PowerPoint PresentationSlide 2Vector Dot Product Section 2.8Dot ProductApplicationsSlide 6Free-Body Diagrams; Equilibrium Sections 2.9 & 2.10Particle EquilibriumRepresenting EquilibriumSlide 10Statically DeterminateFree-Body DiagramSlide 13Quiz #2ME 221 Lecture 4 1ME 221 StaticsLecture #4Sections 2.9 & 2.10ME 221 Lecture 4 2Announcements• Quiz #2 - 15 minutes before the end of the lecture• HW #2 due Friday 5/28Ch 2: 23, 29, 32, 37, 47, 50, 61, 82, 105, 113Ch 3: 1, 8, 11, 25, 35• Quiz #3 on Friday, May 28• Exam # 1 will be on Wednesday, June 2ME 221 Lecture 4 3Vector Dot ProductSection 2.8•Determining the angle between 2 vectorsME 221 Lecture 4 4Dot ProductConsider two vectors A and B with included angle ABBy definition, the dot product isA • B = |A| |B| cos ME 221 Lecture 4 5Applications•Determine the angle between two arbitrary vectors1cosA BA Bg·ME 221 Lecture 4 6ME 221 Lecture 4 7Free-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.ME 221 Lecture 4 8Particle 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: F = 0ME 221 Lecture 4 9Representing EquilibriummiVector DiagramR = F1 + F2 + F3 + F4 = 0Vector EquationF1F2F3F4F1F2F3F4ME 221 Lecture 4 10Representing EquilibriumMatrix Form1 2 3 41 2 3 41 2 3 4000x x x xy y y yz z z zF F F FF F F FF F F F                                                1 2 3 40x x x xF F F F   x-components1 2 3 40y y y yF F F F   y-components1 2 3 40z z z zF F F F   z-componentsComponentFormME 221 Lecture 4 11Statically Determinate•For 3-D equilibrium, there are three scalar equations: Fx = 0 , Fy = 0 , Fz = 0•Problems with more than three unknowns cannot be solved without more information, and such problems are called statically indeterminate.ME 221 Lecture 4 12Free-Body DiagramA free-body diagram is a pictorial representation of the equation F = 0 and has:–all of the forces represented in their proper sense and location–indication of the coordinate axes used in applying F = 0(Even though this is covered on a single slide, free-body diagrams (Even though this is covered on a single slide, free-body diagrams are arguably the most important topic of the entire course.)are arguably the most important topic of the entire course.)ME 221 Lecture 4 13ME 221 Lecture 4 14Quiz