Finding Tension in String Connected to Electrically Repelled Sphere

In summary, the given system consists of two uniformly charged spheres suspended by strings of equal length from vertically adjustable supports. The spheres are in static equilibrium with angles of 14.9° and 20.7° with respect to the vertical. The tension in the string supporting sphere Z is 2.41E-5 N. Using equations for force components and setting them to zero, it is determined that the x-component of tension in each string is equivalent due to the electric force. However, the y-component can not be found without knowing the masses of the spheres. It is suggested that assuming the spheres are at the same height would simplify the question to equating horizontal tension components.
  • #1
velouria131
13
0

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.
 
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  • #2
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.
 
  • #3
apelling said:
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.
 
  • #4
But you have its x component Tx and an angle ∅ and Tx=Tcos∅
 
  • #5


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!
 

Related to Finding Tension in String Connected to Electrically Repelled Sphere

1. How does the electric charge of the sphere affect the tension in the string?

The electric charge of the sphere will create a repulsive force between the sphere and the string. This force will pull on the string, causing it to stretch and increase the tension.

2. What is the equation for calculating tension in a string connected to an electrically repelled sphere?

The equation for tension in a string connected to an electrically repelled sphere is T = k * q * Q / r^2, where T is the tension, k is the Coulomb's constant, q is the charge of the sphere, Q is the charge of the object the sphere is repelling, and r is the distance between the sphere and the object.

3. How does the distance between the sphere and the object affect the tension in the string?

The tension in the string is directly proportional to the distance between the sphere and the object. As the distance increases, the tension decreases, and vice versa.

4. Can the tension in the string be negative in this scenario?

No, the tension in the string cannot be negative. It is a physical force that always acts in the direction of the string, and a negative tension would imply that the string is being compressed rather than stretched.

5. How does the strength of the electric charge affect the tension in the string?

The strength of the electric charge has a direct impact on the tension in the string. The greater the charge of the sphere and the object, the stronger the repulsive force between them, and therefore, the higher the tension in the string.

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