Calculate the size of the gravitational pull of a sphere of mass 10 kg on a mass 2.0 kg when their centers are 200 mm apart. What is the force of the 2.0 kg mass on the 10 kg mass?
To calculate the gravitational force between two masses, we can use Newton's law of universal gravitation, which states that the force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between their centers.
The formula can be expressed as:
F = G * (m1 * m2) / r^2
Where:
F = Force of gravity
G = Gravitational constant (approximately 6.67430 × 10^-11 N (m/kg)^2)
m1 = Mass of the first object
m2 = Mass of the second object
r = Distance between their centers
In this case, m1 (mass of the sphere) is 10 kg, m2 (mass of the other object) is 2.0 kg, and r (distance between their centers) is 200 mm.
First, let's convert the distance from millimeters to meters:
r = 200 mm = 200 / 1000 = 0.2 m
Now we can calculate the gravitational force:
F = G * (m1 * m2) / r^2
F = 6.67430 × 10^-11 * (10 * 2.0) / (0.2)^2
Simplifying further:
F = 6.67430 × 10^-11 * 20 / 0.04
F = 0.000000000667430 * 500
F = 0.000000333715 N (Newtons)
Therefore, the force of the 2.0 kg mass on the 10 kg mass is approximately 0.000000333715 Newtons.