and 5153 COM amp Centroids ENGR B36 Statics Pat Aderhold 10 15 2014 Distributed Forces It means what you think it means In reality every force is distributed A lot more work to treat it as such ID: 656868
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Slide1
Chapter 5: Distributed Forces-and-5/1-5/3: C.O.M. & Centroids
ENGR B36 - Statics
Pat Aderhold
10/
15/
2014Slide2
Distributed ForcesIt means what you think it meansIn reality every force is distributedA lot more work to treat it as such
Sometimes it’s the only accurate approach
Don’t
really
work with distributed forces for a couple more days... but here’s a tasteSlide3
Distributed ForcesUn-simplified versions of things we’ve seenArea small compared to other dimensions of interest (moment arms)
Meriam
, JL and
Kraige
, LG. Statics 7
th
Ed. Wiley 2012.
p.
234Slide4
Distributed ForcesWhere simplifications gives wrong answerCan distribute over line, area or volume
Meriam
, JL and
Kraige
, LG. Statics 7
th
Ed. Wiley 2012.
p.
235Slide5
Distributed ForcesNow put that all on the back burnerNeed to develop some other tools firstSlide6
“Center of Gravity”
Meriam
, JL and
Kraige
, LG. Statics 7
th
Ed. Wiley 2012.
p.235Slide7
Center of Gravity - Deeper ThoughtsIt doesn’t really existChange in orientation of object changes distances between its atoms and those on earthAnd what about far away from the surface of the earth, where gravitational field not parallel
Long story short
=> Easier / better use
Center of MassSlide8
Center of MassSometimes its easySymmetry “cancels out” effects from both parts => C.O.M. in the middle
Sometimes its tricky
Complex shapes
Not always
on
the body itselfSlide9
C.O.M. and CentroidsA real object has a C.O.M.A geometric shape has a Centroid
If uniform density
=> they’re in the same place
But how do you actually
calculate
it?Slide10
Centroid for a Line
Meriam
, JL and
Kraige
, LG. Statics 7
th
Ed. Wiley 2012.
p.238Slide11
Centroid for an AreaMeriam, JL and Kraige, LG. Statics 7
th
Ed. Wiley 2012.
p.
238Slide12
Centroid for a VolumeMeriam, JL and Kraige, LG. Statics 7
th
Ed. Wiley 2012.
p.
240Slide13Slide14
The TakeawayIt’s not intuitiveBook’s sample problems aren’t very explicitThere’s some Calculus and some Geometry that you may have forgotten
Practice on white boardSlide15
Sample Problem 5/1Meriam, JL and Kraige, LG. Statics 7
th
Ed. Wiley 2012.
p.
242Slide16
Sample Problem 5/2Meriam, JL and Kraige, LG. Statics 7
th
Ed. Wiley 2012.
p.
242Slide17
Sample Problem 5/3Meriam, JL and Kraige, LG. Statics 7
th
Ed. Wiley 2012.
p.
243Slide18
Practice Problem 5/3
Meriam
, JL and
Kraige
, LG. Statics 7
th
Ed. Wiley 2012.
p.
246Slide19
HomeworkRead 5/4: Composite Bodies and FiguresPractice Problems 5/8, 5/20 and
5/34
Start thinking about which Chapter 4
Problems you’ll want to see during reviewSlide20
Practice Problem 4/112Meriam, JL and Kraige
, LG. Statics 7
th
Ed. Wiley 2012.
p.
219