MEM202-Chapter-2

MEM202-Chapter-2 - Chapter2 ForceVectors Objectives:...

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Chapter 2 Force Vectors Objectives : udents will be able to: Students will be able to: a) Add forces and resolve them to components using Parallelogram Law, Law of Sine, and Law of Cosine . b) Express force and position in Cartesian vector form. c) Determine the magnitudes and directions of force and position vectors. d) Use dot product to determine the angle between two vectors r the projection of one vector onto another. MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 1 or the projection of one vector onto another.
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Scalars and Vectors Scalars Vectors l Vl Vl i t Examples: Mass, Volume Force, Velocity Characteristics: have a magnitude have a magnitude ositive or negative) lways positive) (positive or negative) (always positive) and direction ddition rule: mple arithmetic arallelogram law Addition rule: Simple arithmetic Parallelogram law or Cartesian components otation: one old font, a line, Notation: None Bold font, a line, or an arrow C B , , A MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 2
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Graphical Representation of a Vector MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 3
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Vector Operation Multiplication and Division of a Vector by a Scalar MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 4
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Vector Operation Vector Addition Given vectors A and B Parallelogram Law: o vectors are joined Triangle Construction : he tail of one vector is What is R = A + B? What is R’ = A–B? Two vectors are joined at their tails to form a parallelogram. The tail of one vector is joined with the head of the other vector MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 5
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Vector Operation Vector Subtraction ( arallelogram Law iangle Construction R ’ = A B = A + ( – B ) Parallelogram Law Triangle Construction MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 6
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Vector Operation Resolution of Vector Resolve vector R into two components having known lines of action (Parallelogram law in reverse) Extend parallel lines from the head of R to form components Two methods commonly used in vector operations: MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 7 1. Law of Sine and Law of Cosine 2. Cartesian vector
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Vector Addition of Forces Law of Sine and Law of Cosine–A Review Ambiguous Case of Law of Sine Given two sides A , and B , and an opposite angle, b , determine the third side, C and the other two angles, a and c c a’ c b B A a B C B A C B A C’ C MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 8 c b a sin sin sin c b a sin sin sin
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Vector Addition of Forces Example 2.1 Determine the magnitude nd direction of the N 150 Parallelogram Law and direction of the resultant force R F 115 65   15 65 2 360 10 ? F 115 2 N 100 5 ? R 15 65 25 90 15 Law of Cosine     N
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This note was uploaded on 10/07/2011 for the course MEM 202 taught by Professor Cook during the Fall '08 term at Drexel.

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MEM202-Chapter-2 - Chapter2 ForceVectors Objectives:...

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