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 and there is a 90 degree angle at 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
What do you mean a 90 degree angle at sphere B? Ninety degrees between what and what? I assume the 12 degrees is measured between A and B.
It very simple, you must study hard much if you look for wanting better marks in you're physics, you know good
To solve this problem, let's break it down step by step.
Step 1: Determine the force of gravity acting on sphere A.
The force of gravity acting on sphere A can be calculated using the formula F = mg, where m is the mass of the sphere and g is the acceleration due to gravity. In this case, the mass of sphere A is 0.10 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the force of gravity on sphere A is F = (0.10 kg)(9.8 m/s^2) = 0.98 N.
Step 2: Calculate the tension in the wire.
The tension in the wire can be found using the formula T = mg + F_e, where T is the tension, m is the mass, g is the acceleration due to gravity, and F_e is the electrostatic force. In this case, the tension equals the force of gravity because there is no electrostatic force acting on the sphere initially. So, T = 0.98 N.
Step 3: Calculate the electrostatic force between the spheres.
The electrostatic force between the spheres can be calculated using the formula F_e = k(q1*q2)/(r^2), where k is the Coulomb's constant, q1 and q2 are the charges on the spheres, and r is the distance between the centers of the spheres. In this case, we are given that sphere B has charge -q, and there is an angle of 12 degrees between the two spheres. We can use trigonometry to find the distance between the centers of the spheres. The vertical distance between the two spheres is 2 m, and the horizontal distance is given by d = 2 m * tan(12 degrees). Thus, the distance between the center of sphere B and the vertical line passing through sphere A is approximately d = 0.418 m. The total distance between the centers of the spheres is r = 2m + d = 2.418 m.
Step 4: Solve for the initial charge on sphere B.
Now we have all the information we need to calculate the initial charge on sphere B. First, let's rearrange the formula for the electrostatic force to solve for q2: q2 = (F_e * r^2) / (k * q1). Plugging in the known values, we get q2 = (T * r^2) / (k * q1). As mentioned in the problem, when the two spheres are brought into contact, 1/2 of the charge is transferred. So, the initial charge on sphere B is q2_initial = (T * r^2) / (2 * k * q1). Plugging in the values, we have q2_initial = (0.98 N * (2.418 m)^2) / (2 * (9.0 x 10^9 N m^2/C^2) * q1). We are asked to find q2_initial, so we'll need to know the value of q1.
At this point, we need information about the initial charge on sphere A to calculate the initial charge on sphere B. The problem does not provide this information, so we cannot proceed further to calculate the initial charge on sphere B.
Therefore, without knowing the initial charge on sphere A, we cannot determine the initial charge on sphere B.