Newton's Law of Gravitation: States that all objects in the universe attract one another.
Gravitational Force of Attraction: Describes the attraction between two masses.
Equation for Gravitational Force:
Force gravitational = G (Gravitational Constant) * (mass1 * mass2) / distance squared.
Terms and Definitions
Gravitational Constant (G): A very small constant, approximately 6.673 x 10^-11 Nm^2/kg^2.
Mass: The amount of matter in an object. Both the Kleenex box and remote are masses.
Distance (R): Measured from center to center of two objects.
Applications and Explanation
Noticeable Force: Small masses like a Kleenex box and a remote don't attract noticeably because G is so small. One mass must be very large (like a planet) to have a noticeable force.
Newton's Third Law: Every action has an equal and opposite reaction. The gravitational force M1 exerts on M2 is equal to the force M2 exerts on M1.
Equations and Calculations
Gravitational Force Equation:
Big G * (mass1 * mass2) / R^2 = Force gravitational.
Acceleration of Gravity:
On or above a large mass using the equation: G * (mass of Earth or large body) / R^2.
R = Distance from the center of mass to the other object.*
Examples and Applications
Example Scenario:
Earth (large mass) and Kleenex box (small mass).
Calculating Gravity:
The gravitational force on an object depends on mass and radius, not the object's materials.
Acceleration: As distance from Earth's center increases, acceleration due to gravity decreases exponentially.
Additional Applications
Objects Orbiting: One object orbiting another, like the Moon around Earth.
Elliptical Paths: Treated as circular for simplicity.
Important Distance: Center of Earth to center of the Moon.
Circular Motion and Centripetal Force
Centripetal Acceleration: Caused by the gravitational force in a circular path.
Calculation:
Centripetal Force = M2 * V^2 / R.
V (tangential velocity) depends on the mass of the central object (not the satellite).*
Conclusion
Understanding gravitational forces and calculations helps explain planetary motion and forces between Earth and objects.
Key takeaway: Gravitational interactions, governed by Newton's laws, are foundational for understanding physical interactions at a cosmic scale.