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Copyright 2007 `0 + #    6Ȃ  _    Z* n  c 8ALOGOArrow"`OH  0޽h ? 3380___PPT10.-im/ZK0 >6P(  X  0ici  0T ` f$Forging new generations of engineers&%0(2%3`  C 8A 6x6_PLTW_Logo_R P  s *޽h ?"` 33y___PPT10Y+D=' = @B +  @(  r  S Dݜ` `    H  0޽h ? 3380___PPT10.-p6 ]U0*q(    6(3fo |DLet s suppose some campers have pitched their tents and are ready to prepare their supper. They build a structure to support their pot over the campfire to cook:d f <3d` P R i s *̙P p j 0d p  XFree-Body Diagram of Point A  2" 8 pP ` @` PfB U 6D3>P fB V 6D3>P `B W 0DP P P `B X 0DP`B Y 0D PfB [B 6D1  l2 \ <dP pp Z2 ] s *P p fB ^ 6Df3)0 0 fB _ 6Df3)  fB ` 6Df3)  fB a 6Df3)0  l c <3d @P l e <3d  P l d <3dP P l g <3d0 pP  h H+G$H p@0 CPoint A  n HGDHh 0` CPoint B  o HGH pP 0 CPoint C  { 0ИP ?  1P 28  0   @ `2 k 000  lB m <Df3o` 0 lB q <Do` `  r 0 @ p`  LFB. 2f3 f3fB s 6Df3oPp p fB t 6Df3o@ p @  0  ~@ `  u 0 0  LFC. 2f3 f3fB v 6Df3o@ @@ fB w 6Df3o @@  x 0$ P  1P 2fB y 6Do0  fB z 6Do`  lB } <Df3o`    n W?Reaction ForcesArial BlackP  t^d޽h& ?^ff3?0hno ̙33y___PPT10Y+D=' = @B +$ ##@Dm "(   e  63fo p The weight of the pot, P, is 50 lbs. The pot hangs from a rope that bisects the symmetric structure that is 5 ft tall and 3 ft wide. We need angle theta in order to solve for the x and y components.8 p  h ` fB  6D3>P fB  6D3>P `B   0DP P P `B   0DP`B   0D PfB  B 6D1  l2   <dP pp Z2   s *P p fB  6Df3)0 0 fB  6Df3)  fB   6Df3)  fB   6Df3)0  l   <3d @P l   <3d  P l   <3dP P l   <3d0 pP l   <3d` P    HG$H p@0 CPoint A    H0GDHh 0` CPoint B    H GH pP 0 CPoint C  '  0Q ?  1P 2`B )  0DPPP`B *  0DP`B +  0D   .  0<p`  45 ft 2 /  0 `` 46 ft 2fB 1 6D  ` fB 2  6D P fB 3  6DpfB 4 B 6DPP 8  p k ` p N  0t 1P 2 @  p i  p`2 D  00 @ lB E <Df3o0` ` lB F  <Do @  @ `  T    G  0|  @ `  MFBX. 2f3 f3fB H  6Df3oPp p fB I  6Df3o@ p fB O  6DopfB P  6DoplB Q <Df3o@` ` lB R <Df3o lB S <Df3o@ @N  @ `  U  0  V  0(  @ `  MFBY. 2f3 f3fB W  6Df3oPp p fB X  6Df3o@ p N  @ `  Y   P Z  0   @ `  MFCY. 2f3 f3fB [  6Df3oPp p fB \  6Df3o@ p N  @ `  ]   p  ^  0  @ `  MFCX. 2f3 f3fB _  6Df3oPp p fB `  6Df3o@ p 8 `  j  fb a B 6op c  0  45 ft 2 d  0"  @`  43 ft 22 e  CIZENHQ `T+TIZ`T+TIZ`T+TIZ`TP| f  0& P@ >q  2 g 0* % `P  Btan q = opp / adj q = tan-1(opp / adj) q = tan-1 (5 ft / 3 ft) q = 59TG 2>" m n W?Reaction ForcesArial BlackP  t^d޽h& ?