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ME 221 Statics LECTURE #9 Sections: 3.1 - 3.3

Lecture 9 covers statics fundamentals, moments of force, rigid bodies vs. particles, and vector cross products. Learn to apply calculations in real-world engineering problems.

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ME 221 Statics LECTURE #9 Sections: 3.1 - 3.3

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  1. ME 221 StaticsLECTURE #9Sections: 3.1 - 3.3 Lecture 9

  2. Exam #1 Results Average Score: ? Scores posted on Angel Solution to be posted on Angel today See syllabus for regrade policy

  3. 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 Lecture 9

  4. Chapter 3Rigid Bodies; Moments • Consider rigid bodies rather than particles • Necessary to properly model problems • Moment of a force • Problems Lecture 9

  5. F F Rigid Bodies • The point of application of a force is very important in how the object responds • We must represent true geometry in a FBD and apply forces where they act. Lecture 9

  6. B A Transmissibility • A force can be replaced by an equal magnitude force provided it has the same line of action and does not disturb equilibrium Lecture 9

  7. M A O d F Moment • A force acting at a distance is a moment M d is the perpendicular distance from F’s line of action to O Defn. of moment: M = Fd • Transmissibility tells us the moment is the same about O or A Lecture 9

  8. 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 Lecture 9

  9. A x B B q A B q A AxB ^ n = AxB Cross Product The cross product of two vectors results in a vector perpendicular to both. The right-hand rule decides the direction of the vector. A x B = - B x A B x A Lecture 9

  10. - + 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: Lecture 9

  11. General Component Cross Product Consider the cross product of two vectors ˆ - AzBy i Or, matrix determinate gives a convenient calculation Lecture 9

  12. + - (AyBz-AzBy) i - (AxBz-AzBx) j = + (AxBy-AyBx)k Lecture 9

  13. Problems A = 5i + 3j B = 3i + 6j Find • A·B • The angle between A and B • AxB • BxA Lecture 9

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