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Statics Lecture 6: Forces, Moments, and Equilibrium

This lecture covers sections 3.6-3.9, including topics such as forces, moments, couples, and equivalent force systems. It also includes example problems and exam review for ME221 Statics.

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Statics Lecture 6: Forces, Moments, and Equilibrium

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  1. ME221 StaticsLECTURE # 6Sections 3.6 – 3.9 Lecture 6

  2. Homework #2 • Due today Quiz #3 • Today Lecture 6

  3. 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 Lecture 6

  4. B Let F1 = -F2 y A Mo=rA x F2+ rB x F1 =(rB - rA ) x F1 =rAB x F1= C O x z Moment of a Couple F1 d rAB=rB/A F2 rB rA The Moment of two equal and opposite forces is called a Couple |C|=|F1| d Lecture 6

  5. Moment of a Couple (continued) • 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 Lecture 6

  6. Moment of a Couple (continued) • 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 Lecture 6

  7. Equivalent Force Systems • Replacing a given set of forces with an equivalent force-moment system Lecture 6

  8. 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: Lecture 6

  9. B A 1- Point B is on the line of action of the force A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibrium Lecture 6

  10. B F A +F -F 2- Point B is not on the line of action of the force Start with a rigid body having force F applied to it. Replace this force with a force and couple at A. Add “zero” to the body in the form of adding +F and -F Lecture 6

  11. Let rB/A be the relative position of B with respect to A. C F B rB/A A +F +F -F Next, group two forces to create couple C Define couple with cross product C = rB/A x F In essence, the force F has been moved from point B to A with the addition of couple C. Lecture 6

  12. For More Than One Force A similar procedure is used when there are many forces on the body: R = SFi C = Sci = Sri x Fi Lecture 6

  13. Example Problems Lecture 6

  14. ME 221 StaticsExam #1 Review Lecture 6

  15. Exam 1 • Wednesday, June 2 • No class on Monday, May 31 Lecture 6

  16. 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 Lecture 6

  17. 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 Lecture 6

  18. 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 Lecture 6

  19. Exam 1 Topics • All of Chapters 1 & 2 except 2.11 Springs • Up to 3.4 in Chapter 3 • Newton’s Laws • Units • Scalars & vectors; defining, adding, etc. • Laws of sine and cosine • Resolution of a vector into components Lecture 6

  20. Exam 1 Topics • 3D coordinates & unit base vectors • Directional cosines • Non-orthogonal vector components • Scalar & cross products of vectors • 2D & 3D equilibrium problems • Moments & couples • Drawing good free-body diagrams Lecture 6

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