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Lecture02_ME343F09

# Lecture02_ME343F09 - Chapter 3 Vectors Chapter 3 Vectors...

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Unformatted text preview: Chapter 3: Vectors Chapter 3: Vectors Overview Overview Vector Definition Trig Review Analytical Vector Analysis Graphical Vector Analysis Examples Scalar Quantities Scalar Quantities Magnitude Quantity Length Duration Temperature Vector Quantities Vector Quantities Magnitude and Direction Displacement Velocity Acceleration Force Trig Review: Right Triangles Trig Review: Right Triangles SOH­CAH­TOA a2 = b2 + c2 Sin(<c) = c/a <b a c Horizontal Projection: b = a cos ( <c) Vertical projection: <a b <c c = a sin(<c) Cos(<c)= b/a Tan (<c) = c/a General Triangles General Triangles Law of Sines: <b a b c = = sin(∠a ) sin(∠b) sin(∠c ) c a <c c 2 = a 2 + b − 2ab * cos(∠c) Interior angles of a triangle sum to 180° b <a Law of Cosines: 2 Analytical Vector Analysis Analytical Vector Analysis Use of Trig tools to manipulate vector quantities Projection Directional Properties Horizontal components Vertical components ­A C B A Analytical Vector Analysis Analytical Vector Analysis A ­A C B Given the vectors shown calculate B­A+C Graphical Vector Analysis Graphical Vector Analysis Scaled Drawings Tip to tail convention Tedious and time consuming CAD Tools – Solid Works Graphical Vector Analysis Graphical Vector Analysis A ­A C B Given the vectors shown calculate B­A+C Examples Given: Examples β=28° x=20’ d=16’ L=25’ Find: Length of Support Cylinder Vertical height of conveyor tip above truck frame Solution Solution Using law of Cosines for cylinder length Cylinder = ( x + d − 2 xd cos( β ) 2 2 9.53' = 20 2 +16 2 − 2 *16 * 20 * cos(28) Conveyor Height Height = 25' sin( 28) = 11.74' Example 2 Example 2 Given the Engine pictured, determine the crank angle Example Example Calculate the Length of the cylinder required to orient the loader in the configuration shown Example Example Calculate the Length of the cylinder required to orient cylinder vertically. Also calculate the resulting angle of the lift arm with the frame Home Work Home Work Due Next Class 9/21/09 3­(1, 7, 14, 15, 17, 19, 21, 27, 33, 39) ...
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