<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bg1.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>1 </div><div class="t m0 x3 h3 y3 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y4 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x5 h4 y5 ff2 fs1 fc1 sc0 ls1 ws1">UNIVERSIDADE FEDERAL DA BAHIA </div><div class="t m0 x6 h4 y6 ff2 fs1 fc1 sc0 ls1 ws1">ESCOLA POLITÉNICA </div><div class="t m0 x4 h4 y7 ff2 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y8 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y9 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 ya ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 yb ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x7 h4 yc ff2 fs1 fc1 sc0 ls1 ws1">PROF. CARLOS ARTHUR M T CAVALCANTE </div><div class="t m0 x4 h3 yd ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 ye ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 yf ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y10 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y11 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x8 h5 y12 ff2 fs2 fc1 sc0 ls1 ws1">APOSTILA<span class="_0 blank"> </span> </div><div class="t m0 x4 h5 y13 ff2 fs2 fc1 sc0 ls1 ws1"> </div><div class="t m0 x9 h5 y14 ff2 fs2 fc1 sc0 ls1 ws1">ENG002 <span class="ff3 ls0">\u2013</span> MECÂNICA <span class="_0 blank"> </span>GERAL II<span class="_0 blank"> </span> </div><div class="t m0 x4 h3 y15 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 xa h2 y16 ff1 fs0 fc1 sc0 ls1 ws1">Versão v0<span class="ls0 ws0">6_070</span>82017 </div><div class="t m0 x4 h3 y17 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y18 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y19 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y1a ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y1b ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y1c ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y1d ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y1e ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y1f ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y20 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y21 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y22 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y23 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y24 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y25 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y26 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y27 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y28 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y29 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y2a ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y2b ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x4 h3 y2c ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 xb h3 y2d ff1 fs1 fc1 sc0 ls1 ws1">Salvador </div><div class="t m0 xc h3 y2e ff1 fs1 fc1 sc0 ls1 ws1">Agosto, 2017 </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi xd y2f w3 h6" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bg2.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>2 </div><div class="t m0 xe h7 y30 ff3 fs3 fc2 sc0 ls1 ws2">Sumário<span class="ff2 ws1"> </span></div><div class="t m0 x2 h3 y31 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h8 y32 ff4 fs0 fc0 sc0 ls1 ws1">SUMÁRIO <span class="_2 blank"></span><span class="ls13 ws3">.........................................................................................................................................................<span class="ls1 ws1"> <span class="_2 blank"></span>2<span class="ff5 fs4"> </span></span></span></div><div class="t m0 x2 h8 y33 ff4 fs0 fc0 sc0 ls1 ws1">APRESENTAÇÃO<span class="_0 blank"> </span> <span class="_2 blank"></span><span class="ls13 ws3">...............................................................................................................................................<span class="ls1 ws1"> <span class="_2 blank"></span>5<span class="ff5 fs4"> </span></span></span></div><div class="t m0 x2 h8 y34 ff4 fs0 fc0 sc0 ls1 ws4">1<span class="ff5 fs4 ls2 ws1"> </span><span class="ws1">INTRODUÇÃO<span class="_0 blank"> </span> <span class="_0 blank"> </span><span class="ls13 ws3">.............................................................................................................................................</span> <span class="_2 blank"></span>6<span class="ff5 fs4"> </span></span></div><div class="t m0 x2 h8 y35 ff4 fs0 fc0 sc0 ls1 ws4">2<span class="ff5 fs4 ls2 ws1"> </span><span class="ws1">CINEMÁTICA DE PARTÍ<span class="_0 blank"> </span>CULAS <span class="_3 blank"></span><span class="ls13 ws3">......................................................................................................................<span class="ls1 ws1"> <span class="_2 blank"></span>7<span class="ff5 fs4"> </span></span></span></span></div><div class="t m0 xf h8 y36 ff5 fs0 fc0 sc0 ls1 ws5">2.1<span class="fs4 ls3 ws1"> </span><span class="ls4">P</span><span class="fs5 ws6">OSIÇÃO</span><span class="ws1"> <span class="_4 blank"></span><span class="ls5 ws7">......................................................................................................................................................<span class="ls1 ws1"> 8<span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y37 ff5 fs0 fc0 sc0 ls1 ws5">2.2<span class="fs4 ls3 ws1"> </span><span class="ws4">V<span class="fs5 ws6">ELOCIDADE</span><span class="ws1"> <span class="_4 blank"></span><span class="ls5 ws7">.................................................................................................................................................<span class="ls1 ws1"> 9<span class="fs4"> </span></span></span></span></span></div><div class="t m0 xf h8 y38 ff5 fs0 fc0 sc0 ls1 ws5">2.3<span class="fs4 ls3 ws1"> </span><span class="ws4">A<span class="fs5 ws6">CELERAÇÃO</span><span class="ws1"> <span class="_5 blank"></span><span class="ls5 ws7">...............................................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">10</span><span class="fs4 ls1"> </span></span></span></span></span></div><div class="t m0 xf h8 y39 ff5 fs0 fc0 sc0 ls1 ws5">2.4<span class="fs4 ls3 ws1"> </span><span class="ws4">C<span class="fs5 ws1">OMPONENTES </span>C<span class="fs5 ws1">ARTESIANAS DO<span class="_4 blank"></span>S <span class="fs0 ws4">V</span>ETORES <span class="fs0 ls4">P</span><span class="ws6">OSIÇÃO<span class="fs0 ls7">,</span></span> <span class="fs0 ws4">V</span>ELOCIDAD<span class="_4 blank"></span>E E <span class="fs0 ws4">A</span><span class="ws6">CELERAÇÃO</span><span class="fs0"> <span class="_2 blank"></span><span class="ls5 ws7">.................................................<span class="ls6 ws1"> <span class="ls14 ws8">11</span><span class="fs4 ls1"> </span></span></span></span></span></span></div><div class="t m0 x10 h8 y3a ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 y3b ff5 fs6 fc0 sc0 ls1 ws9">2.4.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 01 </span><span class="ff6">\u2013</span><span class="ws1"> Movimento 3D <span class="_7 blank"></span><span class="ls9 wsa">......................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">13</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y3c ff5 fs6 fc0 sc0 ls1 ws9">2.4.1.2<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 02 </span><span class="ff6">\u2013</span><span class="ws1"> movimento 2D. <span class="_2 blank"></span><span class="ls9 wsa">.....................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">15</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y3d ff5 fs6 fc0 sc0 ls1 ws9">2.4.1.3<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 03 </span><span class="ff6">\u2013</span><span class="ws1"> movimento 1D. <span class="_2 blank"></span><span class="ls9 wsa">.....................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">18</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y3e ff5 fs0 fc0 sc0 ls1 ws5">2.5<span class="fs4 ls3 ws1"> </span><span class="ws4">S<span class="fs5 ws1">OBRE A ARBITRARIEDADE DA <span class="_4 blank"></span>ESCOLHA DO SISTEMA DE <span class="_4 blank"></span>COORDENADAS<span class="_4 blank"></span><span class="fs0"> <span class="ls5 ws7">..................................................................</span><span class="ls6"> <span class="ls14 ws8">20</span></span><span class="fs4"> </span></span></span></span></div><div class="t m0 x10 h8 y3f ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 y40 ff5 fs6 fc0 sc0 ls1 ws9">2.5.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 04. <span class="_3 blank"></span><span class="ls9 wsa">.................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">20</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y41 ff5 fs6 fc0 sc0 ls1 ws9">2.5.1.2<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 05. <span class="_3 blank"></span><span class="ls9 wsa">.................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">22</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y42 ff5 fs6 fc0 sc0 ls1 ws9">2.5.1.3<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 06. <span class="_3 blank"></span><span class="ls9 wsa">.................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">23</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y43 ff5 fs0 fc0 sc0 ls1 ws5">2.6<span class="fs4 ls3 ws1"> </span><span class="ws4">S<span class="fs5 ws1">OBRE A VINCULAÇÃO ENTRE O<span class="_4 blank"></span> SISTEMA DE COOR<span class="_4 blank"></span>DENADAS E OS ÂNGUL<span class="_4 blank"></span>OS DOS VETORES<span class="fs0">.<span class="_4 blank"></span> <span class="_7 blank"></span><span class="ls5 ws7">..........................................<span class="ls6 ws1"> <span class="ls14 ws8">24</span><span class="fs4 ls1"> </span></span></span></span></span></span></div><div class="t m0 x10 h8 y44 ff5 fs4 fc0 sc0 ls1 ws1"> </div><div class="t m0 x12 h8 y45 ff5 fs4 fc0 sc0 ls1 ws1"> </div><div class="t m0 x11 h8 y46 ff5 fs6 fc0 sc0 ls1 ws9">2.6.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 07 <span class="_3 blank"></span><span class="ls9 wsa">..................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">24</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y47 ff5 fs6 fc0 sc0 ls1 ws9">2.6.1.2<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 08. <span class="_3 blank"></span><span class="ls9 wsa">.................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">26</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y48 ff5 fs0 fc0 sc0 ls1 ws5">2.7<span class="fs4 ls3 ws1"> </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTO </span><span class="ws4">R<span class="fs5 ws1">ELATIVO A UM </span>S<span class="fs5 ws1">ISTE<span class="_4 blank"></span>MA DE <span class="fs0 ws4">C</span>OORDENADAS <span class="_4 blank"></span>EM <span class="fs0 ws4">T</span><span class="ws6">RANSLAÇÃO</span><span class="fs0"> <span class="_5 blank"></span><span class="ls5 ws7">...........................................................