A small ball with a mass of 30.0 g and a charge of −0.200 μC is suspended from the ceiling by a string. The ball hangs at a distance of 5.00 cm above an insulating floor. If a second small ball with a mass of 50.0 g and a charge of 0.400 μC is rolled directly beneath the first ball, will the second ball leave the floor? What is the tension in the string when the second ball is directly beneath the first ball?
To determine if the second ball will leave the floor and find the tension in the string when the second ball is beneath the first ball, you need to consider the forces acting on the system.
First, let's analyze the forces on the suspended ball:
1. Gravitational force (Fg): The weight of the ball can be calculated using the formula Fg = m * g, where m is the mass of the ball (30.0 g) and g is the acceleration due to gravity (9.8 m/s^2).
Fg = (30.0 g) * (9.8 m/s^2) = 294 g * m/s^2
2. Electrostatic force (Fe): The electrostatic force is given by Coulomb's Law, which states that Fe = k * (q1 * q2) / r^2, where k is the electrostatic constant, q1 and q2 are the charges of the two balls, and r is the distance between them.
To calculate the electrostatic force, we need to convert the charges from microcoulombs (μC) to coulombs (C) and the distance from centimeters (cm) to meters (m).
Fe = (8.99 * 10^9 N * m^2/C^2) * ((-0.200 * 10^-6 C) * (0.400 * 10^-6 C)) / (0.05 m)^2
Next, let's compare the gravitational force and the electrostatic force:
If the magnitude of the electrostatic force is greater than the gravitational force, the second ball will leave the floor. Otherwise, it will not.
Now, let's determine the tension in the string when the second ball is directly beneath the first ball:
When the two balls are aligned vertically, the string will experience tension due to supporting the weight of the first ball and overcoming the electrostatic force between the two balls.
To find the tension (T), we need to consider the net force acting on the first ball. The net force is given by the vector sum of the gravitational force and the electrostatic force.
Net force (Fnet) = Fg - Fe
The tension in the string (T) equals the magnitude of the net force.
To summarize, you need to calculate the gravitational force, the electrostatic force, and the net force to determine if the second ball will leave the floor. Additionally, to find the tension in the string when the second ball is beneath the first ball, you need to calculate the magnitude of the net force.