Original Question:
Neutral metal sphere A, of mass 0.10kg, hangs from an insulating wire 2.0m long. An identical metal sphere B, with charge -q is brought into contact with sphere A. Sphere A goes 12 degrees away from Sphere B. Calculate the initial charge on Sphere B.
Note: when one object with charge Q is brought in contact with a neutral object 1/2 the charge is transferred to the neutral object.
I don't understand how to do this.
Ans: 3.9x10^-6C
Posted by drwls:
After the spheres touch, each one acquires a charge of -q/2, and the Coulomb repulsion force pushes them away from each other. If each one hangs inclined A = 12 degrees, and T is the tension in the wire,
T cos A = M g
T sin A = k (Q/2)^2/(2L sinA)^2
k is the Coulomb constant, 8.99 x 10^9 N�m^2/C^2
2L sin A is the separation of the spheres
T can be eliminated by dividind one equation by the other
tan A = k (Q/2)^2/(2L sinA)^2/(Mg)
M g tan A = k Q^2/(16 L sin A)^2
This should let you solve for Q
Question - I don't understand what Mg is supposed to be. Also how did you get 16? and on the right side? Is that supposed to be the tension?
I found the distance between A and B to be 0.4158. Can you please explain the rest? I'm not getting the right answer.
In the given problem, Mg refers to the weight of sphere A. "M" represents the mass of sphere A and "g" stands for the acceleration due to gravity.
The number 16 comes from squaring the term 2L sin A present in the denominator. This is due to the inverse square relationship of the Coulomb force. When calculating the magnitude of the force between two charges, you need to square the distance between them. Therefore, the term (2L sin A)^2 appears in the equation.
On the right side of the equation, "k" represents the Coulomb constant and "Q" is the charge on sphere B. This equation represents the Coulomb repulsion force between the two spheres.
Now, to solve for the initial charge on sphere B (Q), you need to rearrange the equation. Here's a step-by-step breakdown:
1. Start with the equation: M g tan A = (k Q^2) / (16 L sin A)^2
2. Multiply both sides of the equation by (16 L sin A)^2:
M g (16 L sin A)^2 * tan A = k Q^2
3. Take the square root of both sides of the equation:
Q = √[M g (16 L sin A)^2 * tan A / k]
To simplify things, you can substitute the given values into the equation and calculate the result. The mass of sphere A (M) is 0.10 kg, the acceleration due to gravity (g) is 9.8 m/s^2, the length of the wire (L) is 2.0 m, the angle of inclination (A) is 12 degrees, and the Coulomb constant (k) is 8.99 x 10^9 N·m^2/C^2.
After plugging in these values, you should get the initial charge on sphere B, which is 3.9x10^-6 C.