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Chapter 13: Kinetics of a Particle: Force and Acceleration

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Sir Isaac Newton 1642-1727 Formulated basic concepts and laws of mechanics Universal Gravitation Calculus Light and optics

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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 unbalanced force. Static law

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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

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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.

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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

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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.

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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 Weight is not an inherent property of an object: –mass is an inherent property Weight depends upon location.

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

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13.3 Equation of Motion for a System of Particles

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