<span class="ls6 ws1"> <span class="ls14 ws8">27</span><span class="fs4 ls1"> </span></span></span></span></span></span></div><div class="t m0 x10 h8 y49 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 y4a ff5 fs6 fc0 sc0 ls1 ws9">2.7.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 09 </span><span class="ff6">\u2013</span><span class="ws1"> Movimento Relativo. <span class="ls9 wsa">............................................................................</span> <span class="ls15 wsb">28</span><span class="fs4"> </span></span></div><div class="t m0 xf h8 y4b ff5 fs0 fc0 sc0 ls1 ws5">2.8<span class="fs4 ls3 ws1"> </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTOS </span><span class="ws4">D<span class="fs5 ws6">EPENDENTES</span><span class="ws1"> <span class="_5 blank"></span><span class="ls5 ws7">.........................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">31</span><span class="fs4 ls1"> </span></span></span></span></span></div><div class="t m0 x10 h8 y4c ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 y4d ff5 fs6 fc0 sc0 ls1 ws9">2.8.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 10 </span><span class="ff6">\u2013</span><span class="ws1"> Movimentos Dependentes. <span class="ls9 wsa">..................................................................</span> <span class="ls15 wsb">32</span><span class="fs4"> </span></span></div><div class="t m0 x11 h8 y4e ff5 fs6 fc0 sc0 ls1 ws9">2.8.1.2<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 11 </span><span class="ff6">\u2013</span><span class="ws1"> Movimentos Dependentes. <span class="ls9 wsa">..................................................................</span> <span class="ls15 wsb">36</span><span class="fs4"> </span></span></div><div class="t m0 xf h8 y4f ff5 fs0 fc0 sc0 ls1 ws5">2.9<span class="fs4 ls3 ws1"> </span><span class="ws4">C<span class="fs5 ws1">OMPONENTES </span>T<span class="fs5 ws1">ANGENCIAL E </span><span class="lsb">N</span><span class="fs5 ws6">OR<span class="_2 blank"></span>MAL<span class="fs0 ws1"> <span class="ls5 ws7">..........................................................................................................</span><span class="ls6"> <span class="ls14 ws8">39</span></span><span class="fs4"> </span></span></span></span></div><div class="t m0 x10 h8 y50 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 y51 ff5 fs6 fc0 sc0 ls1 ws9">2.9.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 12. <span class="_3 blank"></span><span class="ls9 wsa">.................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">42</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y52 ff5 fs6 fc0 sc0 ls1 ws9">2.9.1.2<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 13 </span><span class="ff6">\u2013</span><span class="lsc ws1"> <span class="ff6 ls1">Análise \u201ccompleta\u201d de um movimento familiar para consolidar </span></span></div><div class="t m0 x7 h8 y53 ff5 fs6 fc0 sc0 ls1 ws1">conceitos e metodologia.<span class="ls9 wsa">..............................................................................................................</span> <span class="ls15 wsb">44</span><span class="fs4"> </span></div><div class="t m0 x11 h8 y54 ff5 fs6 fc0 sc0 ls1 ws9">2.9.1.3<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 14_A<span class="ls9 wsa">..............................................................................................................</span> <span class="ls15 wsb">51</span><span class="fs4"> </span></span></div><div class="t m0 x11 h8 y55 ff5 fs6 fc0 sc0 ls1 ws9">2.9.1.4<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 14_B <span class="_5 blank"></span><span class="ls9 wsa">..............................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">52</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 y56 ff5 fs6 fc0 sc0 ls1 ws9">2.9.1.5<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 15. Exemplo-Ilustrativo de um movimento 3D. <span class="_7 blank"></span><span class="ls9 wsa">............................................<span class="ls1 ws1"> <span class="_2 blank"></span><span class="ls15 wsb">56<span class="fs4 ls1 ws1"> </span></span></span></span></span></div><div class="t m0 xf h8 y57 ff5 fs0 fc0 sc0 ls1 ws4">2.10<span class="fs4 lsd ws1"> </span>S<span class="fs5 ws1">ISTEMA DE </span>C<span class="fs5 ws1">OORDENADAS </span><span class="ls4">P</span><span class="fs5 ws1">OLAR<span class="_4 blank"></span>ES E <span class="fs0 ws4">C</span>OMPONENTES <span class="fs0 lse">R</span>ADI<span class="_4 blank"></span>AL E <span class="fs0 ws4">T</span>RANSVERSAL D<span class="_4 blank"></span>A <span class="fs0 ws4">V</span>ELOCIDADE E DA </span></div><div class="t m0 xd h8 y58 ff5 fs0 fc0 sc0 ls1 ws4">A<span class="fs5 ws6">CELERAÇÃO</span><span class="ws1"> <span class="_5 blank"></span><span class="ls5 ws7">...............................................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">62</span><span class="fs4 ls1"> </span></span></span></span></div><div class="t m0 x13 h8 y59 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 y5a ff5 fs4 fc0 sc0 ls1 ws1"> </div><div class="t m0 x12 h8 y5b ff5 fs4 fc0 sc0 ls1 ws1"> </div><div class="t m0 xf h8 y5c ff5 fs0 fc0 sc0 ls1 ws4">2.11<span class="fs4 lsd ws1"> </span>S<span class="fs5 ws1">ISTEMA DE </span>C<span class="fs5 ws1">OORDENADAS </span>C<span class="fs5 ws1">ILÍND<span class="_4 blank"></span>RICAS <span class="ff6 fs0 ws4">\u2013</span> <span class="fs0 ws4">C</span>OMPONENTES <span class="fs0 ws4">R</span><span class="ws6">ADIAL<span class="fs0 ls7">,</span></span> <span class="fs0 ws4">T<span class="_4 blank"></span><span class="fs5 ws1">RANSVERSAL E <span class="fs0 ws4">A</span><span class="ws6">XIAL<span class="_4 blank"></span><span class="fs0 ls6 ws1"> <span class="ls5 ws7">.......................................</span> <span class="ls14 ws8">74</span><span class="fs4 ls1"> </span></span></span></span></span></span></div><div class="t m0 x13 h8 y5d ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x2 h8 y5e ff4 fs0 fc0 sc0 ls1 ws4">3<span class="ff5 fs4 ls2 ws1"> </span><span class="ws1">CINÉTICA DE PARTÍCUL<span class="_0 blank"> </span>AS: APLICAÇÃO DIRET<span class="_0 blank"> </span>A DA 2ª LE<span class="_0 blank"> </span>I DE NEWT<span class="_0 blank"> </span>ON <span class="_2 blank"></span><span class="ls13 ws3">.....................................................<span class="ls1 ws1"> <span class="_2 blank"></span><span class="ls14 ws8">76<span class="ff5 fs4 ls1 ws1"> </span></span></span></span></span></div><div class="t m0 xf h8 y5f ff5 fs0 fc0 sc0 ls1 ws5">3.1<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws6">NTRODUÇÃO</span><span class="ws1"> <span class="_2 blank"></span><span class="ls5 ws7">................................................................................................................................<span class="_0 blank"> </span>..............<span class="ls6 ws1"> <span class="ls14 ws8">76</span><span class="fs4 ls1"> </span></span></span></span></div><div class="t m0 xf h8 y60 ff5 fs0 fc0 sc0 ls1 ws5">3.2<span class="fs4 ls3 ws1"> </span><span class="ws4">A<span class="fs5 ws1"> </span>2<span class="fs5 ls16 ws1">ª </span><span class="ls10">L</span><span class="fs5 ws1">EI DE </span><span class="lsb">N</span><span class="fs5 ws1">EWTON DO </span><span class="lsa">M</span><span class="fs5 ws6">OVIMENTO</span><span class="ws1"> <span class="_7 blank"></span><span class="ls5 ws7">............................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">76</span><span class="fs4 ls1"> </span></span></span></span></span></div><div class="t m0 xf h8 y61 ff5 fs0 fc0 sc0 ls1 ws5">3.3<span class="fs4 ls3 ws1"> </span><span class="ls11">Q</span><span class="fs5 ws1">UANTIDADE DE </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTO </span><span class="ls10">L</span><span class="fs5 ws1">IN<span class="_4 blank"></span>EAR DE UMA <span class="fs0 ls4">P</span><span class="ws6">AR<span class="_4 blank"></span>TÍCULA<span class="fs0 lsf">.</span><span class="ws1"> <span class="fs0 ws4">T</span>AXA DE <span class="fs0 ws4">V</span>ARIAÇÃO DA <span class="fs0 ws4">Q<span class="_4 blank"></span><span class="fs5 ws1">UANTIDADE DE </span></span></span></span></span></div><div class="t m0 xd h8 y62 ff5 fs0 fc0 sc0 lsa">M<span class="fs5 ls1 ws1">OVIMENTO </span><span class="ls10">L<span class="fs5 ls1 ws6">INEAR</span><span class="ls1 ws1"> <span class="_3 blank"></span><span class="ls5 ws7">....................................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">79</span><span class="fs4 ls1"> </span></span></span></span></span></div><div class="t m0 xf h8 y63 ff5 fs0 fc0 sc0 ls1 ws5">3.4<span class="fs4 ls3 ws1"> </span><span class="ws4">S<span class="fs5 ws1">ISTEMAS DE </span>U<span class="fs5 ws6">NIDADES</span><span class="ws1"> <span class="_7 blank"></span><span class="ls5 ws7">................................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">80</span><span class="fs4 ls1"> </span></span></span></span></span></div><div class="t m0 x10 h8 y64 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 xf h8 y65 ff5 fs0 fc0 sc0 ls1 ws5">3.5<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">QUAÇÕES DE </span><span class="lsa">M</span><span class="fs5 ws6">OVIMENTO</span><span class="ws1"> <span class="_9 blank"></span><span class="ls5 ws7">...........................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">82</span><span class="fs4 ls1"> </span></span></span></span></div><div class="t m0 xf h8 y66 ff5 fs0 fc0 sc0 ls1 ws5">3.6<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">XEMPLOS </span><span class="lsf">I</span><span class="fs5 ws6">LUSTRATIVOS</span><span class="ws1"> <span class="_9 blank"></span><span class="ls5 ws7">...............................................................................................................................<span class="ls6 ws1"> <span class="ls14 ws8">83</span><span class="fs4 ls1"> </span></span></span></span></div><div class="t m0 x10 h8 y67 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div></div><a class="l" data-dest-detail='[2,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:718.040000px;width:457.550000px;height:20.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[5,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:701.830000px;width:457.550000px;height:16.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[6,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:685.620000px;width:457.550000px;height:16.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[7,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:669.410000px;width:457.550000px;height:16.