ࡱ> `!$KOV}m9jd L"xKP.?ZSQ)EA+ͩm şi -H.:?A:Cqr%t0'oCh(n G>Q$˲b79Ѕg3̡uc\i$~=ѾhN`!OۍkY22a>D @px?HAƿy{zm ڨeM< *S (*BBP,J&}Dl4FRy3,,oͼH!h_5r$" }͊0z ԗp2j5Ñ{2ږ8 \XRcr(xbuYᚴ%{#蕌YudBt{Vx$oPt-Tf<o 8i DHWƜ݊c~S7+)}{?EHuGɹ^[ˤ>,NLphr~X#Fi&sP6WfBcֶP<5q'"l.q`ȺhVuOjȢiD&#.zL.4zRN;v#dIznzGtCs)b93:ή U˕*,wӊ`!@ 6K7%3@Chxcdd``~ @bD"LGc21Bq3Laj`:$d3H1igYjx|K2B* R l7Sÿ9`M`t@Hfnj_jBP~nb,M@i00Ժ1p]Ő 5U42pz*.5 l,׊D0A`v C4!v 8~3 0y{Ĥ\Y\ː2f:$C`!DA\~٢" Y@|xcdd``~ @bD"LGc21Bq3Lar`Z$d3H1igY8P#7T obIFHeA*CM Wfj7 M-VK-WMcPI( FZ7Wp`ݙ PSG0j*#7I!AP& Qp()JdXs F>f040pAC R`׀C7;LLJ% y.c/E`!Cd*hql<`@C0xcdd``~ @bD"LGc21Bq3LaJ`:$d3H1igY[Vjx|K2B* Rl7Sÿ9`M`t@Hfnj_jBP~nb't@1q`aucx֝Ͱ jhBMe+0IT13B]j$Y! %E +`.5Ã' .h(pC phf``CI)$5!e`u2F`!$Xoү׋'ó޾t Ƚxcdd`` @bD"LGc21Bq3LaZ(d3H1igY Nj䆪aM,,He`P@I35vFS|C\+J!n}`RH^8HoHfnj_jBP~nbCQ`>J`4ʰ N._&Iv/#RpeqIj.CeS6`!!#X1V0Rxcdd`` @bD"LGc21Bq3Laj`\(d3H1igY8 jx|K2B* Rl7Sÿ9`M`t@Hfnj_jBP~nbct@1q900Ժ1bv[~3 0y{v121)W2ALc,`!WR4A̕p `oxJAs6M75BQ06^0 D]1MZk07"CVpȊd`3s93C0㚀![Rte!}?F 3}93ƃ9#bj vXb>@0}Nkخu*^zT`lJA9іfHmԤBO*C/YOGm=@_Wo6'HM2eСDKNQ3nO13ٽkThI]wڵHg}՛a6Z͛,$Usb~|>Z#| ^xU)%K̚ ݱ:5N<ų72YkQxپ|h>P_?b3Tsz'J-l^`!+d+7^&(xoheǟ{..Mr-Bƈڊ0Qs9\PtPWnvC(C6esT_Ă"u/Q?ۋ"cCY=s5/MR.}<#;7%yޥc2R K%^ZZ+5PҊ%|_vƐ֡%b7л kLw칮܁~v*D>s* {Ngnّ4Zͻ6ELiT (-ۛU=>]J2ޖ@bf$wv*e$M_1MPh*?zrdwٰ:oR"64N3C#~0DCDsՂ K:,sK`0OZbNbiuۦOZeCV\VvEXhFL3Z8)fU1 \lAǀ #BÀ'h̏4ːPļv5㺘i~Ӏ,1ކ}]+d9й_ Ȗ*,cJH풾w2>9l22)mt Df}N[Zjp̺p:D˭ OzZw߸=N gqt]A3l5qܫwz9?O2H#|dBYj>%VPs%"ΓVPs+5zRdWAmkޔE+l5!4!=#Ad/ȫh߰8Κy#6m-!Ps4 5Aޤ)DMA]DMB#PaA"9j] j̺R=3Tء^tΧ G3؀+qRlM/ޯn729\ ojH.DuxgVQf'z@O2@UL٬C,iI%WxVx=v諀1!i5bH#4Vklzމ/;]}?g/7Mѱ!4 seN`!x,umە;7 Ƚ rxcdd``d!0 ĜL  312E&(1dbf2QA?H; 6P#7T obIFHeA*CT 2f0 y]`!UBFک1Y@(&xklUܙytgiXQ!MT@@A"%@ZB߶P (nbDH4bMD؀ UD s4)ͦw{ιw]MB*G>*&#`ADB.B1`UehGU@z[B'hI*3P>ež& ~tDodQ3Ƙ?rpF]|vQ[/0W;#lfWم vOW+#|f+u1W=FjzIV̅>3KFA^$?=A/jO~V"_aGcYWO3_t36"8oi ;Xia7ڬ[lc!CU~~bP['ef ͯj=,OY#Gqft&Ӎax/μ'M}=tʙv1Dk˙vmZsY ,+ Feo|1ՇȻ ,G Ƅ;:;># "&OG~5=ESګʀ\nxecw]y6(k.GB]ʻ}^ ʠRJUQ[,w۳A覆&xT\yqt>pL'n =2lu,c.{?Uh{+FwTCQH_CrZ]bu!5FOFy  jNsaY5Q9ɀȻ$w$ybu 0!%\>#|2%a-{ E'N'Bs's#}JNJit\&m.h2$ 9*Br.\7[W3_m!(?)s6ڍjEDkSLkyj)YVYɪ*Yk4X<[y"c) w_a|:6|^Q :gΐܩ U]1H$!Y^ɓ"!b>L6YEC2 80$4H%xb{eH4mFnt39\PHA,o`ƓtgmvL `!t48dX(xMhAfdY<Հ'/^lUڈ[,mz= "TzT<,T^<{3ebwoY6 ^6YJ ƣ(Z+D.rr\[px Oa"TO|bYM^q`Ѽ ~ry> uq+fSӚڒXo-fuG[f O-#ٖs8~1~?(g 3^e7d^]1ȊHvhGJ_mNBXSJf@Jog$4+Lh>܀H5Gޚ@"!v{-n[$9*^ojTKG_kՐV^滋LȮ8l;̥RkV"O)vӯ-/0>`jӨXZǢ}Lw4$%Oeϊ_oj =*%}l֞ޕlVbt?ԯ̈v!vP'Ƕ&:֧6곍%ݡ&W(߫%$XK$)gr4O}j,稊#qcL\zɧ|ݣ^$IOr?ԱΒe،;'I !$I*y)[*eH] C_/8h$c0@=P z e)_y+!GOkX i xϏGǫC&mF!q'd![p@\"PQ.kmOAFpB 78p@BXX!kQF\=ݞzW^uu%z?ߪ^UR;i_ O(uA>WVo^S1E:nJ]DOx'ノץk7jxzk՛T[FB!tlzCcGرjNj.GҬjFo<&jG<՟[y4vY'qm4DKh=x_h4GOT:n+^hCF:ͲV[Y VF5CX1 c4ViΣw0Ѭ+0߷: Ӝo6xMfJjNdPۃzB? ү{U f{=dAs3Sg IQLfz[4U&~\jbe{խwvo y5of+4G@ع%>e"ECFc-k3 T*Ԭ)$E賡&[j1չ<5Q]-#CX4?LP0{a &ZEN]ѬJ+4x}[4*^,kb.UJb>ԛŽTofR.+=K-[lTe+_j(&ّ0LXzR}d>dcaRE Q>(%FׁchÀ 봺n8`)vX嘙 ?UN Ũb!GdPng9uY8/0CIMlMK#a}4m~b{_IjmhLjِa7 Alt kOCfj3z24]ۦ}/V3Ӄf{>(Ү MY[O[mVΌlLC)`.W26zf_ WviW}3&~|NTlfKlI2 ֲ;֍C=tx|=:f-7b]qGKJ`!Ba`W !