Two identical small insulating balls are suspended by separate 0.17 m threads that are attached to a common point on the ceiling. Each ball has a mass of 7.40 10-4 kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle of 26° between the threads.
To solve this problem, we can use Coulomb's Law to determine the charge on each ball.
Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:
F = k * (q1 * q2) / r^2
Where:
F is the electrostatic force between the charges
k is the electrostatic constant (k = 9 x 10^9 N*m^2/C^2)
q1 and q2 are the charges on the objects
r is the distance between the objects
In this case, since both balls have an identical positive charge, we can represent their charge as q.
The weight of each ball can be calculated using the formula:
Weight = mass * gravitational acceleration
Given that the mass of each ball is 7.40 x 10^-4 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of each ball.
Weight = (7.40 x 10^-4 kg) * (9.8 m/s^2)
Once we have the weight of each ball, we can equate it to the electrostatic force between the balls to solve for the charge.
Weight = F
Using Coulomb's Law, we can write the equation as:
(mass * gravitational acceleration) = k * (q^2) / r^2
Solving this equation for q, we can find the charge on each ball.
Now, we need to calculate the distance between the balls. Since they form an angle of 26° between the threads, we can consider the angle as the angle between the threads and the vertical direction. This means that the angle between the threads and the horizontal direction is 90° - 26° = 64°.
Using trigonometry, we can find the length of each thread (or the distance between the balls) using the equation:
r = length of thread * sin(angle)
Let's calculate the length of each thread:
r = (0.17 m) * sin(64°)
With the distance between the balls and the weight of each ball, we can now determine the charge on each ball using the equation derived from Coulomb's Law.
I will calculate the values for you.