ME221Lecture 61 ME221 Statics LECTURE # 6 Sections 3.6 – 3.9

ME221Lecture 62 Homework #2 Due today Quiz #3 Today

ME221Lecture 63 Homework #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 7

ME221Lecture 64 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 65 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 66 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 67 Equivalent Force Systems Replacing a given set of forces with an equivalent force-moment system

ME221Lecture 68 Equivalent 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:

ME221Lecture 69 A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibrium B A 1- Point B is on the line of action of the force

ME221Lecture Point B is not on the line of action of the force Start with a rigid body having force F applied to it. A B F Replace this force with a force and couple at A. Add “zero” to the body in the form of adding +F and -F +F+F -F-F

ME221Lecture 611 Next, group two forces to create couple C A B +F+F C +F+F -F-F F r B/A Let r B/A be the relative position of B with respect to A. Define couple with cross product C = r B/A x F In essence, the force F has been moved from point B to A with the addition of couple C.

ME221Lecture 612 For More Than One Force A similar procedure is used when there are many forces on the body: R =  F i C =  c i =  r i x F i

ME221Lecture 613 Example Problems

ME221Lecture 614 ME 221 Statics Exam #1 Review

ME221Lecture 615 Exam 1 Wednesday, June 2 No class on Monday, May 31

ME221Lecture 616 Exam 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 calculator

ME221Lecture 617 Exam 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 answers

ME221Lecture 618 Exam 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 ~2/3

ME221Lecture 619 Exam 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 3

ME221Lecture 620 Exam 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 & couples