Two 10.0-kg balls, each with a charge of 11.0 C, are separated by a distance of
0.500 km in interstellar space, far from other masses and charges.
(b) Calculate the force of gravity between the two balls.
(c) Calculate the electric force between the two balls.
This is straight plug and chug computation. Both are 1/r^2 fields. The gravity pulls them together and the like charges repel. I am not going to do the arithmetic for you.
To calculate the force of gravity between two objects, we can use the formula:
F_gravity = (G * m1 * m2) / r^2
where:
F_gravity is the gravitational force between the objects,
G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the center of the objects.
In this case, the masses of the balls are both 10.0 kg, and the distance between them is 0.500 km.
(b) Calculate the force of gravity between the two balls:
F_gravity = (6.67430 × 10^-11 N m^2/kg^2) * (10.0 kg) * (10.0 kg) / (0.500 km)^2
Using the given values, we can calculate the force of gravity.
F_gravity = (6.67430 × 10^-11 N m^2/kg^2) * (10.0 kg) * (10.0 kg) / (0.500 km)^2
F_gravity = 0.00013348 N
So, the force of gravity between the two balls is 0.00013348 N.
To calculate the electric force between two charged objects, we can use the formula:
F_electric = (k * q1 * q2) / r^2
where:
F_electric is the electric force between the objects,
k is the Coulomb's constant (8.988 × 10^9 N m^2/C^2),
q1 and q2 are the charges of the objects, and
r is the distance between the centers of the objects.
In this case, the charges of the balls are both 11.0 C, and the distance between them is 0.500 km.
(c) Calculate the electric force between the two balls:
F_electric = (8.988 × 10^9 N m^2/C^2) * (11.0 C) * (11.0 C) / (0.500 km)^2
Using the given values, we can calculate the electric force.
F_electric = (8.988 × 10^9 N m^2/C^2) * (11.0 C) * (11.0 C) / (0.500 km)^2
F_electric = 0.43538 N
So, the electric force between the two balls is 0.43538 N.
To calculate the force of gravity between the two balls, you can use Newton's law of universal gravitation, which states that the force of gravity between two objects with masses (m1 and m2) separated by a distance (r) is given by the formula:
F_gravity = (G * m1 * m2) / r^2
Where:
G is the gravitational constant, which has a value of approximately 6.67430 x 10^-11 N*(m^2)/kg^2.
Given that the masses of the two balls (m1 and m2) are both 10.0 kg, and the distance (r) is 0.500 km, we need to convert the distance to meters first.
0.500 km = 0.500 * 1000 = 500 meters
Now we can plug in the values into the formula:
F_gravity = (6.67430 x 10^-11 N*(m^2)/kg^2) * (10.0 kg) * (10.0 kg) / (500 meters)^2
Calculating this equation will give us the force of gravity between the two balls.
To calculate the electric force between the two balls, we can use Coulomb's law, which states that the electric force between two charged objects with charges (q1 and q2) separated by a distance (r) is given by the formula:
F_electric = (k * |q1 * q2|) / r^2
Where:
k is the electrostatic constant, which has a value of approximately 8.99 x 10^9 N*(m^2)/C^2.
Given that the charges of the two balls (q1 and q2) are both 11.0 C, and the distance (r) is the same as before (500 meters), we can plug in the values into the formula:
F_electric = (8.99 x 10^9 N*(m^2)/C^2) * (|11.0 C * 11.0 C|) / (500 meters)^2
Calculating this equation will give us the electric force between the two balls.