What is the force of gravity between two spheres that have a mass of 6 kg and are separated by 36 m?
To calculate the force of gravity between two spheres, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of their distance.
The formula to calculate the force of gravity (F) is:
F = (G * m1 * m2) / r^2
Where:
F = force of gravity
G = gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
m1 = mass of the first sphere
m2 = mass of the second sphere
r = distance between the centers of the spheres
In this case, the mass of both spheres is given as 6 kg, and they are separated by a distance of 36 m. Plugging these values into the formula:
F = (6.674 × 10^-11 N m^2/kg^2 * 6 kg * 6 kg) / (36 m)^2
Here's how to calculate it step by step:
1. Multiply the masses of the spheres: 6 kg * 6 kg = 36 kg^2
2. Square the distance between the spheres: (36 m)^2 = 1296 m^2
3. Multiply the gravitational constant, mass product, and divide by the squared distance:
F = (6.674 × 10^-11 N m^2/kg^2 * 36 kg^2) / 1296 m^2
4. Simplify the units: kg^2 / m^2 cancels out, leaving the unit as newtons:
F = (6.674 × 10^-11 N * 36) / 1296
F ≈ 1.852 × 10^-13 N
Therefore, the force of gravity between the two spheres with a mass of 6 kg, separated by 36 m, is approximately 1.852 × 10^-13 Newtons.