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Unformatted text preview: Chapter 3: Vectors Overview Vector Definition Trig Review Analytical Vector Analysis Graphical Vector Analysis Examples Scalar Quantities Magnitude Quantity Length Duration Temperature Vector Quantities Magnitude and Direction Displacement Velocity Acceleration Force 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
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 Use of Trig tools to manipulate vector quantities Projection Directional Properties Horizontal components Vertical components
A C B A Analytical Vector Analysis
A A C B Given the vectors shown calculate BA+C Graphical Vector Analysis Scaled Drawings Tip to tail convention Tedious and time consuming CAD Tools Solid Works Graphical Vector Analysis
A A C B Given the vectors shown calculate BA+C Examples Given:
=28 x=20' d=16' L=25' Find: Length of Support Cylinder Vertical height of conveyor tip above truck frame Solution Using law of Cosines for cylinder length Cylinder = ( x + d - 2 xd cos( )
2 2 9.53' = 20 2 +16 2 - 2 *16 * 20 * cos(28) Conveyor Height Height = 25' sin( 28) = 11.74' Example 2 Given the Engine pictured, determine the crank angle Example Calculate the Length of the cylinder required to orient the loader in the configuration shown 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 Due Next Class 9/21/09 3(1, 7, 14, 15, 17, 19, 21, 27, 33, 39) ...
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- Fall '09