How many electrons must be removed from each of two 5.40kg copper spheres to make the electrical force of repulsion between them egual in magnitude to the gravatational attraction between them?
Set columb force equal to gravity force.
GMM/r^2=kqq/r^2
solve for q, which is coulombs.
then
numberelectrons= q/e
To determine the number of electrons that must be removed from each copper sphere, we need to compare the electrical force of repulsion between the spheres to the gravitational attraction between them.
Let's break down the steps to find the answer:
1. Find the mass of each copper sphere:
The given mass of each copper sphere is 5.40 kg.
2. Calculate the gravitational force of attraction between the copper spheres:
The formula to calculate the gravitational force between two objects is:
F_gravity = (G * m1 * m2) / r^2
Where:
F_gravity is the gravitational force,
G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the spheres, and
r is the distance between the centers of the spheres.
Since the spheres are identical, the masses are the same (5.40 kg), and we can assume the distance between their centers is negligible (considered as the sum of their radii).
3. Calculate the electrical force of repulsion between the copper spheres:
The electrical force of repulsion between two charged objects can be calculated using Coulomb's law:
F_electric = (k * q1 * q2) / r^2
Where:
F_electric is the electrical force of repulsion,
k is the electrostatic constant (8.988 × 10^9 N m^2/C^2),
q1 and q2 are the charges on the spheres (in Coulombs), and
r is the distance between the centers of the spheres.
Since the charges have the same magnitude (the electrons removed), we can assume the charges are equal and opposite.
4. Set the gravitational force equal to the electrical force and solve for the number of electrons:
Equate the expressions for the gravitational force and electrical force:
(G * m1 * m2) / r^2 = (k * q1 * q2) / r^2
Simplifying, we can cancel out the r^2 terms:
G * m1 * m2 = k * q1 * q2
Since the masses (m1 and m2) are given and the charges on both spheres are equal (q1 = q2 = q), we can focus on finding 'q.'
Rearrange the equation to solve for 'q':
q = sqrt((G * m1 * m2) / k)
Now, substitute the known values for G, m1, m2, and k into the equation, and solve for 'q.'
Finally, divide 'q' by the charge of one electron (1.6 × 10^-19 C) to find the number of electrons that must be removed.
Please provide the given values for the masses of the copper spheres so we can proceed with the calculation.