^ff3O@    e  ̙33y___PPT10Y+D=' = @B +$ ##PDt$"( $c $ $ 68 3fo@ p8Solve for the scalar, x and y components of each force:98E 8 p s$` `2 "$ 0pPlB #$ <Df3o p lB $$ <DoP`N  @ `  %$ p  &$ 0 @ `  MFBX. 2f3 f3fB '$ 6Df3oPp p fB ($ 6Df3o@ p  )$ 0X? @ 1P 2fB *$ 6DopfB +$ 6DolB ,$ <Df3o P lB -$ <Df3opPplB .$ <Df3oPN  @ `  /$ pp 0$ 0HD  @ `  MFBY. 2f3 f3fB 1$ 6Df3oPp p fB 2$ 6Df3o@ p N  @ `  3$ 0@` 4$ 0dJ  @ `  MFCY. 2f3 f3fB 5$ 6Df3oPp p fB 6$ 6Df3o@ p N  @ `  7$ P 8$ 0xP  @ `  MFCX. 2f3 f3fB 9$ 6Df3oPp p fB :$ 6Df3o@ p  [$ 0 V G `  #FBX = FB cos(59) FBY = FB sin(59)v$ 2     & 8 `  q$ ` lB B$ <Df3o`0 0 N  @ `  D$ P`   E$ 0`  @ `  MFBX. 2f3 f3fB F$ 6Df3oPp p fB G$ 6Df3o@ p lB L$ <Df3o0 N  @ `  N$ 0  O$ 0Lg  @ `  MFBY. 2f3 f3fB P$ 6Df3oPp p fB Q$ 6Df3o@ p lB V$ <Df3o`0 N  0  W$ @ X$ 0m  0  LFB. 2f3 f3fB Y$ 6Df3o@ @@ fB Z$ 6Df3o @@ 2 \$ CIZENHQ `T+TIZ`T+TIZ`T+TIZ`T <  ]$ 0s @P:  J 59$ 2XB ^$ 0D   n$ 0,x  p #FCX = FC cos(59) FCY = FC sin(59)v$ 2     6 8  0  r$ 0 lB _$ <Df3op0 0 N  @ `  `$ ``   a$ 0̃  @ `  MFCX. 2f3 f3fB b$ 6Df3oPp p fB c$ 6Df3o@ p lB d$ <Df3opp0 N  @ `  e$   f$ 00  @ `  MFCY. 2f3 f3fB g$ 6Df3oPp p fB h$ 6Df3o@ p lB i$ <Df3opp0 N  0  j$ @ k$ 0  0  LFC. 2f3 f3fB l$ 6Df3o@ @@ fB m$ 6Df3o @@ 2 o$B CNENG]HJ'9Q `T>QN`T>QN'9>QN'9p'  p$ 0 @0:  N 59$ 2 t$ n W?Reaction ForcesArial BlackP $ t^d޽h& ?^ff3/ \$o$ ̙33y___PPT10Y+D=' = @B + `g((  -CH1CDd1C ( ( 6\ 3fo  nSum the forces in the positive x and y directions. Assume the positive y-direction is up (+), and the positive x direction is to the right (). ***Remember the forces will sum to zero because we are assuming that the structure is in static equilibrium.Vm\1m 8    f( N  @ `  G(    H( 0<  @ `  MFBX. 2f3 f3fB I( 6Df3oPp p fB J( 6Df3o@ p _@ P` p  e(P` p `2 D( 0` ` lB E( <Df3oP  lB F( <Do0 0  K( 04    1P 2fB L( 6Do0 0 fB M( 6Do0 0 lB N( <Df3o`  lB O( <Df3o @ lB P( <Df3o` `@ N  @ `  Q( P   R( 0  @ `  MFBY. 2f3 f3fB S( 6Df3oPp p fB T( 6Df3o@ p N  @ `  U(  p  V( 0  @ `  MFCY. 2f3 f3fB W( 6Df3oPp p fB X( 6Df3o@ p N  @ `  Y(    Z( 0  @ `  MFCX. 2f3 f3fB [( 6Df3oPp p fB \( 6Df3o@ p  _( 0ā P   3  2 g( n W?Reaction ForcesArial BlackP ( t^d޽h& ?^ff3 ̙33y___PPT10Y+D=' = @B + !#LD(  L F    L  ` N  @ `  L    L 0ˁ  @ `  MFBX. 2f3 f3fB L 6Df3oPp p fB L 6Df3o@ p mN P` p   L P` p `2  L 0` ` lB  L <Df3oP  lB  L <Do0 0   L 0Ё    1P 2fB L 6Do0 0 fB L 6Do0 0 lB L <Df3o`  lB L <Df3o @ lB L <Df3o` `@ N  @ `  L P   L 0Ձ  @ `  MFBY. 2f3 f3fB L 6Df3oPp p fB L 6Df3o@ p N  @ `  L  p  L 0Dہ  @ `  MFCY. 2f3 f3fB L 6Df3oPp p fB L 6Df3o@ p N  @ `  L    L 0  @ `  MFCX. 2f3 f3fB L 6Df3oPp p fB L 6Df3o@ p U8   "L j L 0   jSolve for the two unknowns using these two equations. S FX = 0; FBX - FCX = 0 FB cos(59) - FC cos(59) = 0 +S FY = 0; FBY + FCY - P = 0 FB sin(59) + FC sin(59) - 50 = 0 |60P2; 2!0x2# 20P26                L 0    3+ 2XB !L 0D  #L n W?Reaction ForcesArial BlackPH L 0޽h ? 