ME 221Lecture 91 ME 221 Statics LECTURE #9 Sections:

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

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

ME 221Lecture 94 Chapter 3 Rigid Bodies; Moments Consider rigid bodies rather than particles –Necessary to properly model problems Moment of a force Problems

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.

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

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

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

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 ^

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: +-

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

ME 221Lecture = (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

ME 221Lecture 913 Problems A = 5i + 3j B = 3i + 6j Find A·B The angle between A and B AxB BxA