Finding Tension in String Connected to Electrically Repelled Sphere

[velouria131]

Homework Statement

Two uniformly charged spheres are suspended by strings of length L from vertically adjustable supports. The spheres are in static equilibrium.

The angles with respect to the vertical are Q=14.9°, and T=20.7°.

The tension in the string supporting sphere Z (Z with respect to angle T, W is the other sphere and hangs with respect to angle Q) is 2.41E-5 N. Calculate the tension in the other string.

Homework Equations

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

Fg = mg

The Attempt at a Solution

Alright, here is a brief overview of what I have done. I first recognized that the system was in static equilibrium. Thus, for each sphere I wrote equations representing the force components, and set each equation to zero. Each sphere operates under the same conditions.

Sphere Z lies to the left (T is force due to tension, Fe is force due to Electric repulsion)

Tx = Tcos∅
Ty = Tsin∅
T = 2.41E-5 N

0 = Tx - Fe
0 = Ty - mg

Sphere W lies to the right:

Tx = Tcostheta
Ty = Tsintheta

0 = -Tx + Fe
0 = Ty - mg

So, I recognize that in each case, the x-component of the tension in each string is equivalent. This makes sense because the forces on each sphere with respect to the x-axis are due to the electric force. This force has an equal and opposite effect. I cannot figure out how to find the total tension in the second string, even though I know the x component etc. Any help in progressing from this point would be greatly appreciated.

 

[apelling]

The question states that the spheres are on vertically adjustable supports. Are we allowed to assume that the spheres are at the same height, because this would simplify the question to equating horizontal tension components.

 

[velouria131]

The question states that the spheres are on vertically adjustable supports. Are we allowed to assume that the spheres are at the same height, because this would simplify the question to equating horizontal tension components.

Yes, absolutely. There is a diagram I can include if that is needed. The horizontal components are equivalent. However, the masses are not given, so I haven't a clue how to find the y component of the tension in the second string.

 

[apelling]

But you have its x component Tx and an angle ∅ and Tx=Tcos∅

 

[Nickie]

I would first check if my equations and assumptions are correct. It seems like you have correctly identified the forces acting on each sphere and set them equal to zero in the x and y directions. However, I would double check if the electric force equation is correct and if the angles and signs are properly accounted for.

Once you have confirmed that your equations are correct, you can solve for the unknown variables using simultaneous equations. In this case, you have two unknowns (the tension in the second string and the electric force) and two equations (one for each sphere). Solving these equations simultaneously will give you the values for both unknowns.

Alternatively, you can also use the total tension equation for each sphere, which takes into account both the x and y components of the tension and set it equal to the weight of the sphere. This will give you a single equation with one unknown (the tension in the second string).

Overall, it seems like you have a good understanding of the problem and have made good progress. I would recommend double checking your equations and using simultaneous equations or the total tension equation to solve for the unknown variables. Good luck!