ME221Lecture 111 ME221 Statics LECTURE # 11 Sections 3.6 – 3.7

ME221Lecture 112 Homework #4 Chapter 3 problems: –1, 4, 8, 11, 17, 25, 26, 28, 35 & 40 –To be solved using hand calculations –May check work using MathCAD, etc. –Due Friday, September 26 Quiz #3 Today

ME221Lecture 113 Moment of a Force about an Axis x y z O F B n ^ A r AB =r B/A |M n | =M A ·n ^ =n·(r B/A x F ) ^ Same as the projection of M A along n | M n |= n x n y n z r B/Ax r B/A y r B/Az F x F y F z

ME221Lecture 114 x y z O F B n ^ A r AB =r B/A MAMA MnMn Mp Resolve the vector M A into two vectors one parallel and one perpendicular to n. M n =|M n |n ^ M p = M A - M n =n x [(r B/A x F) x n] ^

ME221Lecture 115 Moment of a Couple x y z O F2F2 B rArA F1F1 r AB =r B/A rBrB A Let F 1 = -F 2 d M o =r A x F 2 + r B x F 1 =(r B - r A ) x F 1 =r AB x F 1 = C The Moment of two equal and opposite forces is called a Couple |C|=|F 1 | d

ME221Lecture 116 The two equal and opposite forces form a couple (no net force, pure moment) The moment depends only on the relative positions of the two forces and not on their position with respect to the origin of coordinates Moment of a Couple (continued)

ME221Lecture 117 Since the moment is independent of the origin, it can be treated as a free vector, meaning that it is the same at any point in space The two parallel forces define a plane, and the moment of the couple is perpendicular to that plane Moment of a Couple (continued)

ME221Lecture 118 Example