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: Larger masses exert stronger forces.
* Inversely proportional to the square of the distance between their centers: The farther apart the objects, the weaker the force.
* Gravitational Constant (G): This is a fundamental constant that determines the strength of gravitational attraction. Its value is approximately 6.674 x 10⁻¹¹ N⋅m²/kg².
Formula
The gravitational force (F) between two objects is calculated using the following formula:
F = G * (m₁ * m₂) / r²
Where:
* F = Gravitational force (in Newtons)
* G = Gravitational constant (6.674 x 10⁻¹¹ N⋅m²/kg²)
* m₁ = Mass of the first object (in kg)
* m₂ = Mass of the second object (in kg)
* r = Distance between the centers of the objects (in meters)
Calculations
1. Convert distance to meters: 20 cm = 0.2 meters
2. Plug in the values:
F = (6.674 x 10⁻¹¹ N⋅m²/kg²) * (2 kg * 5 kg) / (0.2 m)²
3. Calculate:
F ≈ 1.67 x 10⁻⁸ N
Answer:
The gravitational force that a 2-kg mass exerts on a 5-kg mass 20 cm away is approximately 1.67 x 10⁻⁸ Newtons.