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[8,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:657.210000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[9,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:645.000000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[10,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:632.790000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[11,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:620.590000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[13,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:608.380000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[13,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:597.390000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[15,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:586.410000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[18,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:575.420000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[20,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:563.210000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[20,"XYZ",68,674,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:551.010000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[20,"XYZ",68,633,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:540.020000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[22,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:529.030000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[23,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:518.050000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[24,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:505.840000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[24,"XYZ",68,633,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:493.630000px;width:458.050000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[24,"XYZ",68,633,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:481.430000px;width:457.550000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[24,"XYZ",68,577,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:470.440000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[26,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:459.450000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[27,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:447.250000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[28,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:435.040000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[28,"XYZ",68,715,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:424.050000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[31,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:411.850000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[32,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:399.640000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[32,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:388.650000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[36,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:377.670000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[39,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:365.460000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[42,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:353.250000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[42,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:342.270000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[44,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:331.280000px;width:458.050000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[44,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:320.290000px;width:457.550000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[51,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:309.310000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[52,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:298.320000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[56,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:287.330000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[62,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:275.130000px;width:458.050000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[62,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:262.920000px;width:457.550000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[64,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:250.710000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[66,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:238.510000px;width:458.050000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[66,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:226.300000px;width:457.550000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[74,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:214.090000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[75,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:201.890000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[76,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:181.680000px;width:457.550000px;height:20.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[76,"XYZ",68,735,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:169.470000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[76,"XYZ",68,360,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:157.260000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[79,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:145.060000px;width:458.050000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[79,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:132.850000px;width:457.550000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[80,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:120.640000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[81,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:108.440000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[82,"XYZ",68,524,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:96.229000px;width:443.350000px;height:12.211000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[83,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:84.022000px;width:443.350000px;height:12.207000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[83,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:71.815000px;width:422.100000px;height:12.207000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi xd y2f w4 h9" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bg3.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>3 </div><div class="t m0 x10 h8 y68 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y69 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y6a ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y6b ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y6c ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y6d ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y6e ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y35 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x13 h8 y6f ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 xf h8 y70 ff5 fs0 fc0 sc0 ls1 ws5">3.7<span class="fs4 ls3 ws1"> </span><span class="ls11">Q</span><span class="fs5 ws1">UANTIDADE DE </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTO </span><span class="ws4">A<span class="fs5 ws1">NG<span class="_4 blank"></span>ULAR DE UMA PAR<span class="_4 blank"></span>TÍCULA<span class="fs0 ls6"> <span class="ls5 ws7">............................................................................</span><span class="ls1"> <span class="ls14 wsc">112</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 x10 h8 y71 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y72 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y73 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 xf h8 y74 ff5 fs0 fc0 sc0 ls1 ws5">3.8<span class="fs4 ls3 ws1"> </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTO SUJEITO A UMA </span><span class="ws4">F<span class="fs5 ws1">OR<span class="_4 blank"></span>ÇA <span class="fs0 ws4">C</span><span class="ws6">ENTRAL<span class="fs0 lsf">.</span></span> <span class="fs0 ws4">C</span>ONSERVA<span class="_4 blank"></span>ÇÃO DA <span class="fs0 ls11">Q</span>UANTIDAD<span class="_4 blank"></span>E DE <span class="fs0 lsa">M</span>OVIMENTO </span></span></div><div class="t m0 xd h8 y75 ff5 fs0 fc0 sc0 ls1 ws4">A<span class="fs5 ws6">NGULAR</span><span class="ws1">. <span class="_7 blank"></span><span class="ls5 ws7">................................................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">117</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y76 ff5 fs0 fc0 sc0 ls1 ws5">3.9<span class="fs4 ls3 ws1"> </span><span class="ls10">L</span><span class="fs5 ws1">EI DA </span><span class="ws4">G<span class="fs5 ws1">RAVITAÇÃO </span>U<span class="fs5 ws1">NIVERSAL D<span class="_4 blank"></span>E <span class="fs0 lsb">N</span><span class="ws6">EWTON</span><span class="fs0"> <span class="_7 blank"></span><span class="ls5 ws7">..................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">119</span><span class="fs4"> </span></span></span></span></span></span></div><div class="t m0 x10 h8 y77 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 xf h8 y78 ff5 fs0 fc0 sc0 ls1 ws4">3.10<span class="fs4 lsd ws1"> </span>T<span class="fs5 ws1">RAJETÓRIA DE UMA PARTÍC<span class="_4 blank"></span>ULA SOB A AÇÃO D<span class="_4 blank"></span>E UMA <span class="fs0 ws4">F</span>ORÇA <span class="fs0 ws4">C</span><span class="ws6">ENTRAL<span class="fs0 ls5 ws7">................................................................</span></span><span class="fs0">. <span class="_4 blank"></span><span class="ls14 wsc">121<span class="fs4 ls1 ws1"> </span></span></span></span></div><div class="t m0 xf h8 y79 ff5 fs0 fc0 sc0 ls1 ws4">3.11<span class="fs4 lsd ws1"> </span>A<span class="fs5 ws1">PLICAÇÃO DE </span>M<span class="fs5 ws1">ECÂNICA </span><span class="ls12">E</span><span class="fs5 ws6">SPA<span class="_4 blank"></span>CIAL<span class="fs0 ws1"> <span class="_7 blank"></span><span class="ls5 ws7">..............................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">123</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 x13 h8 y7a ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 y7b ff5 fs4 fc0 sc0 ls1 ws1"> </div><div class="t m0 x12 h8 y7c ff5 fs4 fc0 sc0 ls1 ws1"> </div><div class="t m0 x13 h8 y7d ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 y7e ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x2 h8 y13 ff4 fs0 fc0 sc0 ls1 ws4">4<span class="ff5 fs4 ls2 ws1"> </span><span class="ws1">CINÉTICA DE PARTÍCUL<span class="_0 blank"> </span>AS: MÉTODO <span class="_0 blank"> </span>DO TRABALHO E <span class="_0 blank"> </span>ENERGIA <span class="ls13 ws3">.............................................................</span> <span class="_4 blank"></span><span class="ls14 wsc">133<span class="ff5 fs4 ls1 ws1"> </span></span></span></div><div class="t m0 xf h8 y7f ff5 fs0 fc0 sc0 ls1 ws5">4.1<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws6">NTRODUÇÃO</span><span class="ws1"> <span class="_2 blank"></span><span class="ls5 ws7">................................................................................................................................