Question

Two equally charged, 1.00 g spheres are placed with 2.00 cm between their centers. when released, each begins to accelerate at 225 m/s2.

Answer 1

To address this problem, we must apply Coulomb's law for the electrostatic force and Newton's law of universal gravitation to find the forces on charged spheres, and then use Newton's laws of motion to determine their resultant movements and the conditions for equilibrium points.

Step-by-step explanation:

The question asks to determine the forces acting on charged spheres placed on or near a circular track, the motion that results from these forces, and potential equilibrium points on the track. To answer this question, we use Newton's laws of motion, Coulomb's law for electric forces, and the universal law of gravitation.

Initially, we find the electrostatic force using Coulomb's law, F = k |q1 * q2| / r^2, where k is Coulomb's constant, q1 and q2 are the charges on the spheres, and r is the distance between them. Then, we calculate the gravitational force using Newton's law of universal gravitation, F = G * m1 * m2 / r^2, where G is the gravitational constant, m1 and m2 are the masses of the spheres, and r is again the distance between them. The acceleration of the spheres due to these forces can be determined by applying Newton's second law, F = m * a, where m is the mass of the sphere and a is its acceleration.

To find the equilibrium points, we set the net force to zero and solve for the positions where the electric and gravitational forces cancel each other out. In positions where the net force is not zero, the sphere will move, and its final speed can be found using kinematic equations if it has a constant acceleration.

Answer 2

1) Force = m*a = 1.00 g * (1kg / 1000 g) * 225 m/s^2 = 0.225 N

2) Charge

Force = K (charge)^2 /(distance)^2 => charge = √ [Force * distance^2 / k]

k = 9.00 * 10^9 N*m^2 / C^2

charge = √ [0.225 N * (0.02 m)^2 / 9.00* 10^9 N*m^2 / C^2 ]

charge = 0.0000001 C = 0.0001 mili C