}t+{T ``Љ- x]HQϽݙ]uM""d^ 0vVEr{{0ߔ؈B{@(^DT |( z fL{o9rgv(%e a0_!(<%Bj#mx,lW `_ti,@w)yP')ֈ]^*ɦx-EoJkO]`}G/}ìٽ A[^DءLwp O[n&a+jr3-ꉝH]L';V4zoPFlr_ƚ/.ACnbf5>c<  k|\k9ִVrI''stR*ּaOCyɼ$N &3nq S1Ij899K1IqX9sְbsՕu'z!|E,_+p!ou,] 7(äFs@~'/k6 X5!}n$`!3E$Q9Kf6"4jMnDg:Yg-(Gg2 1SkHk2eX3X35ޝGVg}RE2DXs:"i䃄ɸK$^U0ylMkqv]S1(S< crj|zttIQg5m!KE(ܔɤЁW~i\`!..{w1u+@ YxOhPyK6]SMA ` "˜LD6Q׃\aε9ﰋsЃ<6Fn^Da^d:[ߟؒO~~ym0o* &h) # jҵ>FF%Ph{H_OA?i9' r ir,, "x}eY WwCp1>#nAg(;GjaQw4edDT<[ ?e׌b8/1&7ľ_0hPa|4] <-9Aގak?Q{μޭ^>g~ֹ4ZRdY_*¢d h< ;$Il& RN&vR$}_)j \\xʹ֖2!0gQrN֐sƒ2VyXa:!ѱiEsh]&SU0Lrd' ]&ؓ\kL+ӳ`WzW=J1;L5 'c!$%{}*:+xc2J aAu uL \1g5X%~)Us]eöJL?Aa?|6-ᓓy]& AĞSk&_3#d6q8{f2 ;`OTV/"{VYO`! fDmqk84 hjxR=KA};8r :)he#."&]#9%4h{KQKR+xJwo޾]k(B<:RY\)%0 'AIٺ4E Ӈ3 r9z>ǝ5?m9jFw _d*xdUe穈8g9$1v0:3+6Kɖ*Y]V{W01rUjZ(;ޮZS*w4VPTR|9 F$#M^Xō2jy$5{n& [w9-MMڽ: w\.G\:: lɱ+֖ J +ܓW׀(~R{q䨏fɋ%aK1X& <^B/0޻J[*ayũ#\!5Y[/{H o-d(E%#Fau R5Y-RCVonZ93FoLq4RN.;wKƮz;#u?{/nlu 診nWtoή~- /:דR;QfX,EYIW5+|Z+ H3<(   -Equation Equation.COEE206CorelEquation! 2.0 Equation.Equation Equation.COEE206CorelEquation! 2.0 Equation0Equation Equation.COEE206CorelEquation! 2.0 Equation.?Equation Equation.COEE206CorelEquation! 2.0 Equation2@Equation Equation.COEE206CorelEquation! 2.0 Equation5AEquation Equation.COEE206CorelEquation! 2.0 Equation7BEquation Equation.COEE206CorelEquation! 2.0 Equation9CEquation Equation.COEE206CorelEquation! 2.0 Equation;DEquation Equation.COEE206CorelEquation! 2.0 Equation=EEquation Equation.COEE206CorelEquation! 2.0 Equation?FEquation Equation.COEE206CorelEquation! 2.0 EquationAGEquation Equation.COEE206CorelEquation! 2.0 EquationJNEquation Equation.COEE206CorelEquation! 2.0 EquationeWEquation Equation.COEE206CorelEquation! 2.0 Equation}ZEquation Equation.COEE206CorelEquation! 2.0 Equation[Equation Equation.COEE206CorelEquation! 2.0 Equation\Equation Equation.COEE206CorelEquation! 2.0 Equation]Equation Equation.COEE206CorelEquation! 2.0 Equation/0(  0;[0 0 000$([\{b00 000000000  0=] 0 0 0000 2 3 !A0C0E0G0I0c00000000000000000!%),.:;?]}acdeghijklmnopDTimes New Roman(0(B 0 DArialNew Roman(0(B 0 " DMonotype Sorts(0(B 0 0DGenevae Sorts(0(B 0 @DSymbole Sorts(0(B 0 PDMath1e Sorts(0(B 0 @ .@  @@``  @n?" dd@  @@`` ?     & -&)o2$$KOV}m9jd2$||Mu"w2$OۍkY22a>D U2$ 6K7%3H^2$A\~٢" YL2$d*hql<K2$Xoү׋'ó޾,= 2$!#X1V i 2$WR4A̕pr 2$1JE5hQI!  2$d+73$2$x,umە;72$UBFک1Y$$2$t48d"$z e)_y+!GX 2$a`W !}t+{J&2$..{w1u+-*2$ fDmqk8"-2$MU(@z? .# lAA1? 