<span class="_0 blank"> </span>............<span class="ls1 ws1"> <span class="ls14 wsc">133</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y80 ff5 fs0 fc0 sc0 ls1 ws5">4.2<span class="fs4 ls3 ws1"> </span><span class="ws4">T<span class="fs5 ws1">RABALHO DE UMA FORÇ<span class="_4 blank"></span>A<span class="fs0"> <span class="_3 blank"></span><span class="ls5 ws7">...........................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">134</span><span class="fs4"> </span></span></span></span></span></span></div><div class="t m0 x10 h8 y81 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y82 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y83 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y84 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 xf h8 y85 ff5 fs0 fc0 sc0 ls1 ws5">4.3<span class="fs4 ls3 ws1"> </span><span class="ws4">F<span class="fs5 ws1">ORÇAS QUE NÃO REALIZAM <span class="_4 blank"></span>TRABALHO<span class="fs0"> <span class="_5 blank"></span><span class="ls5 ws7">..........................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">141</span><span class="fs4"> </span></span></span></span></span></span></div><div class="t m0 xf h8 y86 ff5 fs0 fc0 sc0 ls1 ws5">4.4<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">NERGIA </span><span class="ws4">C<span class="fs5 ws1">INÉTICA DE UM<span class="_4 blank"></span>A PARTÍCULA<span class="fs0 ws4">:</span> <span class="fs0 ls4">P</span>RINCÍPIO DO<span class="_4 blank"></span> <span class="fs0 ws4">T</span>RABALHO E <span class="fs0 ls12">E</span><span class="ws6">NE<span class="_4 blank"></span>RGIA<span class="fs0 ws1"> <span class="ls5 ws7">........................................................</span> <span class="_4 blank"></span><span class="ls14 wsc">142<span class="fs4 ls1 ws1"> </span></span></span></span></span></span></div><div class="t m0 xf h8 y87 ff5 fs0 fc0 sc0 ls1 ws5">4.5<span class="fs4 ls3 ws1"> </span><span class="ws4">A<span class="fs5 ws1">PLICAÇÃO DO </span><span class="ls4">P</span><span class="fs5 ws1">RINCÍPIO DO </span>T<span class="fs5 ws1">R<span class="_4 blank"></span>ABALHO E <span class="fs0 ls12">E</span><span class="ws6">NERGIA<span class="_4 blank"></span><span class="fs0 ws1"> <span class="_7 blank"></span><span class="ls5 ws7">................................................................<span class="_0 blank"> </span>.........................<span class="ls1 ws1"> <span class="ls14 wsc">143</span><span class="fs4"> </span></span></span></span></span></span></span></div><div class="t m0 xf h8 y88 ff5 fs0 fc0 sc0 ls1 ws5">4.6<span class="fs4 ls3 ws1"> </span><span class="ls4">P</span><span class="fs5 ws1">OTÊNCIA E </span><span class="ws4">E<span class="fs5 ws6">FICIÊNCIA</span><span class="ws1"> <span class="_7 blank"></span><span class="ls5 ws7">...............................................................................................................................<span class="ls1 ws1"> 1<span class="ls14 wsc">45</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 xf h8 y89 ff5 fs0 fc0 sc0 ls1 ws5">4.7<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">XEMPLOS </span><span class="lsf">I</span><span class="fs5 ws6">LUSTRATIVOS</span><span class="ws1"> <span class="_9 blank"></span><span class="ls5 ws7">.............................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">146</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x10 h8 y8a ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y8b ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y56 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y8c ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y8d ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 xf h8 y8e ff5 fs0 fc0 sc0 ls1 ws5">4.8<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">NERGIA </span><span class="ls4">P</span><span class="fs5 ws6">OTENCIAL</span><span class="ws1"> <span class="_5 blank"></span><span class="ls5 ws7">...................................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">157</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y8f ff5 fs0 fc0 sc0 ls1 ws5">4.9<span class="fs4 ls3 ws1"> </span><span class="ws4">F<span class="fs5 ws1">ORÇAS </span>C<span class="fs5 ws6">ONSERVATIVAS</span><span class="ws1"> <span class="_3 blank"></span><span class="ls5 ws7">.............................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">160</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 xf h8 y90 ff5 fs0 fc0 sc0 ls1 ws4">4.10<span class="fs4 lsd ws1"> </span>C<span class="fs5 ws1">ONSERVAÇÃO DE </span><span class="ls12">E</span><span class="fs5 ws6">NERGI<span class="_4 blank"></span>A<span class="fs0 ws1"> <span class="_2 blank"></span><span class="ls5 ws7">.........................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">162</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 xf h8 y91 ff5 fs0 fc0 sc0 ls1 ws4">4.11<span class="fs4 lsd ws1"> </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTO SOB UMA FORÇA CON<span class="_2 blank"></span>S<span class="_0 blank"> </span>ERVATIVA CEN<span class="_4 blank"></span>TRAL<span class="fs0"> <span class="_7 blank"></span><span class="ls5 ws7">....................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">163</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 xf h8 y92 ff5 fs0 fc0 sc0 ls1 ws4">4.12<span class="fs4 lsd ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">XEMPLOS </span><span class="lsf">I</span><span class="fs5 ws6">LUSTRATIVOS</span><span class="ws1"> <span class="_9 blank"></span><span class="ls5 ws7">.............................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">164</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x13 h8 y93 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 y94 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 y95 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 y96 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x2 h8 y97 ff4 fs0 fc0 sc0 ls1 ws4">5<span class="ff5 fs4 ls2 ws1"> </span><span class="ws1">CINÉTICA DE PARTÍCUL<span class="_0 blank"> </span>AS: MÉTODO <span class="_0 blank"> </span>DO IMPULSO E QU<span class="_0 blank"> </span>ANTIDADE D<span class="_0 blank"> </span>E MOVIM<span class="_0 blank"> </span>ENTO <span class="_2 blank"></span><span class="ls13 ws3">.............................<span class="ls1 ws1"> <span class="_2 blank"></span><span class="ls14 wsc">171<span class="ff5 fs4 ls1 ws1"> </span></span></span></span></span></div><div class="t m0 xf h8 y98 ff5 fs0 fc0 sc0 ls1 ws5">5.1<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws6">NTRODUÇÃO</span><span class="ws1"> <span class="_2 blank"></span><span class="ls5 ws7">................................................................................................................................<span class="_0 blank"> </span>............<span class="ls1 ws1"> <span class="ls14 wsc">171</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y99 ff5 fs0 fc0 sc0 ls1 ws5">5.2<span class="fs4 ls3 ws1"> </span><span class="ls4">P</span><span class="fs5 ws1">RINCÍPIO DO </span><span class="lsf">I</span><span class="fs5 ws1">MPULSO E </span><span class="ls11">Q</span><span class="fs5 ws1">UANTID<span class="_4 blank"></span>ADE DE <span class="fs0 lsa">M</span><span class="ws6">OVIMENTO<span class="_4 blank"></span><span class="fs0 ws1"> <span class="_5 blank"></span><span class="ls5 ws7">...................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">171</span><span class="fs4"> </span></span></span></span></span></span></div><div class="t m0 xf h8 y9a ff5 fs0 fc0 sc0 ls1 ws5">5.3<span class="fs4 ls3 ws1"> </span><span class="lsa">M</span><span class="fs5 ws1">OVIMENTO </span><span class="lsf">I</span><span class="fs5 ws6">MPULSIVO</span><span class="ws1"> <span class="_a blank"></span><span class="ls5 ws7">.............................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">175</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y9b ff5 fs0 fc0 sc0 ls1 ws5">5.4<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">XEMPLOS </span><span class="lsf">I</span><span class="fs5 ws6">LUSTRATIVOS</span><span class="ws1"> <span class="_9 blank"></span><span class="ls5 ws7">.............................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">176</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x10 h8 y9c ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div></div><a class="l" data-dest-detail='[88,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:758.930000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[90,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:746.730000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[95,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:734.520000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[97,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:722.310000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[102,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:710.100000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[104,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:697.900000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[107,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:685.690000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[108,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:673.480000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[110,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:661.280000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[112,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:649.070000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[113,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:636.860000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[114,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:624.660000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[116,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:612.450000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[117,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:600.240000px;width:458.050000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[117,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:588.030000px;width:457.550000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[119,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:575.830000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[120,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:563.620000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[121,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:551.410000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[123,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:539.210000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[125,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:527.000000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[127,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:514.790000px;width:458.050000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[127,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:502.590000px;width:457.550000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[129,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:490.380000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[131,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:478.170000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[133,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:457.960000px;width:457.550000px;height:20.