2 suspended balls with charge q. find q

[Kastner86]

Homework Statement

Two Styrofoam balls with the same mass m = 7E-8 kg and the same positive charge q are suspended from the same point by insulating threads of length L = 0.92 m. The separation of the balls is d = 0.024 m. What is the charge q?

I am unable to add a graphic at this time. But i understand this is a common electrophysics problem, i think the problem describes it pretty well.

Homework Equations

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

The Attempt at a Solution

One thing I will do first is find the value "h", the vertical distance between 1/2d and the ceiling (essentially completing the triangle)

Well I wasn't exactly sure where to start, and that may be part of the problem, so here is the thought process, I hope you can follow.

I know Fnet = 0 Fy = 0 Fx = 0

I know to get q i need to find F from each charge.

(note: FTy represents the Tension Force from the string in the y direction.)

So Fy = -mg + FTy = 0 so mg = FTy

How do find FTy? I understand it is a component of FT. would it be FTy = FT x (h/L) ??

So Fy = -mg + FT x (h/L) and from this i could get FT? is that correct?

If this is correct, I can also find FTx.

FTx = FT x (1/2d)/L

And Fx should = (FT x (1/2d)/L) - (k*q1*q2)/d^2

Since Fx = 0 i can set the above equation to 0 and solve for q??

This is what I tried to do anyways, does this make sense?

Any input is appreciated!

 

[rl.bhat]

Your approach is correct.
FTy = mg.....(1)
FTx = k*q1*q2/d^2...(2)
Substitute the values of FTx and FTy, then divide eq.(1) by eq.(2). From that you get the value of q.

 

[tomcue]

I would approach this problem by first identifying the relevant equations and variables involved. The given information includes the mass of the balls, the length and separation of the strings, and the force of gravity acting on the balls. The relevant equation for this situation is the Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. We can express this mathematically as F = (k*q1*q2)/r^2, where F is the force, k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.

To find the charge q, we can use the fact that the net force on the balls is zero, since they are suspended in equilibrium. This means that the force from the strings must be equal and opposite to the force from the charges. Using this information, we can set up the following equations:

Fy = -mg + FTy = 0 (since Fy = 0)

Fx = (FTx + Fdx) - (k*q1*q2)/d^2 = 0 (since Fx = 0)

where FTy and FTx are the tension forces in the y and x directions, respectively, and Fdx is the force of gravity in the x direction.

We can solve for FTy and FTx using trigonometry, as you have suggested. FTy = FT x (h/L) and FTx = FT x (1/2d)/L. Substituting these values into the equations above, we can solve for Fdx and then for q.

Finally, it is important to note that the value of q will depend on the value of k, which is a constant in the Coulomb's Law equation. Therefore, you will need to know the value of k in order to find the exact value of q. I hope this explanation helps you to better understand the problem and how to approach it.