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ME 221Lecture 91 ME 221 Statics LECTURE #9 Sections: 3.1 - 3.3
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Exam #1 Results Average Score: ? Scores posted on Angel Solution to be posted on Angel today See syllabus for regrade policy
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ME 221Lecture 93 Homework #4 Chapter 3 problems: –1, 4, 8, 11, 17, 25, 26, 28, 35 & 40 –To be solved using hand calculations –May check work using MathCAD, Matlab, etc. –Due Friday, September 26
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ME 221Lecture 94 Chapter 3 Rigid Bodies; Moments Consider rigid bodies rather than particles –Necessary to properly model problems Moment of a force Problems
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ME 221Lecture 95 Rigid Bodies The point of application of a force is very important in how the object responds F F We must represent true geometry in a FBD and apply forces where they act.
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ME 221Lecture 96 Transmissibility A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibrium B A
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ME 221Lecture 97 Moment A force acting at a distance is a moment Transmissibility tells us the moment is the same about O or A F d M O M A d is the perpendicular distance from F’s line of action to O Defn. of moment: M = Fd
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ME 221Lecture 98 Vector Product; Moment of Force Define vector cross product –trig definition –component definition cross product of base vectors Moment in terms of cross product Example problems
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ME 221Lecture 99 Cross Product The cross product of two vectors results in a vector perpendicular to both. B A A x B The right-hand rule decides the direction of the vector. B x A A B A x B = - B x A n = AxB ^
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ME 221Lecture 910 Base Vector Cross Product Base vector cross products give us a means for evaluating the cross product in components. Here is how to remember all of this: +-
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ME 221Lecture 911 General Component Cross Product Consider the cross product of two vectors ˆ A z B y i Or, matrix determinate gives a convenient calculation
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ME 221Lecture 912 - + = (A y B z -A z B y ) i - (A x B z -A z B x ) j + (A x B y -A y B x )k
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ME 221Lecture 913 Problems A = 5i + 3j B = 3i + 6j Find A·B The angle between A and B AxB BxA
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