3|3f@ m g4MdMd@B 0ppp@ <4BdBdlpC 0uʚ;ʚ;r0___PPT10 2___PPT9/ 0? %#  INTRODUCTION TO MECHANICS ,$$1 Erian Armanios School of Aerospace Engineering 2 21  INTRODUCTIONWhat is Mechanics? Science which describes and predicts the conditions of rest or motion of bodies under the action of forces Mechanics of rigid bodies Mechanics of deformable bodies Mechanics of fluids kMk     $ ( Mechanics of rigid bodies Negligible deformation deformation do not affect the conditions of equilibrium or motion resistance of material to failure Statics bodies at rest dynamics bodies in motion d d      $*'#Fundamental Concepts and PrinciplespAristotle ( 384-322 B.C.) Archimedes (287-212 B.C.) Newton ( 1642-1727) Satisfactory formulation modified by D Alembert, Lagrange, Hamilton Limitations Einstein s theory of relativity ^HP HP   > H 8 Space Associated with position coordinates measured from origin Time Associated with event Mass Characterize and compare bodies Force Action of one body on another actual contact or at a distance !  !      )  Force Represented by a vector point of application magnitude direction Space, time and mass Absolute concepts, independent of each other Force depends on mass and acceleration Study conditions of rest or motion of particles and rigid bodies in terms of the 4 basic concepts )Tb)  T  b*!Particle and Rigid BodyParticle very small amount of matter occupies a single point in space associated with set of concurrent forces Rigid Body combination of large number of particles occupying fixed positions w.r.t. each other associated with nonconcurrent forces \ f { f {  +"Fundamental PrinciplesLParallelogram Law addition of forces resultant of 2 forces is the diagonal B::L>/ Transmissibility condition of equilibrium or motion of a rigid body unchanged if force acting at a given point is replaced by a force of same magnitude and direction at a different point along same line of action .,# Newton s 3 fundamental laws If resultant force acting on a particle is zero, particle will remain at rest if originally at rest and will move with constant speed if originally in motion If resultant force non zero, the particle will have an acceleration proportional to the magnitude of the resultant and in direction of this resultant The forces of action and reaction between bodies in contact have the same magnitude, line of action and opposite sense ./$ 8Newton s law of gravitation 1%Dimensions and UnitsAssociated with the 4 basic concept Fundamental by choice Length : L, meter (m) [mm,cm, km], ( ft) Time: T, second ( sec) [min, hour] Mass: M, Kilogram (kg) [mg,g], (slug) Force: derived $s$     V5 4Application: Find the dimensions of constant R in : ( 35&FORCESForce A push or pull Expressed as a vector Magnitude expressed in a system of units ( lb, N) Direction Point of application: idealized region of application Line of action: passing through point of application and has same direction %<% ) !>  V6' Force Represented as vectors follow parallelogram law for addition Ex1: Determine the horizontal and vertical components of F &8&  47(  X6  Other forces?9*&Unit Vectors and Orthogonal Components>Unit Vectors direction indicators unit magnitude dimensionless. 