Compare the gravitational force on an 11 kg mass at the surface of the Earth (with radius 6.3 X 10^6 m and mass 6 X 10^24 kg) with that on the surface of the Moon (with mass 1/81.3 ME and radius 0.27 RE). What is the force on the Earth? What is the force on the moon?
Weight = G m M/R^2,
where m is the mass of the object and M is the mass of the earth or moon. R is the radius of the earth or moon
The weight on the moon is earth weight times
(1/83)/(0.27)^2 = 0.165
On earth, W = M g = 108 N
On the moon, it is 0.165 times that.
this is wrong
To compare the gravitational force on the 11 kg mass at the surface of the Earth and the surface of the Moon, we can use Newton's law of universal gravitation. The formula for the gravitational force is:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between two objects
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
First, let's calculate the gravitational force on the Earth:
Mass of Earth (m1) = 6 × 10^24 kg
Mass of the object (m2) = 11 kg
Radius of Earth (r) = 6.3 × 10^6 m
Plugging these values into the formula, we get:
F = (6.67430 × 10^-11) * [(6 × 10^24) * 11] / (6.3 × 10^6)^2
Calculating this expression will give us the gravitational force on the Earth.
Next, let's calculate the gravitational force on the Moon:
Mass of the Moon (m1) = (1/81.3) * 6 × 10^24 kg (since the Moon's mass is 1/81.3 times the mass of the Earth)
Mass of the object (m2) = 11 kg
Radius of the Moon (r) = 0.27 * 6.3 × 10^6 m (since the Moon's radius is 0.27 times the radius of the Earth)
Plugging these values into the formula, we get:
F = (6.67430 × 10^-11) * [((1/81.3) * 6 × 10^24) * 11] / (0.27 * 6.3 × 10^6)^2
Calculating this expression will give us the gravitational force on the Moon.
By comparing the values of the gravitational forces on the Earth and the Moon, we can determine how they differ.