3333___PPT10i.؂Y+D=' = @B +R  y q p-,( \  , , 0< P   3  2XB !, 0D @ XB ", 0D XB #,@ 0DP XB $,@ 0D ` P XB %, 0D@@0 @XB &, 0D XB ',@ 0D `XB (,@ 0D  XB ),@ 0Dpp0`8  ,,D , 0  \Equation 1: FB cos(59) - FC cos(59) = 0 Equation 2: FB sin(59) + FC sin(59) - 50 = 0 Equation 1 shows that FB equals FC : FB cos(59) = FC cos(59) cos(59) cos(59) Replace FC with FB in Equation 2 since they are the same: FB sin(59) + FB sin(59) - 50 = 0 2 FB sin(59) = 50 2 sin (59) 2 sin (59) FB = 29.16 lbs d\0P2 2      )      3  +    2 `2 *, 0P`  -, n W?Reaction ForcesArial BlackP , t^d޽h& ?^ff3 ̙33y___PPT10Y+D=' = @B +w #g0(  0u 0 6 3fo`   If FB = 29.16 lbs, then FC = 29.16 lbs because of Equation 1. Solve for the scalar x and y components: FBX = FB cos(59) = 29.16 lbs * cos (59) = 15 lbs FBY = FB sin(59) = 29.16 lbs * sin (59) = 25 lbs These scalar quantities are the same for the components of FC.>)F0F2  N  *  e  0 0`܌ P   3  2N8  pJ d0& p`2 -0 0P @ lB .0 <Df3o P lB /0 <Do@ P  00 0G P `J :50 lbs 2lB 10 <Df3o 0 lB 20 <Df3oP@ P lB 30 <Df3o@   40 0  z  >15 lbs 2f3 50 08 @0 *  >25 lbs 2f3 60 0t 0 *  >25 lbs 2f3 70 0  pz  >15 lbs 2f3 8    f0` T @+ c0#   fB 80 6D3>p @fB 90 6D3>pp`B ;0 0Dp `B <0 0Dp`B R0 0Do lB S0 <Df3o? m  W0 0 @O  >15 lbs 2f3lB X0B <Df3o?RlB Y0 <Df3o?p p lB [0 <Df3o?  \0 0 !@ >15 lbs 2f3 ]0 0   + >25 lbs 2f3 ^0 0` !+ >25 lbs 2f3 _0 0    :50 lbs 2T  @ b0#  `f `0 6G) @ a0 6! f3o @ `*Reactions at the supports of the structure+(2+ g0 n W?Reaction ForcesArial BlackP 0 t^d޽h& ?^ff3 ̙33y___PPT10Y+D=' = @B +v) ((W^'(    2W?Force/Free Body DiagramsArial Black0 @  6$) 3fo Supports are translated into forces and moments in a free body diagrams. The following are three common supports and the forces and moments used to replace them.