Newton's Law of Universal Gravitation:
The force of gravity (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.
F = (G * m1 * m2) / r²
Where:
* F is the force of gravity (in Newtons, N)
* G is the gravitational constant (6.674 × 10⁻¹¹ N m²/kg²)
* m1 is the mass of the first object (in kilograms, kg)
* m2 is the mass of the second object (in kilograms, kg)
* r is the distance between the centers of the two objects (in meters, m)
Let's apply this to our problem:
1. Identify the objects:
* Object 1: The man (m1 = 70.0 kg)
* Object 2: Earth (m2 = 5.972 × 10²⁴ kg)
2. Determine the distance between their centers:
* The distance (r) is the radius of Earth (6.371 × 10⁶ m).
3. Plug the values into the formula:
F = (6.674 × 10⁻¹¹ N m²/kg² * 70.0 kg * 5.972 × 10²⁴ kg) / (6.371 × 10⁶ m)²
4. Calculate the force:
F ≈ 686 N
Therefore, the force of gravity on a 70.0 kg man standing on Earth's surface is approximately 686 Newtons.
Note: This calculation assumes the man is standing at sea level. If he were at a higher altitude, the force of gravity would be slightly less due to the increased distance from Earth's center.