2 2I1J4Useful resultsdEx 2: Determine the components and direction of a force of F Newtons with A B as its line of action 6^^=!K3 Y7Components of ForceDot product scalar product &  L2H0Moment of a forceMoment of a force about a point turning effect of a force Common sense vector representation sum of the moments of the components of a force Resultant of a system of forces concurrent nonconcurrentv S  S   8) #Moment of a force about a point Common sense definition measure of the force to turn a body Vector magnitude: magnitude of force x perpendicular distance between line of action of force and point direction: perpendicular to the plane defined by the point and the line of action of the force^ + +  ^8 6Moment of a force about a point Vector representation F  6P  ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,?lKd@   d lA@  d`"  n?" dd@   @@``PR    @ ` ` p>> " (  28 y yj   :B7 C DEHFP @1?q 6 6 n(dx  G b q %(@B yx2  HG1?   `xaxa1 ?P  T Click to edit Master title style! !@  Z$xaxa1 ?  RClick to edit Master text styles Second Level Third Level Fourth Level Fifth Level!     S   `xaxa1?: LGeorgia Tech - Aerospace Eng   `xaxa1?@ @  ^*    `xaxa1?RF Z*`  Hd޽h @ ? i(3e ,soarings.ppt - Soaring 0 [S@(  p  01 ?   A  ZXgxaxa1 ? @  SClick to edit Master notes styles Second Level Third Level Fourth Level Fifth Level"     TB  s *޽h ? a(80___PPT10.[8U  0 0(   B  s *޽h ? a(80___PPT10.[yZK0 bZP (    # lxaxa1 ?P <$D  0    # ldxaxa1 ? `  <$ 0  "z      p ,$D  0Z  s * P `B   0D `B   0D @ `B   0D @@ `B   0D @ `B   0D@ @ `B  0D @ 0 `B  0D@ p 0 H  0޽h ? i(3e___PPT10.+ED ' = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =-6B#slide(fromRight)*<3<*2Dp' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*+p+0+ ++0+ +i ZK0 `(    # lxxaxa1 ?P<$D  0     # ltxaxa1 ?<$ 0  H  0޽h ? i(3eqi___PPT10I.+ jD' = @B Dl' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*~%(D' =-6B#slide(fromRight)*<3<*~D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*~%(D' =-6B#slide(fromRight)*<3<*~D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+p+0+ ++0+ + ZK0 p*( w   3 r|xaxa1 ?Pp <$ 0  H  0޽h ? i(3e___PPT10.+.jDF' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =-6B#slide(fromRight)*<3<*1D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*1s%(D' =-6B#slide(fromRight)*<3<*1sD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*s%(D' =-6B#slide(fromRight)*<3<*sD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+8+0+ + ZK0 $( w   3 r@"xaxa1 ?P<$D  0     3 r<#xaxa1 ?<$ 0  H  0޽h ? i(3ey___PPT10Y.+D' = @B D|' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-6B#slide(fromRight)*<3<*4D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*4H%(D' =-6B#slide(fromRight)*<3<*4HD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Ha%(D' =-6B#slide(fromRight)*<3<*HaD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*a%(D' =-6B#slide(fromRight)*<3<*aD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+p+0+ ++0+ +! ZK0 P*( w P P 3 r7xaxa1 ?Pp <$ 0  H P 0޽h ? i(3e___PPT10.