Understanding Gravitational Force
The gravitational force between two masses is defined by Newton's Law of Universal Gravitation. This law states that every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Formula for Gravitational Force
The formula for calculating gravitational force (F) is:
- F = G * (m1 * m2) / r^2
Where:
- G is the gravitational constant (approximately 6.674 × 10^-11 N(m/kg)^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two masses
Calculating the Gravitational Force Between Earth and a 1 kg Object
To find the gravitational force between the Earth and a 1 kg object on its surface:
- Mass of the Earth (m1): Approximately 5.972 × 10^24 kg
- Mass of the object (m2): 1 kg
- Radius of the Earth (r): Approximately 6.371 × 10^6 meters
Substituting Values
Using the formula:
- F = G * (5.972 × 10^24 kg * 1 kg) / (6.371 × 10^6 m)^2
Calculating this gives:
- F ≈ 9.81 N
Conclusion
Thus, the magnitude of the gravitational force between the Earth and a 1 kg object on its surface is approximately 9.81 newtons. This value is commonly referred to as the weight of the object due to Earth's gravity.