ME 221Lecture 71 ME 221 Statics Lecture #7 Sections 2.9 & 2.10

ME 221Lecture 72 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

ME 221Lecture 73 Exam 1 Wednesday, September 17 Details on Monday Quiz #2 is today

ME 221Lecture 74 Vector Dot Product Section 2.8 Determining the angle between 2 vectors

ME 221Lecture 75 Dot Product Consider two vectors A and B with included angle   A B By definition, the dot product is A B = |A| |B| cos 

ME 221Lecture 76 Applications Determine the angle between two arbitrary vectors Components of a vector parallel and perpendicular to a specific direction · · · ||

ME 221Lecture 77

ME 221Lecture 78 Free-Body Diagrams; Equilibrium Sections 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.

ME 221Lecture 79 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:  F = 0

ME 221Lecture 710 Representing Equilibrium mimi Vector Diagram R = F 1 + F 2 + F 3 + F 4 = 0 Vector Equation F1F1 F2F2 F3F3 F4F4 F1F1 F2F2 F3F3 F4F4

ME 221Lecture 711 Representing Equilibrium Matrix Form x-components y-components z-components Component Form

ME 221Lecture 712 Statically Determinate For 3-D equilibrium, there are three scalar equations:  F x = 0,  F y = 0,  F z = 0 Problems with more than three unknowns cannot be solved without more information, and such problems are called statically indeterminate.

ME 221Lecture 713 Free-Body Diagram A 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 are arguably the most important topic of the entire course.)

ME 221Lecture 714 Quiz #2