Chapter 2 - ENGI 1400 Engineering Mechanics I STATICS...

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ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 2-P1 Chapter 2 Vectors and Force Vectors ; WHAT YOU SHOULD LEARN & UNDERSTAND FROM THIS CHAPTER? ¾ Scarlar/Vectors, Vector Operations ¾ 3D Cartesian Vector Notation, Cartesian Vector Addition and Subtraction ¾ Position Vectors and Force Vectors along a Line ¾ Dot Product ; READING MATERIALS IN TEXTBOOK – CHAPTER 2 (All Sections 2.1 – 2.9) ; Fundamental RINCIPLES and APPLICATION EXAMPLES – throughout the whole course APPLICATION OF VECTOR ADDITION There are four concurrent cable forces acting on the bracket. How do you determine the resultant force acting on the bracket?
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ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 2-P2 2.1. Scalars and Vectors (Section 2.1) Most of the physical quantities in Mechanics can be characterized by either Scalars or Vectors Scalars Vectors Examples : mass, volume, length force, velocity, position, moment Characteristics : It has a magnitude It has a magnitude and a direction (positive or negative) Addition rule : Simple arithmetic Parallelogram law and triangle Special Notation : None Bold font, an arrow For example, a vector A is expressed as: A (boldface type), its magnitude is always a positive scalar (quantity) (| A | or A - italic type) Graphically by an arrow: tail, head or tip, line of action, sense; magnitude = the length of the arrow; direction = the angle between the arrow’s line of action and a reference axis; tail of the vector and the tip/head of the vector Example: (Fig.2-1 pg18)
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ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 2-P3 1. Vector Multiplication and Division by a Scalar Multiplication: vector A × scalar a = a A (magnitude and direction) Division: A / a = (1/ a ) A (magnitude and direction) 2. Vector Addition Using Either the Parallelogram Law or Triangle Find the “resultant” vector from additions of two vectors (R = A + B)? Method (1): Parallelogram Law: - Join A and B at their tails; - Draw two parallel lines from the head of each vector to form a parallelogram; - Resultant R is the diagonal of the parallelogram
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ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 2-P4 Method (2): Triangle method (always ‘head to tail’): - Connect the head of A to the tail of B ; - Resultant R extends from the tail of A to the head of B Or - Connect the head of B to the tail of A - Resultant R extends from the tail of B to the head of A Î Vector addition is commutative (the vectors can be added in either order), R = A+B = B+A 3. Vector Subtraction - A special case of vector addition, and methods of additions apply. -
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Chapter 2 - ENGI 1400 Engineering Mechanics I STATICS...

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