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ME 221 Statics Lecture #7 Sections 2.9 & 2.10

ME 221 Statics Lecture #7 Sections 2.9 & 2.10. Homework. Due today: Chapter 2 problems: 22, 23, 25, 27, 29, 32, 37, 45, 47 & 50 Due Monday, September 15 Chapter 2 problems: 61, 64, 70, 71, 72, 82, 86, 94, 105 & 113. Exam 1. Wednesday, September 17 Details on Monday Quiz #2 is today.

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ME 221 Statics Lecture #7 Sections 2.9 & 2.10

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  1. ME 221 StaticsLecture #7Sections 2.9 & 2.10 Lecture 7

  2. Homework • Due today: • Chapter 2 problems: • 22, 23, 25, 27, 29, 32, 37, 45, 47 & 50 • Due Monday, September 15 • Chapter 2 problems: • 61, 64, 70, 71, 72, 82, 86, 94, 105 & 113 Lecture 7

  3. Exam 1 • Wednesday, September 17 • Details on Monday • Quiz #2 is today Lecture 7

  4. Vector Dot ProductSection 2.8 • Determining the angle between 2 vectors Lecture 7

  5. A q B Dot Product Consider two vectors A and B with included angle q By definition, the dot product is A • B = |A| |B| cos q Lecture 7

  6. · · · || Applications • Determine the angle between two arbitrary vectors • Components of a vector parallel and perpendicular to a specific direction Lecture 7

  7. Lecture 7

  8. Free-Body Diagrams; EquilibriumSections 2.9 & 2.10 • These two topics will tie Chapter 2 together. • This material is the most important of the topics covered in the class up to this point. Lecture 7

  9. Particle Equilibrium • For a particle to be in equilibrium, the resultant of the forces acting on it must sum to zero. • This is essentially Newton’s second law with the acceleration being zero. • In equation form: SF = 0 Lecture 7

  10. F3 F2 F3 F4 mi F2 F1 F1 F4 Representing Equilibrium Vector Diagram Vector Equation R = F1 + F2 + F3 + F4 = 0 Lecture 7

  11. Matrix Form x-components Component Form y-components z-components Representing Equilibrium Lecture 7

  12. Statically Determinate • For 3-D equilibrium, there are three scalar equations: SFx = 0 , SFy = 0 , SFz = 0 • Problems with more than three unknowns cannot be solved without more information, and such problems are called statically indeterminate. Lecture 7

  13. Free-Body Diagram A free-body diagram is a pictorial representation of the equation SF = 0 and has: • all of the forces represented in their proper sense and location • indication of the coordinate axes used in applying SF = 0 (Even though this is covered on a single slide, free-body diagrams are arguably the most important topic of the entire course.) Lecture 7

  14. Quiz #2 Lecture 7

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