%8 0  ^   6> 3fo`   : 2 `B  0D@@`B  0D  l2  <3f? @   0X0 3f  Y)Roller: Pin Connection: Fixed Support:**`B   0Dpp`B   0D `B   0D ` `B  B 0D  `B  B 0D  `B B 0D @ `B B 0D@  `B B 0D ` `B  0D@ `B  0D  `B B 0D@ `B  0D@pp`B B 0Dpp`B  0D@`B  0D0`B  0D`B B 0D0`B  0D0`p`B B 0Dp``B  0D0lB  <DԔ  0: 3f0 JFy, 2 `B   0D` 0 `B !B 0D` `B "B 0D `B #B 0D  `B $B 0D `B %B 0D 0 `B & 0D p `B ' 0Dp p `B (B 0D `B ) 0D @` `B *B 0D` @ `B + 0D  `B /B 0D@ p `B 0 0D0  `B 1 0D  `B 2B 0D0  `B 3 0D0 `` `B 4B 0D` ` `B 5 0D 0 lB 6 <DԔ` P  7 0PE 3fO   JFy, 2 lB 8 <DԔ` `  9 0J 3f 0A  JFx, 2  : 6G 3fo ! : 2 `B ; 0D0P P `B < 0DP @`B =B 0D0@@`B > 0D0P ` `B ?B 0D ` `B @ 0D 0@lB A <DԔ lB B <DԔ  `B CB 0Dp `B DB 0Dp  p`B EB 0Dp `B FB 0Dp P `B GB 0Dp P `B H 0DP p P `B I 0Dp P p @`B JB 0D@p @`B K 0DP @ `B LB 0D @ `B M 0D @`B N 0Dp p `B O 0Dp p  P 0X 3f  0 JFx, 2  Q 0\^ 3f JFy, 2 2 R  B ~CE$GL0HI`TQ3fo  ~  ~ `T`T ~ `T`T aj S 0c 3f A  JMo, 2 lB T <Do0  @ 0P  X @p ` U 00P @Z2 V s *  l W <GH0 f Z 6 0 p `2 [ 0 `    t^d޽h& ?^ff3R ̙33y___PPT10Y+D=' = @B +$  0 `4(  d  c $T     s *\T 0    H  0޽h ? 3380___PPT10.V$rPpv.Ejm @O ?@M$-) e  Oh+'0hU@ `l   Reaction Forces$POE - Unit 5 - Lesson 5.1 - StaticsPOE Writing Staffsoreaction, forcessoBCSDion!PLTW General PowerPoint TemplatecsWhitefish Bay Schoolst 26tMicrosoft PowerPointt @u@j@'PGSg  )'    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www Sha4'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___wwwݴլݬǭݼճԬݵ⵵ⴴϳݴǬݳݭլݭͬܬǴdzǭլܬǬݼ֬ǬݴճǬ⴬Ǭլδ֬ͳݭݻܼάάլͭⴭδլͭdzǬǬϴǬǬǬǬǬǴܬǬ۬ݭܬݭܭܬϳݴԭǬܴǭܭǬǬǴͬլջլͳܴͭԵլͭݴִխܻͭͭԬǬǬǬܵܭǴǬǬݵǬݻǭdz⭬dzԬԬճԭܳԭܭݭܬͬݭǴݻݼݻݼǬݭǬǬǬܼǬլԵݭͳάխέԭխͬխάάռմݻܻܵ⵵ܼݵܵݻܴմܻܵݵܵݻݵܴݻܴ⻼ݼܭ⵴ݼ⵴ͬⴳͬͬԬͬͬջԬͬͬ֬ǬǴݴǬǬǬǬǬǬǬǬǬǬǬǬǬǬǬǬǬǬǬdzʹݴͬԳխܴͬͬխάլάͭǬǴǬջݴǬǬǬݼܭǬǬǬǬܴ֭ǬdzͬͬմմԬͬܬͬͬݭͬ֬ǬǭǬǭݼݻݴǬǬǬǬǬǬܼ֬ǬdzάܬԬǬǬǭǬǬǬǬǬǬݭǬdzͬͬͬͬͬխͬͬͬͬͬլͬ֬ǬǭǬǬǬǬǬǬܴխǬǬǬǬǬǬǬݭǬdzͭյܵܵܭͬݻܵܳԬͬԬͭǬdzǬǬǬⴭǬǬǬǬǬdzͬܭͬܭͬܬͬԭͬܭͬ֬ǬǴǬǬǭǬǬdzǬǬǬǬϴǬǬdzάլܻܳլǬǬǴǬǬǬǬⴭǬǬǬǬǬǬǬǬǬdzͬխͬͬԬͬͬάԬͬմάͬ֬ǬǴܳխܼջܬǬdzʹܻܵܵܵԬͭǬǴttootttsttüܬdzͬ㽽oFtutnyԬͬ֬ǬǴLtFGLuLýǬǬNjKyܬǬdzݻܵάoG㓽tԬsRԬܻݵǬǬǴ㓽tooLooosǬǬǭnSRܬǬdzݵܻմմջÙڲͬ,MtܴմյýÒԬǬǬm,&SÙԬͬ+&,uԲǬM&+ԲԬL&MSǬԬǬL&&,LsLG&jGuRytttsmmmrnM&Gj&MLsllKyÙ,&GGG&MnͭsRsǬǬǬK&GGjG& LmǭKStԑt&&GjG&&&Mms,SǬǬnLjGGGGG&&LmK,&usKMGj&GGG&&Mnt&GMtsmlmlmM&GjGGGGGGFML&,tRsmLMGGjGjjGjGGGM&&&SsǬKM&&GGG&&&&%tÓͬnM&&&GGG&&&&MÓǬǬǭmL%&&GG&&,RͬsLM&&G&&&&&&SsǬǬKM&GGG&GGGGGuÙͬmtMMjGjGGjGuÙsǬss%G&GGGLÙsmryRS,M&&&,slmmsL&&&uڬn&G&umԬǬǭK,%Sڬs,SǬKSumstzÙý՜.+,0T    On-screen Show PLTWreej : Times New RomanArialVerdanaSymbol!PLTW General PowerPoint TemplateSlide 1Reaction ForcesSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9 Slide 10  Fonts UsedDesign Template Slide Titles -_x Whitefish Bay SchoolsWhitefish Bay Schools  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~     !"#$%&'()*+,-./012346789:;<>?@ABCDKRoot EntrydO)PicturesCurrent User=SummaryInformation( UPowerPoint Document(DocumentSummaryInformation85