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[133,"XYZ",68,721,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:445.760000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[134,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:433.550000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[136,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:421.340000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[137,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:409.140000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[138,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:396.930000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[140,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:384.720000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[141,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:372.520000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[142,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:360.310000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[143,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:348.100000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[145,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:335.890000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[146,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:323.690000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[146,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:311.480000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[148,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:299.270000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[150,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:287.070000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[153,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:274.860000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[155,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:262.650000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[157,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:250.440000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[160,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:238.240000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[162,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:226.030000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[163,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:213.820000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[164,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:201.620000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[164,"XYZ",68,743,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:189.410000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[166,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:177.200000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[168,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:165.000000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[169,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:152.790000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[171,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:132.580000px;width:457.550000px;height:20.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[171,"XYZ",68,721,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:120.370000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[171,"XYZ",68,441,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:108.170000px;width:443.350000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[175,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:95.960000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[176,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:83.753000px;width:443.350000px;height:12.207000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[176,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:71.546000px;width:422.100000px;height:12.207000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi xd y9d w3 ha" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bg4.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>4 </div><div class="t m0 x10 h8 y68 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x10 h8 y69 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 xf h8 y6a ff5 fs0 fc0 sc0 ls1 ws5">5.5<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws6">MPACTO</span><span class="ws1"> <span class="_5 blank"></span><span class="ls5 ws7">................................<span class="_0 blank"> </span>..................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">181</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y6b ff5 fs0 fc0 sc0 ls1 ws5">5.6<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws1">MPACTO </span><span class="ws4">C<span class="fs5 ws1">ENTRAL </span>D<span class="fs5 ws6">IRETO</span><span class="ws1"> <span class="_7 blank"></span><span class="ls5 ws7">..........................................................................................................................<span class="ls1 ws1"> <span class="ls14 wsc">182</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 xf h8 y6c ff5 fs0 fc0 sc0 ls1 ws5">5.7<span class="fs4 ls3 ws1"> </span><span class="ls12">E</span><span class="fs5 ws1">XEMPLOS </span><span class="lsf">I</span><span class="fs5 ws1">LUSTRATIVOS </span><span class="ff6 ws4">\u2013</span><span class="fs5 ws1"> </span><span class="lsf">I</span><span class="fs5 ws1">MP<span class="_4 blank"></span>ACTO <span class="fs0 ws4">C</span>ENTRAL DIR<span class="_4 blank"></span>ETO<span class="fs0"> <span class="ls5 ws7">.....................................................................................</span> <span class="ls14 wsc">186</span><span class="fs4"> </span></span></span></div><div class="t m0 x11 h8 y9e ff5 fs6 fc0 sc0 ls1 ws9">5.7.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 43 <span class="_3 blank"></span><span class="ls9 wsa">................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">186</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 y9f ff5 fs0 fc0 sc0 ls1 ws5">5.8<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws1">MPACTO </span><span class="ws4">C<span class="fs5 ws1">ENTRAL </span><span class="ls17">O<span class="fs5 ls18 wsd">BL<span class="ls1 ws6">ÍQUO</span></span><span class="ls6 ws1"> <span class="ls5 ws7">.......................................................................................................................</span><span class="ls1"> <span class="ls14 wsc">187</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 x10 h8 ya0 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 y5 ff5 fs6 fc0 sc0 ls1 ws9">5.8.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 44 <span class="_3 blank"></span><span class="ls9 wsa">................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">188</span><span class="fs4"> </span></span></span></span></div><div class="t m0 x11 h8 ya1 ff5 fs6 fc0 sc0 ls1 ws9">5.8.1.2<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 45 <span class="_3 blank"></span><span class="ls9 wsa">................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">190</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 ya2 ff5 fs0 fc0 sc0 ls1 ws5">5.9<span class="fs4 ls3 ws1"> </span><span class="lsf">I</span><span class="fs5 ws1">MPACTO </span><span class="ws4">C<span class="fs5 ws1">ENTRAL </span><span class="ls17">O<span class="fs5 ls18 wsd">BL<span class="ls1 ws1">ÍQUO COM RESTRI<span class="_4 blank"></span>ÇÃO DE MOVIMENTO<span class="fs0"> <span class="_a blank"></span><span class="ls5 ws7">...........................................................................<span class="ls1 ws1"> <span class="ls14 wsc">191</span><span class="fs4"> </span></span></span></span></span></span></span></span></div><div class="t m0 x10 h8 ya3 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_6 blank"> </span> </div><div class="t m0 x11 h8 ya4 ff5 fs6 fc0 sc0 ls1 ws9">5.9.1.1<span class="fs4 ls8 ws1"> </span><span class="ws1">Exemplo-Ilustrativo 45 <span class="_3 blank"></span><span class="ls9 wsa">................................................................................................................<span class="ls1 ws1"> <span class="ls15 wsb">192</span><span class="fs4"> </span></span></span></span></div><div class="t m0 xf h8 ya5 ff5 fs0 fc0 sc0 ls1 ws4">5.10<span class="fs4 lsd ws1"> </span><span class="ls4">P</span><span class="fs5 ws1">ROBLEMAS ENVOLVENDO ENER<span class="_4 blank"></span>GIA E QUANTIDAD<span class="_4 blank"></span>E DE MOVIMENTO<span class="fs0"> <span class="_9 blank"></span><span class="ls5 ws7">....................................................................<span class="ls1 ws1"> <span class="ls14 wsc">194</span><span class="fs4"> </span></span></span></span></span></div><div class="t m0 x13 h8 ya6 ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x13 h8 yb ff5 fs4 fc0 sc0 ls1 ws1"> <span class="_8 blank"> </span> </div><div class="t m0 x2 h8 ya7 ff4 fs0 fc0 sc0 ls1 ws1">APÊNDICE A: MOVIMENT<span class="_0 blank"> </span><span class="ls19">O </span>R<span class="_0 blank"> </span>ETILÍNEO (1D)<span class="_0 blank"> </span> <span class="_5 blank"></span><span class="ls13 ws3">..................................................................................................