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MEM202-Chapter-2

# MEM202-Chapter-2 - Chapter2 ForceVectors Objectives a...

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Chapter 2 Force Vectors Objectives : 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 iti t position vectors. d) Use dot product to determine the angle between two vectors or the projection of one vector onto another. MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 1

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Scalars and Vectors Scalars Vectors E l M V l F V l it Examples: Mass, Volume Force, Velocity Characteristics: have a magnitude have a magnitude (positive or negative) (always positive) and direction Addition rule: Simple arithmetic Parallelogram law or Cartesian components Notation: None Bold font, a line, or an arrow C B , , A MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 2
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
Vector Operation Vector Addition Given vectors A and B Wh i R A B? Parallelogram Law: Two vectors are joined Triangle Construction : The tail of one vector is What is R = + What is R’ = A – B? at their tails to form a parallelogram. 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 R A B A + ( Parallelogram Law Triangle Construction ’ = = + ( – B ) MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 6
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’ B A c a’ c b a C B C B A C B A C’ MEM202 ENGINEERING MECHANICS – STATICS CHAPTER 2 FORCE VECTORS 8 c b a sin sin sin c b a sin sin sin