Understanding the Concepts
* Gravity: Gravity is a force of attraction between any two objects with mass. The more massive the objects, the stronger the gravitational pull.
* Newton's Law of Universal Gravitation: This law describes the force of gravity between two objects:
* F = G * (m1 * m2) / r²
* F = force of gravity
* G = gravitational constant (6.674 × 10⁻¹¹ N⋅m²/kg²)
* m1 = mass of object 1 (Earth in this case)
* m2 = mass of object 2 (the man)
* r = distance between the centers of the two objects (Earth's radius)
Calculations
1. Earth's Mass (m1): 5.972 × 10²⁴ kg
2. Earth's Radius (r): 6,371 km (convert to meters: 6,371,000 m)
3. Man's Mass (m2): 80.0 kg
Now, plug these values into the formula:
F = (6.674 × 10⁻¹¹ N⋅m²/kg²) * (5.972 × 10²⁴ kg * 80.0 kg) / (6,371,000 m)²
F ≈ 784 N
Answer: The magnitude of the gravitational force Earth exerts on a man with a mass of 80.0 kg is approximately 784 Newtons.
Note: This is also the man's weight, which is the force of gravity acting on his mass.
