There are two pit balls equally charged and each with a mass of 1.5g. While one ball is suspended by a thread, the other is brought close to it and state of equilibrium is reached. In that situation,the two balls are separated by 2.6cm and the thread attached to the suspended ball makes an angle of 20 degrees with the vertical. Calculate the charge on each the pith balls.

draw the vector diagram, mg donward, horizontal force=kqq/.026^2

tan 20= mg/(kqq/.026^2)
you know mass m, g, k, solve for q.

To calculate the charges on the pit balls, we can use the principle of electrostatic equilibrium. In this situation, the electrostatic force of attraction between the balls is balanced by the tension in the thread.

Let's denote the charge on each ball as q, and the tension in the thread as T.

Step 1: Start by finding the tension T in the thread.
Since the thread makes an angle of 20 degrees with the vertical, we can resolve the tension into two components - one along the vertical direction (T cos 20°) and the other along the horizontal direction (T sin 20°).

Step 2: Calculate the electrostatic force of attraction between the balls.
The electrostatic force between two charged objects can be calculated using Coulomb's law. The formula is F = k * |q1 * q2| / r^2, where F is the electrostatic force, k is the electrostatic constant, q1 and q2 are the charges on the objects, and r is the distance between them.

In this case, the distance between the balls is given as 2.6 cm, which is equivalent to 0.026 m.

Step 3: Set up the equations for equilibrium.
Equilibrium means that the forces in both the vertical and horizontal directions are balanced.
In the vertical direction:
T * cos 20° = mg
In the horizontal direction:
F = T * sin 20°

Step 4: Substitute the expressions for the tension T and force F into the equilibrium equations.
From the vertical equilibrium equation:
T = mg / cos 20°

From the horizontal equilibrium equation:
(k * q^2) / r^2 = (mg / cos 20°) * sin 20°

Step 5: Substitute the given values and solve for the charge q.
Given:
m = 1.5 g = 0.0015 kg
r = 0.026 m
k = 8.99 x 10^9 N m^2 / C^2
g = 9.8 m/s^2

Substituting the values:
(k * q^2) / r^2 = (0.0015 kg * 9.8 m/s^2 / cos 20°) * sin 20°

Simplifying the equation and solving for q:
q^2 = (0.0015 kg * 9.8 m/s^2 * r^2 / k) * sin 20° / cos 20°
q = sqrt((0.0015 kg * 9.8 m/s^2 * r^2 / k) * sin 20° / cos 20°)

Calculate the value of q using the given values.

Please note that the calculated value of q should have units of Coulombs (C).

To calculate the charges on the two pit balls, we can use Coulomb's Law and the concept of electrostatic equilibrium.

Let's break the problem down step by step:

Step 1: Calculate the force of gravity on the suspended ball.
Given that the mass of the ball is 1.5 grams, we need to convert it to kilograms by dividing it by 1000.
Mass (m) = 1.5 g = 1.5/1000 kg = 0.0015 kg

The force of gravity (Fg) on the ball can be calculated using the formula:
Fg = m * g
where g is the acceleration due to gravity, which is approximately 9.8 m/s².
Fg = 0.0015 kg * 9.8 m/s² = 0.0147 N

Step 2: Calculate the tension in the thread.
The tension (T) in the thread can be found by resolving the force of gravity into vertical and horizontal components.
The vertical component of the tension (Tv) counteracts the force of gravity, while the horizontal component (Th) causes the ball to move towards the other ball.

Tv = Fg * cos(angle), where angle is the angle the thread makes with the vertical.
Tv = 0.0147 N * cos(20°) ≈ 0.0137 N

Step 3: Calculate the electrostatic force between the two balls.
The electrostatic force between the balls can be calculated using Coulomb's Law:
Fe = k * (q1 * q2) / r²
where Fe is the electrostatic force, k is the electrostatic constant (approximately 8.99 x 10^9 N m²/C²), q1 and q2 are the charges on the two balls, and r is the separation distance between the balls.

Given that r is 2.6 cm, we need to convert it to meters by dividing it by 100.
r = 2.6 cm / 100 = 0.026 m

Fe = k * (q1 * q2) / r²

Step 4: Equate the vertical component of the tension with the electrostatic force.
Since the balls are in electrostatic equilibrium, the vertical component of the tension in the thread must equal the electrostatic force between the balls.

Solve for q1 or q2 in the equation Tv = Fe to find the charge on either ball.

0.0137 N = (8.99 x 10^9 N m²/C²) * (q1 * q2) / (0.026 m)²

Simplifying the equation, we have:
q1 * q2 = (0.0137 N * (0.026 m)²) / (8.99 x 10^9 N m²/C²)
q1 * q2 ≈ 10.2 x 10^-12 C²

Step 5: Solve for q1 and q2.
Since both balls have the same charge, let's assume q1 = q2 = q.

So:
q² ≈ 10.2 x 10^-12 C²
q ≈ ± √(10.2 x 10^-12 C²)
q ≈ ± 3.19 x 10^-6 C (rounded to two decimal places)

Therefore, the charge on each pit ball is approximately ±3.19 x 10^-6 C (Coulombs).