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Constructing Free-Body Diagrams A Step-by-Step Method modeled on the multiple representation technique of Dr. Alan Van Heuvelan at Rutgers University Separating the universe into point models of objects and force vector models of everything else Leo Takahashi The Beaver Campus of The Pennsylvania State University

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Constructing Free-Body Diagrams for Interacting Objects Featuring Newton’s Third Law L. H. Takahashi, August 2007

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m M v v a a m

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M m v v a FBD Block mg F F N1 f k1 FTFT FBD Slab Mg F N1 FTFT f k1 F N2 f k2 a

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FBD Block mg F F N1 f k1 a FBD Slab Mg F N1 FTFT f k1 F N2 f k2 a FTFT

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FBD Block mg F F N1 f k1 FTFT a +X +y F x = ma x F y = ma y FCos - F T – f k1 = ma F N1 + FSin - mg = 0

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FBD Slab Mg F N1 FTFT f k1 +y F N2 f k2 a +x F x = Ma x F y = Ma y F T - f k1 - f k2 = Ma F N2 - F N1 - Mg = 0

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FCos - F T - f k1 = ma F N1 + FSin - mg = 0 F T - f k1 - f k2 = Ma F N2 - F N1 - Mg = 0 f k1 = k1 F N1 f k2 = k2 F N2 Block Equations Slab Equations Friction Equations

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Applications & Examples of Newton’s Laws. Forces are VECTORS!! Newton’s 2 nd Law: ∑F = ma ∑F = VECTOR SUM of all forces on mass m Need VECTOR addition.

Applications & Examples of Newton’s Laws. Forces are VECTORS!! Newton’s 2 nd Law: ∑F = ma ∑F = VECTOR SUM of all forces on mass m Need VECTOR addition.

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