Understanding the Concepts
* Newton's Law of Universal Gravitation: This law states that every particle in the Universe attracts every other particle with a force that is:
* Proportional to the product of their masses.
* Inversely proportional to the square of the distance between their centers.
* Formula: F = G * (m1 * m2) / r^2
* F = Force of gravity
* G = Gravitational constant (6.674 × 10^-11 N⋅m^2/kg^2)
* m1 = Mass of the Earth (5.972 × 10^24 kg)
* m2 = Mass of the object (1 kg)
* r = Distance between the centers of the Earth and the object (approximately the Earth's radius, 6.371 × 10^6 m)
Calculation
1. Plug in the values:
F = (6.674 × 10^-11 N⋅m^2/kg^2) * (5.972 × 10^24 kg * 1 kg) / (6.371 × 10^6 m)^2
2. Calculate:
F ≈ 9.81 N
Result
The magnitude of the gravitational force between the Earth and a 1-kg mass is approximately 9.81 Newtons. This is the same force that causes the acceleration due to gravity (g) on Earth's surface, which is approximately 9.81 m/s².