<span class="ls1 ws1"> <span class="_4 blank"></span><span class="ls14 wsc">198<span class="ff5 fs4 ls1 ws1"> </span></span></span></span></div><div class="t m0 x2 h3 ya8 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ya9 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yaa ff1 fs1 fc1 sc0 ls1 ws1"> <span class="_b blank"> </span> </div></div><a class="l" data-dest-detail='[177,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:758.930000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[178,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:746.730000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[181,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:734.520000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[182,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:722.310000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[186,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:710.100000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[186,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:699.120000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[187,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:686.910000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[188,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:674.700000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[188,"XYZ",68,729,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:663.720000px;width:393.750000px;height:10.980000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[190,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:652.730000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[191,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:640.520000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[192,"XYZ",68,520,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:628.320000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[192,"XYZ",68,479,null]'><div class="d m1" style="border-style:none;position:absolute;left:132.450000px;bottom:617.330000px;width:393.750000px;height:10.990000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[194,"XYZ",68,674,null]'><div class="d m1" style="border-style:none;position:absolute;left:82.850000px;bottom:605.120000px;width:443.350000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[194,"XYZ",68,316,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:592.920000px;width:422.100000px;height:12.200000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[194,"XYZ",68,261,null]'><div class="d m1" style="border-style:none;position:absolute;left:104.100000px;bottom:580.710000px;width:422.100000px;height:12.210000px;background-color:rgba(255,255,255,0.000001);"></div></a><a class="l" data-dest-detail='[198,"XYZ",68,771,null]'><div class="d m1" style="border-style:none;position:absolute;left:68.650000px;bottom:560.500000px;width:457.550000px;height:20.210000px;background-color:rgba(255,255,255,0.000001);"></div></a></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>5 </div><div class="t m0 x8 h7 y30 ff3 fs3 fc2 sc0 ls1 ws2">Apr<span class="_4 blank"></span>esentação<span class="ff2 ws1"> </span></div><div class="t m0 x2 h3 y31 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yab ff1 fs1 fc1 sc0 ls1 ws1">Essa <span class="_c blank"> </span>apostila <span class="_c blank"> </span>apresenta <span class="_c blank"> </span>o <span class="_c blank"> </span>conteúdo <span class="_c blank"> </span>minist<span class="_0 blank"> </span>rado <span class="_c blank"> </span>na <span class="_c blank"> </span>disciplina <span class="_c blank"> </span>ENG002 <span class="_c blank"> </span><span class="ff7 wse">\u2013</span> <span class="_d blank"> </span>Mecânica <span class="_c blank"> </span>Geral <span class="_c blank"> </span>II <span class="_c blank"> </span>da </div><div class="t m0 x2 h3 yac ff1 fs1 fc1 sc0 ls1 ws1">Universidade <span class="_0 blank"> </span>Federal <span class="_c blank"> </span>da <span class="_0 blank"> </span>Bahia <span class="_c blank"> </span>(UFBA). <span class="_0 blank"> </span>Espero <span class="_c blank"> </span>que <span class="_0 blank"> </span>ela <span class="_c blank"> </span>seja <span class="_0 blank"> </span>e<span class="_0 blank"> </span>fetivamente <span class="_c blank"> </span>um <span class="_0 blank"> </span>instrumento <span class="_c blank"> </span>de </div><div class="t m0 x2 h3 yad ff1 fs1 fc1 sc0 ls1 ws1">aprendizado <span class="_e blank"> </span>dos <span class="_e blank"> </span>estudantes <span class="_e blank"> </span>de <span class="_f blank"> </span>engenharia <span class="_e blank"> </span>ao <span class="_f blank"> </span>desenvolverem <span class="_e blank"> </span>seus <span class="_e blank"> </span>conhecimentos <span class="_e blank"> </span>sobr<span class="_0 blank"> </span>e </div><div class="t m0 x2 h3 yae ff1 fs1 fc1 sc0 ls1 ws1">Cinemática e Dinâmica da partícula. </div><div class="t m0 x2 h3 yaf ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yb0 ff1 fs1 fc1 sc0 ls1 ws1">Esta <span class="_10 blank"> </span>apostila <span class="_10 blank"> </span>deve <span class="_10 blank"> </span>ser <span class="_10 blank"> </span>entendida <span class="_10 blank"> </span>como <span class="_10 blank"> </span>um <span class="_10 blank"> </span>trabalho <span class="_10 blank"> </span>em <span class="_10 blank"> </span>elaboração <span class="_10 blank"> </span>e <span class="_10 blank"> </span>a <span class="_11 blank"> </span>decisão <span class="_10 blank"> </span>de <span class="_10 blank"> </span>torná<span class="_0 blank"> </span>-la </div><div class="t m0 x2 h3 yb1 ff1 fs1 fc1 sc0 ls1 ws1">acessível <span class="_2 blank"></span>aos alunos <span class="_2 blank"></span>matriculados <span class="_4 blank"></span>decorreu <span class="_2 blank"></span>da solicitação <span class="_2 blank"></span>de muitos <span class="_2 blank"></span>deles <span class="_4 blank"></span>pela <span class="_2 blank"></span>disponibili<span class="_0 blank"> </span>zação </div><div class="t m0 x2 h3 yb2 ff1 fs1 fc1 sc0 ls1 ws1">do <span class="_11 blank"> </span>material <span class="_11 blank"> </span>que <span class="_12 blank"> </span>tenho <span class="_11 blank"> </span>a<span class="_0 blank"> </span>presentado <span class="_11 blank"> </span>nas <span class="_11 blank"> </span>aul<span class="_0 blank"> </span>as. <span class="_11 blank"> </span>Após <span class="_11 blank"> </span>meses <span class="_12 blank"> </span>de <span class="_11 blank"> </span>trabalho <span class="_12 blank"> </span>dedicado, <span class="_11 blank"> </span>creio <span class="_11 blank"> </span>t<span class="_0 blank"> </span>er </div><div class="t m0 x2 h3 yb3 ff1 fs1 fc1 sc0 ls1 ws1">completado <span class="_12 blank"> </span>uma primeira <span class="_12 blank"> </span>et<span class="_0 blank"> </span>apa <span class="_12 blank"> </span>d<span class="_0 blank"> </span>e <span class="_13 blank"> </span>desenvolver um <span class="_12 blank"> </span>material didático <span class="_12 blank"> </span>mais apropriado <span class="_12 blank"> </span>às<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 y74 ff1 fs1 fc1 sc0 ls1 ws1">necessidades dos alunos. </div><div class="t m0 x2 h3 yb4 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yb5 ff1 fs1 fc1 sc0 ls1 ws1">A <span class="_2 blank"></span>época <span class="_2 blank"></span>atual <span class="_4 blank"></span>é <span class="_2 blank"></span>caracterizada <span class="_2 blank"></span>pelo <span class="_4 blank"></span>uso <span class="_2 blank"></span>intensivo <span class="_4 blank"></span>da <span class="_2 blank"></span>computação <span class="_4 blank"></span>eletrônica <span class="_2 blank"></span>e <span class="_4 blank"></span>da <span class="_2 blank"></span>álgebra <span class="_2 blank"></span>vetori<span class="_0 blank"> </span>al. </div><div class="t m0 x2 h3 yb6 ff1 fs1 fc1 sc0 ls1 ws1">Por <span class="_14 blank"> </span>isso, <span class="_14 blank"> </span>procurei <span class="_14 blank"> </span>adotar <span class="_14 blank"> </span>uma <span class="_14 blank"> </span>abordagem <span class="_14 blank"> </span>que <span class="_14 blank"> </span>enfatiza <span class="_14 blank"> </span>o <span class="_14 blank"> </span>desenvolvimento <span class="_14 blank"> </span>da <span class="_14 blank"> </span>capacidade <span class="_14 blank"> </span>de </div><div class="t m0 x2 h3 yb7 ff1 fs1 fc1 sc0 ls1 ws1">modelar <span class="_4 blank"></span>os mais <span class="_2 blank"></span>diversos problemas <span class="_2 blank"></span>de cinemática <span class="_4 blank"></span>e <span class="_4 blank"></span>dinâmica da<span class="_4 blank"></span> pa<span class="_4 blank"></span>rtícula por <span class="_2 blank"></span>meio do <span class="_4 blank"></span>cálculo </div><div class="t m0 x2 h3 yb8 ff1 fs1 fc1 sc0 ls1 ws1">vetorial aplicado à solução de problemas de engenharia. </div><div class="t m0 x2 h3 yb9 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yba ff1 fs1 fc1 sc0 ls1 ws1">A <span class="_0 blank"> </span>principal <span class="_c blank"> </span>fonte <span class="_0 blank"> </span>bibliográfica <span class="_c blank"> </span>utilizada <span class="_0 blank"> </span><span class="ff7">foi <span class="_c blank"> </span>o <span class="_0 blank"> </span>li<span class="_0 blank"> </span>vro <span class="_0 blank"> </span>\u201cMecânica <span class="_0 blank"> </span>Vetorial <span class="_0 blank"> </span>pa<span class="_0 blank"> </span>ra <span class="_0 blank"> </span>En<span class="_0 blank"> </span>genheiros\u201d, <span class="_0 blank"> </span>de </span></div><div class="t m0 x2 h3 ybb ff1 fs1 fc1 sc0 ls1 ws1">autoria <span class="_c blank"> </span>dos <span class="_c blank"> </span>Professores <span class="_c blank"> </span>Ferdinand <span class="_c blank"> </span>P. <span class="_c blank"> </span>Beer <span class="_c blank"> </span>e <span class="_c blank"> </span>E. <span class="_c blank"> </span>Russel <span class="_c blank"> </span>Johnston, <span class="_c blank"> </span>Jr. <span class="_c blank"> </span> <span class="_c blank"> </span>Pelo <span class="_c blank"> </span>menos <span class="_c blank"> </span>desde <span class="_c blank"> </span>1980, </div><div class="t m0 x2 h3 ybc ff1 fs1 fc1 sc0 ls1 ws1">professores <span class="_c blank"> </span>da <span class="_d blank"> </span>UFBA <span class="_d blank"> </span>têm <span class="_d blank"> </span>adotado <span class="_d blank"> </span>o <span class="_d blank"> </span>segundo <span class="_c blank"> </span>volume <span class="_d blank"> </span>(Dinâmica), <span class="_c blank"> </span>como <span class="_d blank"> </span>o <span class="_d blank"> </span>li<span class="_0 blank"> </span>vro <span class="_c blank"> </span>texto <span class="_d blank"> </span>para <span class="_d blank"> </span>a </div><div class="t m0 x2 h3 ybd ff1 fs1 fc1 sc0 ls1 ws1">disciplina e, atualmente, ele se encontra na 9ª edição. </div><div class="t m0 x2 h3 ybe ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ybf ff1 fs1 fc1 sc0 ls1 ws1">Por fim, espero que esta apostila inicie um processo virtuoso de melhoria contí<span class="_0 blank"> </span>nua no ensino e </div><div class="t m0 x2 h3 yc0 ff1 fs1 fc1 sc0 ls1 ws1">aprendizagem da disciplina Mecânica Geral II<span class="_4 blank"></span>.