+S&DV' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B#slide(fromRight)*<3<*PD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B#slide(fromRight)*<3<*PD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P@%(D' =-6B#slide(fromRight)*<3<*P@D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P@E%(D' =-6B#slide(fromRight)*<3<*P@ED' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*PE[%(D' =-6B#slide(fromRight)*<3<*PE[D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P[`%(D' =-6B#slide(fromRight)*<3<*P[`D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P`%(D' =-6B#slide(fromRight)*<3<*P`D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B#slide(fromRight)*<3<*PD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B#slide(fromRight)*<3<*PD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-6B#slide(fromRight)*<3<*P+8+0+P + ZK0 *( w   3 rFxaxa1 ?Pp <$ 0  H  0޽h ? i(3e___PPT10.+.jDN' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =-6B#slide(fromRight)*<3<*3D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*3=%(D' =-6B#slide(fromRight)*<3<*3=D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*=G%(D' =-6B#slide(fromRight)*<3<*=GD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*G\%(D' =-6B#slide(fromRight)*<3<*G\D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-6B#slide(fromRight)*<3<*\D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+8+0+ + ZK0 h`( w   3 rTUxaxa1 ?P     3 rPVxaxa1 ?<$ 0  H  0޽h ? i(3e___PPT10.+S&DF' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-6B#slide(fromRight)*<3<* D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %%(D' =-6B#slide(fromRight)*<3<* %D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%F%(D' =-6B#slide(fromRight)*<3<*%FD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Fo%(D' =-6B#slide(fromRight)*<3<*FoD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*oz%(D' =-6B#slide(fromRight)*<3<*ozD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*z%(D' =-6B#slide(fromRight)*<3<*zD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+8+0+ + ZK0    ^ ( w   3 rdxaxa1 ?P<$D  0     3 r|exaxa1 ?`<$  0  2 8 /@ /@xB  HDo? `  xB  HDo?  xB  HD1? ` ` xB  HD1? `  xB  HDo? `     Th ?*J  RF14    N@n1? @ RF24    Nl1? 0  AF$rB  BD1?  rB  BD1?`  rB  BD1?    Hx1?fz /  9xrB  BD1? 0    H|1?p  1ys@  @   @ l2  <1?0    <z1? @  ;qH  0޽h ? i(3e[S___PPT103.+=(D' = @B DV' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!slide(fromLeft)*<3<*D' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =-}6B!slide(fromLeft)*<3<*%D' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%K%(D' =-}6B!slide(fromLeft)*<3<*%K+p+0+ ++0+ +  >6 ( w l  C ܐ0   "F ` `  p  s BC:DExF1?^^'o[;7gp.~ [.DRmm$b.%7@<FALGQOWYZ`a{|~I+eO0`Y9s^C_-Dw jU 6:)$qe!X TWPG:/ !v(n/g6`OOHV>`2g'oBD@                               `@ Y zxB  HDԔ?  ` xB  HDԔ?  