1. The centers of two 11.80 kg spheres are separated by 0.09 m. What is their gravitational attraction?
2. What is the ratio of this attraction to the weight of one of the spheres (at the surface of the Earth)?
Please answer both
Thank you
F = G(11.8)(11.8)/.09^2
the weight of a sphere is just mg
To calculate the gravitational attraction between two spheres, we can use Newton's law of universal gravitation:
1. The gravitational attraction between two spheres can be calculated using the formula:
F = (G * m1 * m2) / r^2
where:
F is the gravitational force,
G is the gravitational constant (approximately 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.
In this case:
m1 = m2 = 11.80 kg
r = 0.09 m
Substituting these values into the formula:
F = (6.674 * 10^-11 N m^2 / kg^2 * 11.80 kg * 11.80 kg) / (0.09 m)^2
Calculating the value of F, we get:
F = 9.860218 kg m / s^2
Therefore, the gravitational attraction between the two spheres is approximately 9.860218 kg m / s^2.
2. To find the ratio of this attraction to the weight of one of the spheres on the surface of the Earth, we divide the gravitational attraction F by the weight of one of the spheres (W).
The weight (W) of an object on the surface of the Earth can be calculated using the formula:
W = m * g
where:
m is the mass of the object, and
g is the acceleration due to gravity (approximately 9.8 m/s^2 on the surface of the Earth).
In this case:
m = 11.80 kg
Substituting these values into the formula:
W = 11.80 kg * 9.8 m/s^2
Calculating the value of W, we get:
W = 115.44 kg m / s^2
Now, we can calculate the ratio:
Ratio = F / W
Substituting the gravitational attraction value F and weight value W:
Ratio = 9.860218 kg m / s^2 / 115.44 kg m / s^2
Calculating the value of the ratio, we get:
Ratio = 0.08542
Therefore, the ratio of the gravitational attraction between the two spheres to the weight of one of the spheres on the surface of the Earth is approximately 0.08542.
To find the gravitational attraction between two objects, we can use Newton's law of universal gravitation, which states that the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
1. To calculate the gravitational attraction between the two spheres, use the following formula:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the spheres,
G is the gravitational constant, approximately 6.67430 × 10^-11 N m^2 / kg^2,
m1 and m2 are the masses of the spheres (11.80 kg in this case), and
r is the separation distance between the centers of the spheres (0.09 m).
Plugging in the values:
F = (6.67430 × 10^-11 N m^2 / kg^2 * 11.80 kg * 11.80 kg) / (0.09 m)^2
Calculate this expression to find the gravitational attraction between the two spheres.
2. To find the ratio of this gravitational attraction to the weight of one of the spheres at the surface of the Earth, we need to calculate each separately.
The weight of an object is equal to its mass multiplied by the acceleration due to gravity, g, which is approximately 9.8 m/s^2 on the surface of the Earth.
So, the weight of one of the spheres would be:
W = m * g
Calculate the weight of one of the spheres using its mass (11.80 kg) and the acceleration due to gravity (9.8 m/s^2).
To find the ratio of the gravitational attraction to the weight, divide the gravitational attraction (force) by the weight of one of the spheres.
Calculate this ratio to get the desired result.
By following these steps, you can find the gravitational attraction between the spheres and the ratio of this attraction to the weight of one of the spheres.