PowerPoint PresentationHomework #2Homework #3Slide 4Slide 5Slide 6Slide 7Equivalent Force SystemsSlide 92- Point B is not on the line of action of the forceSlide 11For More Than One ForceExample ProblemsSlide 14Exam 1Exam FormatExam 1 Helpful HintsExam 1 PitfallsExam 1 TopicsSlide 20ME221 Lecture 6 1ME221 StaticsLECTURE # 6Sections 3.6 – 3.9ME221 Lecture 6 2Homework #2•Due todayQuiz #3•TodayME221 Lecture 6 3Homework #3•Chapter 3 problems:–48, 55, 57, 61, 62, 65 & 72•Chapter 4 problems:–2, 4, 10, 11, 18, 24, 39 & 43•Due Monday, June 7ME221 Lecture 6 4Moment of a CouplexyzOF2BrAF1rAB=rB/ArBA Let F1 = -F2dMo=rA x F2+ rB x F1 =(rB - rA ) x F1=rAB x F1= CThe Moment of two equal and opposite forces is called a Couple|C|=|F1| dME221 Lecture 6 5• 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 coordinatesMoment of a Couple (continued)ME221 Lecture 6 6• 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 planeMoment of a Couple (continued)ME221 Lecture 6 7Equivalent Force Systems•Replacing a given set of forces with an equivalent force-moment systemME221 Lecture 6 8Equivalent Force Systems The action of a force tends to translate the body along the direction of the force and rotate it about an axis not located along the line of action of the force. The External Effects remain the same if the force is moved from one point to another (from A to B ) if:ME221 Lecture 6 9A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibriumBA1- Point B is on the line of action of the forceME221 Lecture 6 102- Point B is not on the line of action of the forceStart with a rigid body having force F applied to it.ABFReplace this force witha force and couple at A.Add “zero” to the bodyin the form of adding+F and -F+F-FME221 Lecture 6 11Next, group two forces to create couple CAB+FC+F-FFrB/ALet rB/A be the relative position of B with respect to A.Define couple with cross productC = rB/A x FIn essence, the force F hasbeen moved from point B toA with the addition of couple C.ME221 Lecture 6 12For More Than One ForceA similar procedure is used when there are many forces on the body:R =  FiC =  ci =  ri x FiME221 Lecture 6 13Example ProblemsME221 Lecture 6 14ME 221 StaticsExam #1 ReviewME221 Lecture 6 15Exam 1•Wednesday, June 2•No class on Monday, May 31ME221 Lecture 6 16Exam Format•Similar to homework problems•5 or 6 (maybe 7) problems•No new concepts•Closed books and closed notes•25% of final grade•Will need a calculatorME221 Lecture 6 17Exam 1 Helpful Hints•Study by working homework problems •Review the examples in the book•Read the exam questions carefully•Work the problems you know first•Use a logical flow to show your knowledge•Be complete – check your answersME221 Lecture 6 18Exam 1 Pitfalls•Vectors have both magnitude and direction •Most answers will have units•Calculated answers should be in decimal form•Use 3 significant figures where appropriate•Answers are generally worth ~1/3 of points•Steps leading to answers are worth ~2/3ME221 Lecture 6 19Exam 1 Topics•All of Chapters 1 & 2 except 2.11 Springs•Newton’s Laws•Units•Scalars & vectors; defining, adding, etc.•Laws of sine and cosine•Resolution of a vector into components•Up to 3.4 in Chapter 3ME221 Lecture 6 20Exam 1 Topics•3D coordinates & unit base vectors•Directional cosines•Non-orthogonal vector components•Scalar & cross products of vectors•2D & 3D equilibrium problems•Drawing good free-body diagrams•Moments &