Final answer:
To make the electric force of repulsion between two copper spheres equal in magnitude to the gravitational attraction between them, we need to remove a certain number of electrons from each sphere. This can be calculated using Coulomb's Law and Newton's Law of Universal Gravitation, by equating the electric force of repulsion to the gravitational attraction. By solving for the number of electrons, we can determine how many need to be removed from each sphere.
Step-by-step explanation:
To make the electric force of repulsion between two copper spheres equal in magnitude to the gravitational attraction between them, we need to find the number of electrons that must be removed from each sphere. The formula to calculate the electric force of repulsion is given by Coulomb's Law: F = k * (q1 * q2) / r^2, where F is the force of repulsion, k is the Coulomb constant, q1 and q2 are the charges of the spheres, and r is the distance between the spheres.
The force of gravitational attraction between two objects is given by Newton's Law of Universal Gravitation: F = G * (m1 * m2) / r^2, where F is the force of gravitational attraction, G is the gravitational constant, m1 and m2 are the masses of the spheres, and r is the distance between the spheres.
Since we want the electric force of repulsion to be equal to the gravitational attraction, we can equate the two formulas: k * (q1 * q2) / r^2 = G * (m1 * m2) / r^2. The masses of the spheres cancel out, leaving us with q1 * q2 = (G * k) / r^2. Given the mass of each sphere, we can calculate the number of electrons by dividing the total charge of each sphere by the charge of a single electron.