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ME 221 Statics Lecture #4 Sections 2.9 & 2.10

ME 221 Statics Lecture #4 Sections 2.9 & 2.10. Announcements Quiz #2 - 15 minutes before the end of the lecture HW #2 due Friday 5/28 Ch 2: 23, 29, 32, 37, 47, 50, 61, 82, 105, 113 Ch 3: 1, 8, 11, 25, 35 Quiz #3 on Friday, May 28 Exam # 1 will be on Wednesday, June 2.

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ME 221 Statics Lecture #4 Sections 2.9 & 2.10

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  1. ME 221 StaticsLecture #4Sections 2.9 & 2.10 Lecture 4

  2. Announcements • Quiz #2 - 15 minutes before the end of the lecture • HW #2 due Friday 5/28 • Ch 2: 23, 29, 32, 37, 47, 50, 61, 82, 105, 113 • Ch 3: 1, 8, 11, 25, 35 • Quiz #3 on Friday, May 28 • Exam # 1 will be on Wednesday, June 2 Lecture 4

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

  4. 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 4

  5. · Applications • Determine the angle between two arbitrary vectors Lecture 4

  6. Lecture 4

  7. 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 class thus far. Lecture 4

  8. 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 4

  9. F3 F2 F3 F4 mi F2 F1 F1 F4 Representing Equilibrium Vector Diagram Vector Equation R = F1 + F2 + F3 + F4 = 0 Lecture 4

  10. Matrix Form x-components Component Form y-components z-components Representing Equilibrium Lecture 4

  11. 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 4

  12. 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 4

  13. Lecture 4

  14. Quiz #2 Lecture 4

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