ME221Lecture 101 ME221 Statics LECTURE # 10 Sections 3.4 & 3.6

ME221Lecture 102 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 Wednesday, September 24

ME221Lecture 103 Last Lecture Cross Product Moment of a Force about a Point Rigid Bodies Today Moment about an Axis Moment of Couple Equivalent Force Couple System

ME221Lecture 104 Vector Moment Definition The moment about point O of a force acting at point A is: M O = r A/O x F Compute the cross product with whichever method you prefer. r A/O A O F

ME221Lecture 105 A O N 60 o x d 0.285tan 60°=0.2m/x x=0.115m sin 60°=d/0.285m d = m M A =200N *0.247m= 49.4 Nm Example Method # 1

ME221Lecture 106 A O N 60 o 200 cos sin 60 M+ =200N (sin 60)(0.4m)- 200N (cos 60)(0.2m) = 49.4 Nm Method # 2

ME221Lecture 107 A O N 60 o Method # 3 r F=200N cos 60 i + 200N sin 60 j r =0.4 i j cos60 200sin60 0 MA=MA= =200 (sin 60)(0.4) (cos 60)(0.2) = 49.4 Nm i j k ^ ^ ^

ME221Lecture 108 A O N 60 o Method # 4 r =0.285 i F=200N cos 60 i + 200N sin 60 j r =0.285 i i j k cos60 200sin60 0 MA=MA= = 49.4 Nm

ME221Lecture 109 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 1010 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 1011 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 1012 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 1013 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 1014 Example