civl%2131%)%stacs% - the university of memphis operations.pdfthe%force%f%=450%lb%...
TRANSCRIPT
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CIVL 2131 -‐ Sta-cs Basic Vector Opera-ons Addi-on and Subtrac-on of Coplanar Forces
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Objec-ves
¢ Understand and be able to u-lize vectors to represent forces
¢ Understand how forces represented as vectors can be added together to find the resultant of a series of coplanar forces
¢ Understand how a force can be resolved into components using the parallelogram law
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Tools
¢ Law of Sines ¢ Law of Cosines ¢ Basic Trigonometry ¢ Pythagorean Theorem
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Forces, Moments, and Vectors
¢ In Sta-cs we will be concerned with two basic elements of mechanics
¢ Forces – the tendency to cause movement along an axis and
¢ Moments – the tendency to cause movement around an axis
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Forces, Moments, and Vectors
¢ Both Forces and Moments can be mathema-cally represented as vectors which allows us to have both a consistent representa-on and a convenient set of tools for manipula-ng the elements for analysis
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Forces, Moments, and Vectors
¢ Vectors are mathema-cal representa-ons which have two components
¢ Magnitude and ¢ Direc-on
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Forces, Moments, and Vectors
¢ If a quan-ty can be represented by magnitude only, then it is a scalar and doesn’t follow the rules of vector manipula-on
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Forces, Moments, and Vectors
¢ Vectors are convenient representa-on because we have both graphical and analy-cal tools to work with them
¢ Remember, a vector has both magnitude and direc-on
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Forces, Moments, and Vectors
¢ Graphically, we can represent our vector quan--es (forces and moments) by using an arrow
¢ If we are going to use a graphical solu-on, the length of the arrow will represent the magnitude of the quan-ty and the direc-on of the arrow will represent the direc-on of the quan-ty
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Forces and vector components
¢ Two forces act on the hook. Determine the magnitude of the resultant force.
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Forces and vector components
¢ What would the magnitude of the 600N force have to change to so that the resultant of the two forces would align along the posi-ve x-‐axis?
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Forces and vector components
¢ The force F = 450 lb acts on the frame. Resolve this force into components ac-ng along members AB and AC, and determine the magnitude of each component.
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Homework
¢ Problem 2-‐7 ¢ Problem 2-‐10 ¢ Problem 2-‐15
¢ Reading through Sec-on 2.7
September 29, 2012 Force Operations