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Unformatted text preview: Engineering Mechanics: Statics Chapter 2: Force Vectors Objectives To show how to add forces and resolve them into components using the Parallelogram Law. To express force and position in Cartesian vector form and explain how to determine the vector’s magnitude and direction. To introduce the dot product in order to determine the angle between two vectors or the projection of one vector onto another. Chapter Outline Scalars and Vectors Vector Operations Vector Addition of Forces Addition of a System of Coplanar Forces Cartesian Vectors Chapter Outline Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product 2.1 Scalars and Vectors Scalar – A quantity characterized by a positive or negative number – Indicated by letters in italic such as A Eg: Mass, volume and length 2.1 Scalars and Vectors Vector – A quantity that has both magnitude and direction Eg: Position, force and moment – Represent by a letter with an arrow over it such as or A – Magnitude is designated as or simply A – In this subject, vector is presented as A and its magnitude (positive quantity) as A A A 2.1 Scalars and Vectors Vector – Represented graphically as an arrow – Length of arrow = Magnitude of Vector – Angle between the reference axis and arrow’s line of action = Direction of Vector – Arrowhead = Sense of Vector 2.1 Scalars and Vectors Example Magnitude of Vector = 4 units Direction of Vector = 20 ° measured counterclockwise from the horizontal axis Sense of Vector = Upward and to the right The point O is called tail of the vector and the point P is called the tip or head 2.2 Vector Operations Multiplication and Division of a Vector by a Scalar Product of vector A and scalar a = a A Magnitude =  If a is positive, sense of a A is the same as sense of A If a is negative sense of a A , it is opposite to the sense of A aA 2.2 Vector Operations Multiplication and Division of a Vector by a Scalar Negative of a vector is found by multiplying the vector by ( 1 ) Law of multiplication applies Eg: A /a = ( 1/a ) A , a≠0 2.2 Vector Operations Vector Addition Addition of two vectors A and B gives a resultant vector R by the parallelogram law Result R can be found by triangle construction Communicative Eg: R = A + B = B + A 2.2 Vector Operations Vector Addition 2.2 2....
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 Three '11
 statics
 Statics, vector addition, resultant force

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