P xB  H CDo?` `   H1? i  =F    H1? @  =F H  0޽h ? i(3e ZK0 *( w   3 rxaxa1 ?Pp <$ 0  H  0޽h ? i(3e  ___PPT10 .+.jD& ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Q%(D' =-6B#slide(fromRight)*<3<*QD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Q%(D' =-6B#slide(fromRight)*<3<*Q+8+0+ +- ZK0   [ ( w   3 rtxaxa1 ?Pp<$  0    s *A ??  8 $D  0  c $A ??0 c 8 $D  0x  ZDxaxa1 ?p @p ,$D  0 XExtends range of application of third law action exerted at a distance Particular case F**  s *A ?? Ke8 $D  0j  B1?PpB  HD1?pd  <1?0pB  HDo?ppB  HDo?0jB  BD1? @jB  BD1?vB  ND1? @0  N$1?z F  Nd1? F  N81? ;M  N1?&/ ;m  <'1?`  rH  0޽h ? i(3eF!>!___PPT10!.+yA׍D ' = @B DA ' = @BA?%,( < +O%,( < +D' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-}6B!slide(fromLeft)*<3<*Dp' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-}6B!slide(fromLeft)*<3<**D' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<**G%(D' =-}6B!slide(fromLeft)*<3<**GD' =%(D' =%(DN' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*GW%(D' =-}6B!slide(fromLeft)*<3<*GWDp' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*Dp' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+4 8?RCB?BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?RCB?BCB#ppt_yB*Y3>B ppt_y<*+p+0+ ++0+ + ZK0 ( w   3 rtxaxa1 ?P<$D  0     3 r\xaxa1 ? <$ 0  l  0A .?? 0 .H  0޽h ? i(3eyq___PPT10Q.+D' = @B Dt' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-6B#slide(fromRight)*<3<*$D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$:%(D' =-6B#slide(fromRight)*<3<*$:D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:d%(D' =-6B#slide(fromRight)*<3<*:dD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-6B#slide(fromRight)*<3<*dD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+p+0+ ++0+ +  z( OWY l  C P  f  s *A e??p eH  0޽h ? i(3e ZK0  $(    3 rxaxa1 ?P<$D  0     3 rxaxa1 ?<$ 0  H  0޽h ? i(3ey___PPT10Y.+ jD' = @B D|' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-6B#slide(fromRight)*<3<*+D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*+]%(D' =-6B#slide(fromRight)*<3<*+]D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]g%(D' =-6B#slide(fromRight)*<3<*]gD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*g%(D' =-6B#slide(fromRight)*<3<*gD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*+p+0+ ++0+ +@ ZK0 0( <   3 rxaxa1 ?` <$ 0   P8 @    @ @ ` pp   p  l  <1?P P  2  <1? p  > 2  <1? ` p  > lB  <D1?@p pp lB  B <D1? P lB  <D1?` P rB  BDԔ? p   H(1?@   ;Fl2 B <1?0    H1?F   C30o$H  0޽h ? i(3e___PPT10.+.jD.' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#slide(fromRight)*<3<*D' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*C%(D' =-6B#slide(fromRight)*<3<*CD' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*CI%(D' =-6B#slide(fromRight)*<3<*CID' =%(D' =%(DP' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =-6B#slide(fromRight)*<3<*I+8