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HES1125 Lecture - 2008 - Wk 1 - Chpt 02 - 6 slides per page

HES1125 Lecture - 2008 - Wk 1 - Chpt 02 - 6 slides per page...

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1 1 Engineering Mechanics: Statics Chapter 2: Force Vectors Chapter Two Outline 2. Force Vectors 2.1 Scalars and Vectors 2.2 Vector Operations 2 3 Vector Addition of Forces 2 2.3 Vector Addition of Forces 2.4 Addition of a System of Coplanar Forces 2.5 Cartesian Vectors 2.6 Addition and Subtraction of Cartesian Vectors 2.7 Position Vectors 2.8 Force Vector Directed along a Line 2.9 Dot Product 2.1 Scalars and Vectors Scalar z Is a quantity characterized by a positive or negative number (ie a magnitude) 3 number (ie a magnitude). z In your text, scalar quantities are indicated by letters in italic such as A. Examples of Scalars: Mass, volume and length 2.1 Scalars and Vectors Vector z Is a quantity that has both magnitude and direction For example: Force and moment. 4 z For handwritten work, vector quantities are represented by a letter with an arrow over it such as A or in your textbook as bold print A. z Magnitude is designated as A or simply A. Therefore, in your text, a vector is presented as A and its magnitude (positive quantity) as A. 2.1 Scalars and Vectors Vector : (Magnitude, Direction and Sense) z Represented graphically as an arrow 5 z Length of arrow = Magnitude of Vector z Angle between the reference axis and arrow’s line of action = Direction of Vector z 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 6 Sense of Vector = Upward and to the right The point O is called the tail of the vector and point P is called the tip or head
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2 2.2 Vector Operations Multiplication and Division of a Vector by a Scalar z The product of vector A and scalar a = a A z Magnitude : aA 7 z If a is positive, sense of a A is the same as A z If a is negative, sense of a A , it is opposite to A 2.2 Vector Operations Multiplication and Division of a Vector by a Scalar z Negative of a vector is found by multiplying the vector by (-1) 8 z Law of multiplication applies Example: A /a = ( 1/a ) A , a 0 2.2 Vector Operations Vector Addition z Addition of two vectors A and B gives a resultant vector R by the parallelogram law. E l R A + B B + A 9 Example: = + or + 2.2 Vector Operations Vector Addition z Resultant Vector R can be found by triangle construction. Example: R = A + B or B + A 10 2.2 Vector Operations Vector Addition z Special case: Vectors A and B are collinear (ie both have the same line of action) 11 2.2 Vector Operations Vector Subtraction z A special case of addition: Example: R ’ = A B = A + (– B ) z Rules of Vector Addition Applies 12
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3 2.3 Vector Addition of Forces Resolution of Multiple Vectors z When two or more forces are added, successive applications of the parallelogram law can be carried out to find the resultant. 13 Forces F 1 , F 2 and F 3 acts at a point O First, find resultant of F 1 + F 2 Second, find resultant F R = ( F 1 + F 2 ) + F 3 2.3 Vector Addition of Forces Example F a and F b are forces exerting on the hook. F c can be found using the parallelogram law 14 • Lines parallel to a and b from the heads of F a and F b are drawn to form a parallelogram
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