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MAE 242Dynamics – Section I

 

Dr. Kostas Sierros

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Important information

• E-mail: Kostas.Sierros@mail.wvu.edu

• Room: G-19 ESB

• Phone: 293-3111 ext 2310

• E!": Tuesday & Thusday 9:30-11:00 !"

and #y a$$ointment

• "!E 2%2 Se'tion 1: E(ey Tuesday &Thusday ):00-9:1* !"

• !ll le'tues +ill ta,e $la'e at 113 "RB-E

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#e$t %oo&s

Enineein "e'hani's: .ynami's

'. i%%eler/ 11th Edition/ Penti'e all/200

and $o#a#ly some moe

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5evision e$amples /

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5evision e$amples /2

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5evision e$amples /6

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Kinematics of a particle0 7%8ectives

• 8on'e$ts su'h as $osition/ dis$la'ement/ (elo'ity anda''eleation ae intodu'ed

• Study the motion o $ati'les alon a staiht line5 Ga$hi'al

e$esentation• 7n(estiation o a $ati'le motion alon a 'u(ed $ath5 se odieent 'oodinate systems

• !nalysis o de$endent motion o t+o $ati'les

• Pin'i$les o elati(e motion o t+o $ati'les5 se o

tanslatin axis

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!ecture

• Kinematics of a particle 48ha$te 126

- 1251-1252

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Material covered

• Kinematics of a particle

- 7ntodu'tion

- Re'tilinea ,inemati's:

8ontinuous motion

- o+ to analy;e $o#lems

- Po#lems

 

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Kinematics of a particle0 Introduction

 Important contributors

9alileo 9alilei+ *ewton+ Euler

Mec1anics

 Stati's  Dynamics

E>uili#ium o a

 #ody that is atest?mo(es +ith

'onstant (elo'ity

!''eleatedmotion o a #ody

• Kinematics: eometi' as$e'ts o the motion• Kinetics: !nalysis o o'es +hi'h 'ause the motion

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#oday:s 7%8ectives

Students should #e a#le to:

15 @ind the ,inemati' >uantities 4$osition/ dis$la'ement/

(elo'ity/ and a''eleation6 o a $ati'le ta(elin

alon a staiht $ath 412526

 

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5ectilinear &inematics0 'ontinuous motion

! $ati'le ta(els alon a staiht-line

 $ath deined #y the 'oodinate axis s

The "7SI#I7* o the $ati'le at any

instant/ elati(e to the oiin/ A/ is

deined #y the $osition (e'to r / o the

s'ala s5 S'ala s 'an #e $ositi(e o

neati(e5 Ty$i'al units o r  and s ae

metes 4m6 o eet 4t65

The dis$la'ement o the $ati'le is deined

as its 'hane in $osition5

e'to om:  r = r’ - r  S'ala om: ∆ s C sD - s

The total distan'e ta(eled #y the $ati'le/ sT/ is a $ositi(e s'ala that e$esents

the total lenth o the $ath o(e +hi'h the $ati'le ta(els5

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,elocity

elo'ity is a measue o the ate o 'hane in the $osition o a

 $ati'le5  7t is a (e'to  >uantity 4it has  #oth manitude and

die'tion65 The manitude o the (elo'ity is 'alled s$eed/ +ith

units o m?s o t?s5

The a(eae (elo'ity o a $ati'le duin a

time inte(al ∆t is

vavg  C r ?∆t

The instantaneous (elo'ity is the time-dei(ati(e o $osition5

v C dr ?dt

S$eed is the manitude o (elo'ity: ( C ds?dt

!(eae s$eed is the total distan'e ta(eled di(ided #y ela$sedtime: 4(s 6a(  C sT? ∆ t

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Acceleration

!''eleation is the ate o 'hane in the (elo'ity o a $ati'le5 7t is a

(e'to  >uantity5 Ty$i'al units ae m?s2

 o t?s2

5The instantaneous a''eleation is the time dei(ati(e o (elo'ity5

e'to om: a C dv?dt

S'ala om: a C d(?dt C d2s?dt2

!''eleation 'an #e $ositi(e 4s$eed in'easin6o neati(e 4s$eed de'easin65

!s the #oo, indi'ates/ the dei(ati(e e>uations o (elo'ity anda''eleation 'an #e mani$ulated to et a ds C ( d(

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'onstant acceleration

The thee ,inemati' e>uations 'an #e inteated o the s$e'ial 'ase

+hen a''eleation is 'onstant 4a C a'6 to o#tain (ey useul e>uations5! 'ommon exam$le o 'onstant a''eleation is a(ity= i5e5/ a #ody

eely allin to+ad eath5 7n this 'ase/ a' C C 9.)1 m?s2 C 3252 t?s2 

do+n+ad5 These e>uations ae:

ta(  ( 'o

+=yields= ∫ ∫ t 

o'

v

v

dt advo

2'oo

s

t41?26at(ss ++=

yields=

∫ ∫ 

t 

o s dt vdso

6s-4s2a64(  ( o'

2o

2   +=yields= ∫ ∫  s

 s'

v

v   oo

dsadvv

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Important points

• .ynami's: !''eleated motion o

 #odies

• inemati's: Geomety o motion

• !(eae s$eed and a(eae (elo'ity

• Re'tilinea ,inemati's o staiht-

line motion

• !''eleation is neati(e +hen $ati'le is slo+in do+n

• F ds C ( d(= elation o a''eleation/

(elo'ity/ dis$la'ement

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Analy;in< pro%lems in dynamics

8oodinate system

• Esta#lish a $osition 'oodinate S alon the $ath ands$e'iy its ixed oiin and $ositi(e die'tion

• "otion is alon a staiht line and theeoe s/ ( and F 'an #e e$esented as ale#ai' s'alas

• se an ao+ alonside ea'h ,inemati' e>uation in odeto indi'ate $ositi(e sense o ea'h s'ala 

inemati' e>uations

• 7 any t+o o F/ (/ s and t ae elated/ then a thid (aia#le'an #e o#tained usin one o the ,inemati' e>uations

• hen $eomin inteation/ $osition and (elo'ity must #e ,no+n at a i(en instant 4so the 'onstants o limits'an #e e(aluated6

• Some e uations must #e used onl +hen a is constant 

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"ro%lem solvin< M)S#S

15  Read the $o#lem 'aeully 4and ead it aain6

25  Physi'al situation and theoy lin, 

35 .a+ diaams and ta#ulate $o#lem data%5 8oodinate systemHHH

*5 Sol(e e>uations and #e 'aeul +ith units

5 Be 'iti'al5 ! mass o an aeo$lane 'an not #e *0

I5 Read the $o#lem 'aeully

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"ro%lem

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"ro%lem 2

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"ro%lem 6