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What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6×10^24 kg and radius of the earth is 6.4×10^6 m)?
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What is the magnitude of the gravitational force between the earth and...
Introduction
To calculate the gravitational force between the Earth and a 1 kg object on its surface, we use Newton's law of universal gravitation. This law states that every mass attracts every other mass 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
The formula for gravitational force (F) is given by:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.674 × 10^-11 N m²/kg²)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two masses
Values Used
- m1 (mass of the Earth) = 6 × 10^24 kg
- m2 (mass of the object) = 1 kg
- r (radius of the Earth) = 6.4 × 10^6 m
Calculation
Substituting the values into the formula:
F = (6.674 × 10^-11) * (6 × 10^24 * 1) / (6.4 × 10^6)^2
Calculating the denominator:
(6.4 × 10^6 m)² = 4.096 × 10^13 m²
Now substituting back into the equation:
F = (6.674 × 10^-11) * (6 × 10^24) / (4.096 × 10^13)
Calculating this gives:
F ≈ 9.81 N
Conclusion
Therefore, the magnitude of the gravitational force between the Earth and a 1 kg object on its surface is approximately 9.81 Newtons. This force is what gives objects weight and is a crucial aspect of understanding gravitational interactions.
To calculate the gravitational force between the Earth and a 1 kg object on its surface, we use Newton's law of universal gravitation. This law states that every mass attracts every other mass 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
The formula for gravitational force (F) is given by:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.674 × 10^-11 N m²/kg²)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two masses
Values Used
- m1 (mass of the Earth) = 6 × 10^24 kg
- m2 (mass of the object) = 1 kg
- r (radius of the Earth) = 6.4 × 10^6 m
Calculation
Substituting the values into the formula:
F = (6.674 × 10^-11) * (6 × 10^24 * 1) / (6.4 × 10^6)^2
Calculating the denominator:
(6.4 × 10^6 m)² = 4.096 × 10^13 m²
Now substituting back into the equation:
F = (6.674 × 10^-11) * (6 × 10^24) / (4.096 × 10^13)
Calculating this gives:
F ≈ 9.81 N
Conclusion
Therefore, the magnitude of the gravitational force between the Earth and a 1 kg object on its surface is approximately 9.81 Newtons. This force is what gives objects weight and is a crucial aspect of understanding gravitational interactions.
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