<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 yc1 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yc2 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h2 yc3 ff1 fs0 fc1 sc0 ls1 ws1">Prof. Dr. Carlo<span class="_0 blank"> </span>s Arthur M T Cavalcante<span class="_c blank"> </span> </div><div class="t m0 x2 h2 yc4 ff1 fs0 fc1 sc0 ls1 ws1">Departamento de Engenharia <span class="_0 blank"> </span>Mecânica (DEM)<span class="_0 blank"> </span> </div><div class="t m0 x2 h2 yc5 ff1 fs0 fc1 sc0 ls1 ws1">Universidade Feder<span class="_0 blank"> </span>al da Bahia (UFB<span class="_0 blank"> </span>A) </div><div class="t m0 x2 h2 yc6 ff1 fs0 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h2 yc7 ff1 fs0 fc1 sc0 ls1 ws1">Salvador, 20<span class="_0 blank"> </span> de fevereiro <span class="_0 blank"> </span>de 2017 </div><div class="t m0 x2 h3 yc8 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yc9 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yca ff1 fs1 fc1 sc0 ls1 ws1"> <span class="_b blank"> </span> </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>6 </div><div class="t m0 x2 h7 y30 ff2 fs3 fc1 sc0 ls1 ws2">1<span class="ff8 ls1a ws1"> </span><span class="ws1">Introdução </span></div><div class="t m0 x2 h3 ycb ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ycc ff1 fs1 fc1 sc0 ls1 ws1">O Universo e<span class="_4 blank"></span>xiste e nós podemos percebê-lo. Ele é g<span class="_4 blank"></span>rande. Tem bilhões de ga<span class="_4 blank"></span>láxias, cada uma </div><div class="t m0 x2 h3 ycd ff1 fs1 fc1 sc0 ls1 ws1">delas com <span class="_0 blank"> </span>bilhões <span class="_0 blank"> </span>de <span class="_0 blank"> </span>estrelas. <span class="_0 blank"> </span>Ele <span class="_0 blank"> </span>está <span class="_0 blank"> </span>se <span class="_0 blank"> </span>expandindo. <span class="_0 blank"> </span>Além <span class="_0 blank"> </span>da m<span class="_0 blank"> </span>atéria <span class="_c blank"> </span>comum (5% <span class="_0 blank"> </span>de <span class="_0 blank"> </span>toda <span class="_0 blank"> </span>a<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 yce ff1 fs1 fc1 sc0 ls1 ws1">matéria <span class="_2 blank"></span>e <span class="_2 blank"></span>energia <span class="_4 blank"></span>visíveis), <span class="_2 blank"></span>tem <span class="_4 blank"></span>a <span class="_2 blank"></span>matéria <span class="_2 blank"></span>escura (25%) <span class="_2 blank"></span>e <span class="_2 blank"></span>tem <span class="_2 blank"></span>a <span class="_4 blank"></span>energia <span class="_2 blank"></span>escura <span class="_4 blank"></span>(70%). <span class="_2 blank"></span>A <span class="_2 blank"></span>C<span class="_0 blank"> </span>iência </div><div class="t m0 x2 h3 ycf ff1 fs1 fc1 sc0 ls1 ws1">não <span class="_11 blank"> </span>encontrou, <span class="_12 blank"> </span>ainda, <span class="_12 blank"> </span>uma <span class="_12 blank"> </span>explicação <span class="_11 blank"> </span>definitiva <span class="_12 blank"> </span>para <span class="_12 blank"> </span>tudo <span class="_11 blank"> </span>iss<span class="_0 blank"> </span>o, <span class="_12 blank"> </span>embora <span class="_11 blank"> </span>a <span class="_12 blank"> </span>teoria <span class="_12 blank"> </span>geral <span class="_12 blank"> </span>da </div><div class="t m0 x2 h3 yd0 ff1 fs1 fc1 sc0 ls1 ws1">relatividade, <span class="_15 blank"> </span>a <span class="_15 blank"> </span>mecânica <span class="_15 blank"> </span>quântica <span class="_15 blank"> </span>e, <span class="_15 blank"> </span>mais <span class="_16 blank"> </span>recentemente, <span class="_15 blank"> </span>a <span class="_15 blank"> </span>teo<span class="_0 blank"> </span>ria <span class="_15 blank"> </span>das <span class="_15 blank"> </span>cordas, <span class="_15 blank"> </span>venham<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 ya1 ff1 fs1 fc1 sc0 ls1 ws1">contribuindo para o entendimento científico da origem e comportamento do Universo. </div><div class="t m0 x2 h3 yd1 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yd2 ff1 fs1 fc1 sc0 ls1 ws1">Apesar <span class="_14 blank"> </span>d<span class="_0 blank"> </span>e <span class="_10 blank"> </span>todos <span class="_14 blank"> </span>os <span class="_10 blank"> </span>avanços, <span class="_17 blank"> </span>a <span class="_17 blank"> </span>Mecânica <span class="_17 blank"> </span>Newtoniana <span class="_17 blank"> </span>(ou <span class="_17 blank"> </span>a <span class="_17 blank"> </span>Mecânica <span class="_17 blank"> </span>C<span class="_0 blank"> </span>lássica) <span class="_17 blank"> </span>permanece </div><div class="t m0 x2 h3 yd3 ff1 fs1 fc1 sc0 ls1 ws1">válida <span class="_14 blank"> </span>e <span class="_17 blank"> </span>mais <span class="_17 blank"> </span>do <span class="_14 blank"> </span>qu<span class="_0 blank"> </span>e <span class="_17 blank"> </span>adequada <span class="_14 blank"> </span>para <span class="_17 blank"> </span>a <span class="_17 blank"> </span>modelagem <span class="_17 blank"> </span>e <span class="_17 blank"> </span>solução <span class="_17 blank"> </span>dos <span class="_17 blank"> </span>problemas <span class="_17 blank"> </span>de <span class="_14 blank"> </span>en<span class="_0 blank"> </span>genharia, </div><div class="t m0 x2 h3 yd4 ff1 fs1 fc1 sc0 ls1 ws1">incluindo movimentos de planetas e satélites artificiais. </div><div class="t m0 x2 h3 yd5 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yd6 ff1 fs1 fc1 sc0 ls1 ws1">A Mecânica é<span class="_0 blank"> </span> a <span class="_0 blank"> </span>ciência que <span class="_0 blank"> </span>estuda a <span class="_0 blank"> </span>posição dos <span class="_0 blank"> </span>objetos <span class="_0 blank"> </span>no Espaço <span class="_0 blank"> </span>à medi<span class="_0 blank"> </span>da em qu<span class="_0 blank"> </span>e o <span class="_0 blank"> </span>tempo </div><div class="t m0 x2 h3 yd7 ff1 fs1 fc1 sc0 ls1 ws1">passa. Isto é, a Mecânica é a ciência que estuda o <span class="ff9 wse">movimento</span> dos objetos. </div><div class="t m0 x2 h3 yd8 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yd9 ff1 fs1 fc1 sc0 ls1 ws1">Os <span class="_10 blank"> </span>conceitos <span class="_10 blank"> </span>de <span class="_10 blank"> </span>Espaço <span class="_10 blank"> </span>e <span class="_10 blank"> </span>Tempo <span class="_10 blank"> </span>s<span class="_0 blank"> </span>ão <span class="_17 blank"> </span>con<span class="_0 blank"> </span>ceitos <span class="_10 blank"> </span>fundamentais <span class="_10 blank"> </span>na <span class="_10 blank"> </span>Mecânica. <span class="_10 blank"> </span>São <span class="_10 blank"> </span>conceitos </div><div class="t m0 x2 h3 yda ff1 fs1 fc1 sc0 ls1 ws1">fundamentais <span class="_0 blank"> </span>porque <span class="_c blank"> </span>são <span class="_0 blank"> </span>considerados <span class="_c blank"> </span>essenciais <span class="_c blank"> </span>para <span class="_0 blank"> </span>a <span class="_0 blank"> </span>d<span class="_0 blank"> </span>efinição <span class="_c blank"> </span>do <span class="_0 blank"> </span>conceito <span class="_c blank"> </span>de <span class="_c blank"> </span><span class="ff9 wse">movimento</span><span class="ls1d">. </span></div><div class="t m0 x2 h3 ydb ff1 fs1 fc1 sc0 ls1 ws1">Mas <span class="_c blank"> </span>isso <span class="_c blank"> </span>não <span class="_0 blank"> </span>quer <span class="_c blank"> </span>dizer <span class="_0 blank"> </span>que <span class="_c blank"> </span>o <span class="_c blank"> </span>conhecimento <span class="_0 blank"> </span>humano <span class="_c blank"> </span>conseguiu <span class="_c blank"> </span>decifrar <span class="_0 blank"> </span>o <span class="_c blank"> </span>significado <span class="_c blank"> </span>desses<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 ydc ff1 fs1 fc1 sc0 ls1 ws1">conceitos. <span class="_11 blank"> </span>Quer <span class="_11 blank"> </span>dizer <span class="_12 blank"> </span>apenas <span class="_11 blank"> </span>que <span class="_11 blank"> </span>os <span class="_12 blank"> </span>conceitos <span class="_12 blank"> </span>(Newtonianos) <span class="_11 blank"> </span>de <span class="_11 blank"> </span>Espaço, <span class="_12 blank"> </span>de <span class="_11 blank"> </span>Tempo <span class="_11 blank"> </span>e <span class="_11 blank"> </span>de<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 ydd ff1 fs1 fc1 sc0 ls1 ws1">Movimento <span class="_17 blank"> </span>são <span class="_10 blank"> </span>válidos <span class="_10 blank"> </span>e <span class="_17 blank"> </span>funcionam <span class="_10 blank"> </span>na<span class="_0 blank"> </span> <span class="_17 blank"> </span>solução<span class="_0 blank"> </span> <span class="_17 blank"> </span>de <span class="_10 blank"> </span>uma <span class="_10 blank"> </span>grande <span class="_17 blank"> </span>maiori<span class="_0 blank"> </span>a <span class="_10 blank"> </span>dos <span class="_17 blank"> </span>problemas <span class="_10 blank"> </span>de </div><div class="t m0 x2 h3 y47 ff1 fs1 fc1 sc0 ls1 ws1">engenharia. </div><div class="t m0 x2 h3 yde ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ydf ff1 fs1 fc1 sc0 ls1 ws1">O estudo da Mecânica divide-se em duas partes: a Estática e a Dinâmica. </div><div class="t m0 x2 h3 ye0 ff1 fs1 fc1 sc0 ls1b ws1"> <span class="ff2 ls1 wse v1">Estática</span><span class="ls1 v1"> é a parte da Mecânica que estuda os corpos em equilíbrio estático ou em repouso. </span></div><div class="t m0 xf h3 ye1 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 xf h4 ye2 ff2 fs1 fc1 sc0 ls1 wse">Dinâmica<span class="ff1 ws1"> é a parte da Mecânica que estuda os corpos em movimento. </span></div><div class="t m0 xf h3 ye3 ff1 fs1 fc1 sc0 ls1c ws1"> <span class="ls1 v1">A Dinâmica divide-se em duas partes: Cinemática e Cinética. </span></div><div class="t m0 x14 h3 ye4 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x14 h4 ye5 ff2 fs1 fc1 sc0 ls1 wse">Cinemática<span class="ff1 ws1"> <span class="_0 blank"> </span>é <span class="_0 blank"> </span>a <span class="_c blank"> </span>parte da<span class="_0 blank"> </span> <span class="_c blank"> </span>Dinâmica qu<span class="_0 blank"> </span>e <span class="_0 blank"> </span>estuda <span class="_0 blank"> </span>o <span class="_c blank"> </span>movimento <span class="_0 blank"> </span>dos <span class="_0 blank"> </span>corpos, <span class="_c blank"> </span>sem <span class="_0 blank"> </span>considerar </span></div><div class="t m0 x14 h3 ye6 ff1 fs1 fc1 sc0 ls1 ws1">as <span class="_14 blank"> </span>causas <span class="_14 blank"> </span>ou <span class="_14 blank"> </span>forças <span class="_14 blank"> </span>geradoras <span class="_14 blank"> </span>do <span class="_14 blank"> </span>movi<span class="_0 blank"> </span>mento. <span class="_14 blank"> </span>Isto <span class="_14 blank"> </span>é, <span class="_14 blank"> </span>estuda <span class="_14 blank"> </span>o <span class="_14 blank"> </span>movi<span class="_0 blank"> </span>mento <span class="_14 blank"> </span>dos <span class="_14 blank"> </span>corpos, </div><div class="t m0 x14 h3 ye7 ff1 fs1 fc1 sc0 ls1 ws1">independentemente <span class="_0 blank"> </span>das <span class="_c blank"> </span>força<span class="_4 blank"></span>s <span class="_c blank"> </span>ou <span class="_0 blank"> </span>das <span class="_0 blank"> </span>causas <span class="_c blank"> </span>que <span class="_0 blank"> </span>são <span class="_c blank"> </span>necessárias <span class="_0 blank"> </span>para <span class="_0 blank"> </span>que <span class="_c blank"> </span>o <span class="_0 blank"> </span>movimento </div><div class="t m0 x14 h3 ye8 ff1 fs1 fc1 sc0 ls1 ws1">ocorra. </div><div class="t m0 x14 h3 ye9 ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x14 h4 yea ff2 fs1 fc1 sc0 ls1 wse">Cinética<span class="ff1 ws1"> <span class="_11 blank"> </span>é <span class="_11 blank"> </span>a<span class="_0 blank"> </span> <span class="_11 blank"> </span>parte <span class="_11 blank"> </span>da<span class="_0 blank"> </span> <span class="_11 blank"> </span>Din<span