ME 221Lecture 41 ME 221 Statics Lecture #4 Sections 2.9 & 2.10

ME 221Lecture 42 Announcements Quiz # 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

ME 221Lecture 43 Vector Dot Product Section 2.8 Determining the angle between 2 vectors

ME 221Lecture 44 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 45 Applications Determine the angle between two arbitrary vectors ·

ME 221Lecture 46

ME 221Lecture 47 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 class thus far.

ME 221Lecture 48 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 49 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 410 Representing Equilibrium Matrix Form x-components y-components z-components Component Form

ME 221Lecture 411 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 412 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 413

ME 221Lecture 414 Quiz #2