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King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 10 Sir Isaac Newton 1642-1727 Proposed fundamental laws that are the basis of modern mechanics 3 laws of motion law of gravitation 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. • 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 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 F a F ma a1 a2 F1 F2 F3 Third law • Law of action-reaction - for every action, there is an equal and opposite reaction • The mutual forces of action and reaction between two particles are equal, opposite, and collinear. • Fb,a= -Fa,b 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. – – – – m1m2 F G 2 r F = forces of attraction G = universal constant of gravitation = 66.73(10-12)m3/(kg.s2) m1,m2 = mass of each of the two particle r = distance between the centers of the two particles Gravity on earth? Newton's Law of Universal Gravitation Compare with F = mg so g = GM/r2 Mm F G 2 r • g depends inversely on the square of the distance • g depends on the mass of the planet • Nominally, g = 9.81 m/s2 or 32.2 ft/s2 – At the equator g = 9.78 m/s2 – At the North pole g = 9.83 m/s2 – g on the Moon is 1/6 of g on Earth. 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/s2, 32.2 ft/s2) • As the mass of a body increases, its’ weight increases proportionally 13.2 The Equation of Motion Free Body and Kinetic Diagram F ma • Free-Body diagram • Kinetic diagram 13.3 Equation of Motion for a System of Particles F ma Fi f i mi a i F ma G