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Understanding Newton's Laws of Motion and Gravitation

This overview delves into the fundamental principles of Newton's Laws of Motion and the Law of Gravitation. We explore problem modeling strategies, including the transformation of real-world issues into simplified equations and the use of free-body diagrams (FBDs). Newton's three laws are examined, detailing motion, equilibrium, and forces' interactions. Additionally, we calculate gravitational forces between celestial bodies, providing practical examples with mass and radius data. The integration of computational tools like Maple and Matlab enhances practical applications and result interpretation.

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Understanding Newton's Laws of Motion and Gravitation

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  1. General Principles • Modeling of problem • Newton’s Law of Motion • Law of Gravitation • Units • Vectors

  2. Problem Solving Strategy: • Physical Model: • Transformation of actual problem into simpler • Assumptions • Using Free Body Diagram: FBD • Mathematical Model: • Newton’s Law: • F=0 and Mo=0 (coord. System) • Set of equations to be solved • Solution of Equations: • Computational Tools: Maple, Matlab, Prog. • Interpretation Results: Does answ. Makes sense?

  3. Newton’s Laws of Motion Law #1: Body is in Equilibrium Body will remain at rest or continue to move with same speed (accel.=0) and direction unless unbalance force is acted on body or particle.

  4. Newton’s Law of Motion Law #2: Non-equilibrium Change of motion of a body is proportional to the next force imposed on the body and is in direction of net force.

  5. Newton’s Law of Motion • Law #3: Action & Reaction If one body exerts a force on a second body, then second body exerts a force on the first body that is equal in magnitude, opposite in direction and collinear (same line of action).

  6. Law#4: Law of Gravitation • Any two bodies are attracted to each other with a force whose magnitude is proportional to the product of their gravitational masses and inversely proportional to the square of the distance between them. m F M F r

  7. Activity 1: Weight • If an object has a mass m=50Kg find the weight of object at surface of earth, moon and sun? G = 66.73x10-12 (m3/Kg/s2) Universal gravitational const. Given: • Mass of earth= 5.976x1024 Kg • Mass of moon= 7.35x1022 Kg • Mass of sun=1.99x1030 Kg • Radius of earth=6.371x106 m • Radius of Moon: 1.738x10^6 m • Radius of Sun: 6.96x10^8 m

  8. Weight & Mass: • Weight: where: and on earth surface: g= 9.807m/s2 (SI) or g= 32.17 ft/s2 (US) • Mass:

  9. Units Tables 1.6 and 1.7 in book

  10. Percent Error A = Value to be Compared B = Reference Value % Error = (A-B)/B (100%)

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