# MSU ME 221 - Lecture 06 (20 pages)

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## Lecture 06

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- Pages:
- 20
- School:
- Michigan State University
- Course:
- Me 221 - Statics

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ME221 Statics LECTURE 6 Sections 3 6 3 9 ME221 Lecture 6 1 Homework 2 Due today Quiz 3 Today ME221 Lecture 6 2 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 ME221 Lecture 6 3 Moment of a Couple Let F1 F2 B y Mo rA x F2 rB x F1 rB rA x F1 rAB x F1 C C F1 d ME221 rB O F1 rAB rB A F2 d A rA x The Moment of two equal and opposite forces is called a Couple z Lecture 6 4 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 ME221 Lecture 6 5 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 ME221 Lecture 6 6 Equivalent Force Systems Replacing a given set of forces with an equivalent force moment system ME221 Lecture 6 7 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 ME221 Lecture 6 8 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 B A ME221 Lecture 6 9 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 ME221 B F A F Lecture 6 F 10 Next group two forces to create couple C Let rB A be the relative position of B with respect to A Define couple with cross product C C rB A x F In essence the force F has F been moved from point B to A with the addition of couple C ME221 Lecture 6 A F B rB A F F 11 For More Than One Force A similar procedure is used when there are many forces on the body R Fi C ci ri x F i ME221 Lecture 6 12 Example Problems ME221 Lecture 6 13 ME 221 Statics Exam 1 Review ME221 Lecture 6 14 Exam 1 Wednesday June 2 No class on Monday May 31 ME221 Lecture 6 15 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 ME221 Lecture 6 16 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 ME221 Lecture 6 17 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 ME221 Lecture 6 18 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 ME221 Lecture 6 19 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 ME221 Lecture 6 20

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