1. King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 10

2. Sir Isaac Newton 1642-1727 Proposed fundamental laws that are the basis of modern mechanics 3 laws of motion law of gravitation

3. First law Law of inertia - a body in motion will stay in motion and a body at rest will stay at rest unless acted upon by a net external force.Law of inertia A particle originally at rest, or moving in a straight line with a constant velocity, will remain in this state provided the particle is not subjected to an unbalance force. Static law

4. Second law A particle acted upon by an unbalanced force F experiences an acceleration that has the same direction as the force and a magnitude that is directly proportional to the force F3 F1 a1 F2 a2

5. Third law Law of action-reaction - for every action, there is an equal and opposite reactionLaw of action-reaction The mutual forces of action and reaction between two particles are equal, opposite, and collinear. F b,a = -F a,b

6. Newton's Law of Universal Gravitation Law of gravitation - all bodies are attracted to one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. –F = forces of attraction –G = universal constant of gravitation = 66.73(10 -12 )m 3 /(kg.s 2 ) –m 1,m 2 = mass of each of the two particle –r = distance between the centers of the two particles

7. Gravity on earth? Newton's Law of Universal Gravitation Compare with F = mg so g = GM/r 2 g depends inversely on the square of the distance g depends on the mass of the planet Nominally, g = 9.81 m/s 2 or 32.2 ft/s 2 –At the equator g = 9.78 m/s 2 –At the North pole g = 9.83 m/s 2 –g on the Moon is 1/6 of g on Earth.

8. Mass and Weight Weight –the amount of gravitational force exerted on a body F = m g W = m g –W: weight (units: N or lbs) –m: mass of the body (units: kg) –g: gravitational acceleration (9.81 m/s 2, 32.2 ft/s 2 ) As the mass of a body increases, its ’ weight increases proportionally

9. 13.2 The Equation of Motion Free Body and Kinetic Diagram Free-Body diagram Kinetic diagram

10. 13.3 Equation of Motion for a System of Particles