q2 = 2q1, but I do not understand how I am supposed to use the masses of the spheres to find out the charge. Is there an equation that I'm missing here??

 

[tiny-tim]

Welcome to PF!

Homework Statement

Two spheres, each having a mass of 50.0 mg, are suspended from a common point by massless threads 50.0 cm long. One of the spheres have been given a charge twice that of the other. The strings make an angle of 6.00 degrees.
What are the charges on each of the spheres?

Hi krnaudio ! Welcome to PF!

There are three forces on each sphere … tension, gravity, and electric …

so make the vector sum zero (or draw a vector triangle )

 

[thomate1]

It seems that you are on the right track with your approach. You correctly identified the key equations and variables involved in this problem. To find the charges on each sphere, you will need to use the fact that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This means that by setting up and solving an equation with the given information, you can find the unknown charges.

One way to approach this problem is to first use the law of cosines to find the distance between the spheres, as you have done. Then, you can use the given angle and the distance between the spheres to find the force of electrostatic repulsion between them. This force must be equal to the weight of the spheres, since they are at equilibrium. From there, you can set up and solve an equation involving the charges and the known force and distance to find the charges on each sphere.

Another approach is to use the given information about the masses and lengths of the strings to find the net force on each sphere due to gravity. Then, by equating this force to the electrostatic force between the spheres, you can again set up and solve an equation to find the charges on each sphere.

In either case, it may be helpful to draw a free body diagram for each sphere to better visualize the forces acting on them. Keep in mind that the charges on each sphere will depend on the distance between them, so make sure to include this variable in your equations. I hope this helps guide you towards finding the solution to this problem.