class="_0 blank"> </span>âmica <span class="_11 blank"> </span>que <span class="_11 blank"> </span>estud<span class="_0 blank"> </span>a <span class="_11 blank"> </span>a <span class="_12 blank"> </span>relação <span class="_11 blank"> </span>existente <span class="_11 blank"> </span>entr<span class="_0 blank"> </span>e <span class="_11 blank"> </span>as <span class="_12 blank"> </span>forças <span class="_11 blank"> </span>e <span class="_11 blank"> </span>os </span></div><div class="t m0 x14 h3 yeb ff1 fs1 fc1 sc0 ls1 ws1">movimentos <span class="_c blank"> </span>dos <span class="_d blank"> </span>corpos. <span class="_d blank"> </span>A <span class="_c blank"> </span>Cinética <span class="_d blank"> </span>é <span class="_c blank"> </span>usada <span class="_d blank"> </span>para <span class="_d blank"> </span>prever <span class="_c blank"> </span>qual <span class="_d blank"> </span>será <span class="_c blank"> </span>o<span class="_0 blank"> </span> <span class="_c blank"> </span>movimento <span class="_d blank"> </span>de <span class="_c blank"> </span>um<span class="_0 blank"> </span> </div><div class="t m0 x14 h3 yec ff1 fs1 fc1 sc0 ls1 ws1">corpo <span class="_0 blank"> </span>em <span class="_0 blank"> </span>função <span class="_0 blank"> </span>das <span class="_0 blank"> </span>forças <span class="_0 blank"> </span>que <span class="_c blank"> </span>atuam sobre <span class="_c blank"> </span>ele; ou <span class="_c blank"> </span>para<span class="_4 blank"></span> <span class="_0 blank"> </span>determinar <span class="_0 blank"> </span>quais<span class="_0 blank"> </span> <span class="_0 blank"> </span>são <span class="_0 blank"> </span>as <span class="_0 blank"> </span>forças </div><div class="t m0 x14 h3 yed ff1 fs1 fc1 sc0 ls1 ws1">necessárias para que um corpo tenha um movimento desejado. </div><div class="t m0 x14 h3 yee ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x14 h3 yef ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y5f ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yf0 ff1 fs1 fc1 sc0 ls1 ws1"> <span class="_b blank"> </span> </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>7 </div><div class="t m0 x2 h7 y30 ff2 fs3 fc1 sc0 ls1 ws2">2<span class="ff8 ls1a ws1"> </span><span class="ws1">Cinemátic<span class="_4 blank"></span>a de Partículas </span></div><div class="t m0 x2 h3 ycb ff1 fs1 fc1 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ycc ff1 fs1 fc2 sc0 ls1 ws1">Todo e qualquer movimento de uma partícula ocorre nas trê<span class="_4 blank"></span>s dimensões espaciais.<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 ycd ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yce ff1 fs1 fc2 sc0 ls1 ws1">No <span class="_14 blank"> </span>caso <span class="_14 blank"> </span>mais <span class="_14 blank"> </span>geral, <span class="_14 blank"> </span>a <span class="_14 blank"> </span>partícula <span class="_14 blank"> </span>se <span class="_14 blank"> </span>move <span class="_14 blank"> </span>de <span class="_14 blank"> </span>t<span class="_0 blank"> </span>al <span class="_14 blank"> </span>modo <span class="_14 blank"> </span>que <span class="_14 blank"> </span>a <span class="_14 blank"> </span>sua<span class="_0 blank"> </span> <span class="_17 blank"> </span><span class="ffa wse">trajetória</span><span class="ls1e"> </span><span class="ff7">é <span class="_14 blank"> </span>uma <span class="_14 blank"> </span>\u201ccurva <span class="_14 blank"> </span>no<span class="_0 blank"> </span> </span></div><div class="t m0 x2 h3 ycf ff7 fs1 fc2 sc0 ls1 ws1">espaço\u201d <span class="_c blank"> </span>e <span class="_c blank"> </span>diz<span class="_0 blank"> </span>emos <span class="_c blank"> </span>que <span class="_d blank"> </span>a <span class="_c blank"> </span>partícula <span class="_d blank"> </span>realiza <span class="_c blank"> </span>um <span class="_d blank"> </span>\u201c<span class="ffa">movim<span class="_0 blank"> </span>ento <span class="_c blank"> </span>no <span class="_d blank"> </span>espaço</span>\u201d. <span class="_c blank"> </span><span class="ff1">D<span class="_0 blank"> </span>enominaremos <span class="_c blank"> </span>este </span></div><div class="t m0 x2 h3 yd0 ff1 fs1 fc2 sc0 ls1 ws1">movimento de <span class="ffa">Movimento 3D</span>. </div><div class="t m0 x2 h3 ya1 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yd1 ff1 fs1 fc2 sc0 ls1 ws1">No <span class="_0 blank"> </span>caso <span class="_c blank"> </span>particular <span class="_0 blank"> </span>em <span class="_c blank"> </span>que <span class="_0 blank"> </span>a <span class="_c blank"> </span>partícula s<span class="_0 blank"> </span>e <span class="_0 blank"> </span>move <span class="_c blank"> </span>de <span class="_c blank"> </span>tal <span class="_0 blank"> </span>modo <span class="_c blank"> </span>que <span class="_0 blank"> </span>a <span class="_0 blank"> </span>sua <span class="_c blank"> </span><span class="ffa wse">traj<span class="_0 blank"> </span>etória</span><span class="ls1f"> </span><span class="ff7">é <span class="_c blank"> </span>uma <span class="_0 blank"> </span>\u201ccurva </span></div><div class="t m0 x2 h3 yd2 ff7 fs1 fc2 sc0 ls1 ws1">no <span class="_15 blank"> </span>plano\u201d, <span class="_15 blank"> </span>dizemos <span class="_15 blank"> </span>que <span class="_15 blank"> </span>partícula<span class="ff1 ls20"> </span>realiza <span class="_15 blank"> </span>um <span class="_15 blank"> </span>\u201c<span class="ffa">m<span class="_0 blank"> </span>ovimento <span class="_15 blank"> </span>no <span class="_15 blank"> </span>plano</span>\u201d. <span class="_15 blank"> </span>Nesta <span class="_15 blank"> </span>apostila, </div><div class="t m0 x2 h3 yd3 ff1 fs1 fc2 sc0 ls1 ws1">denominaremos este movimento de <span class="ffa">Movimento 2D</span>. </div><div class="t m0 xd h2 yf1 ff1 fs0 fc2 sc0 ls1 ws1">Para que f<span class="_4 blank"></span>iquem <span class="_4 blank"></span>bem entendidos conceitos <span class="_4 blank"></span>e palavras: <span class="_2 blank"></span>o<span class="_0 blank"> </span> m<span class="_4 blank"></span>ovi<span class="_0 blank"> </span>mento <span class="_4 blank"></span>da partícula <span class="_4 blank"></span>se dá <span class="_4 blank"></span>nas <span class="_4 blank"></span>três dimensões </div><div class="t m0 xd h2 yf2 ff1 fs0 fc2 sc0 ls1 ws1">do <span class="_0 blank"> </span>espaç<span class="_0 blank"> </span>o, <span class="_0 blank"> </span>apenas <span class="_0 blank"> </span>o<span class="_0 blank"> </span>corre <span class="_0 blank"> </span>que <span class="_c blank"> </span>a <span class="_0 blank"> </span>sua <span class="_0 blank"> </span>trajetó<span class="_0 blank"> </span>ria <span class="_0 blank"> </span>pode <span class="_c blank"> </span>ser <span class="_0 blank"> </span>re<span class="_0 blank"> </span>presentada <span class="_0 blank"> </span>p<span class="_0 blank"> </span>or <span class="_0 blank"> </span>uma <span class="_0 blank"> </span>c<span class="_0 blank"> </span>urva <span class="_0 blank"> </span>contid<span class="_0 blank"> </span>a <span class="_0 blank"> </span>e<span class="_0 blank"> </span>m u<span class="_0 blank"> </span>m <span class="_0 blank"> </span>certo<span class="_0 blank"> </span> </div><div class="t m0 xd h2 yf3 ff1 fs0 fc2 sc0 ls1 ws1">plano (plano este que está no e<span class="_0 blank"> </span>spaço tr<span class="_0 blank"> </span>idimensional).<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 yf4 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yf5 ff1 fs1 fc2 sc0 ls1 ws1">No <span class="_0 blank"> </span>caso <span class="_c blank"> </span>mais <span class="_0 blank"> </span>pa<span class="_0 blank"> </span>rticular <span class="_c blank"> </span>ainda, em <span class="_c blank"> </span>que <span class="_c blank"> </span>a <span class="_0 blank"> </span>partícula<span class="_0 blank"> </span> <span class="_0 blank"> </span>se <span class="_c blank"> </span>move <span class="_c blank"> </span>de <span class="_0 blank"> </span>tal <span class="_c blank"> </span>modo <span class="_0 blank"> </span>qu<span class="_0 blank"> </span>e <span class="_0 blank"> </span>a <span class="_c blank"> </span>sua <span class="_c blank"> </span><span class="ffa wse">trajetória</span><span class="ls1f"> <span class="ls21">é </span></span></div><div class="t m0 x2 hb yf6 ff7 fs1 fc2 sc0 ls1 ws1">uma <span class="_17 blank"> </span>\u201clinha <span class="_10 blank"> </span>reta\u201d, <span class="_17 blank"> </span>diz<span class="_0 blank"> </span>emos <span class="_17 blank"> </span>que <span class="_10 blank"> </span>partícula <span class="_10 blank"> </span>realiza <span class="_10 blank"> </span>um <span class="_17 blank"> </span>\u201c<span class="_0 blank"> </span><span class="ffa">movimento <span class="_10 blank"> </span>retilín<span class="_0 blank"> </span>eo</span>\u201d. <span class="_17 blank"> </span>Nesta <span class="_17 blank"> </span>apostila<span class="_0 blank"> </span>, </div><div class="t m0 x2 h3 yf7 ff1 fs1 fc2 sc0 ls1 ws1">denominaremos este movimento de <span class="ffa">Movimento 1D</span>. </div><div class="t m0 xd h2 yf8 ff1 fs0 fc2 sc0 ls1 ws1">Para que f<span class="_4 blank"></span>iquem <span class="_4 blank"></span>bem entendidos conceitos <span class="_4 blank"></span>e palavras: <span class="_2 blank"></span>o<span class="_0 blank"> </span> m<span class="_4 blank"></span>ovi<span class="_0 blank"> </span>mento <span class="_4 blank"></span>da partícula <span class="_4 blank"></span>se dá <span class="_4 blank"></span>nas <span class="_4 blank"></span>três dimensões </div><div class="t m0 xd h2 y11 ff1 fs0 fc2 sc0 ls1 ws1">do esp<span class="_0 blank"> </span>aço, apenas <span class="_0 blank"> </span>ocorre q<span class="_0 blank"> </span>ue a <span class="_0 blank"> </span>sua trajetó<span class="_0 blank"> </span>ria pod<span class="_0 blank"> </span>e ser <span class="_0 blank"> </span>representada por <span class="_0 blank"> </span>uma cer<span class="_c blank"> </span>ta reta <span class="_0 blank"> </span>(reta esta <span class="_0 blank"> </span>que está<span class="_0 blank"> </span> </div><div class="t m0 xd h2 yf9 ff1 fs0 fc2 sc0 ls1 ws1">no espaço tridimensional).<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 ydd ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y47 ff1 fs1 fc2 sc0 ls1 ws1">O <span class="_d blank"> </span>estudo <span class="_c blank"> </span>detalhado <span class="_d blank"> </span>dos <span class="_d blank"> </span><span class="ff9">Movimentos <span class="_d blank"> </span>1D</span>, <span class="_d blank"> </span>seus <span class="_d blank"> </span>diversos <span class="_c blank"> </span>ti<span class="_0 blank"> </span>pos <span class="_d blank"> </span>e <span class="_d blank"> </span>suas <span class="_d blank"> </span>aplicaçõe<span class="_4 blank"></span>s <span class="_d blank"> </span>na <span class="_d blank"> </span>solução <span class="_d blank"> </span>de </div><div class="t m0 x2 h3 yde ff1 fs1 fc2 sc0 ls1 ws1">diversos tipos de problemas de engenharia é apresentado no Apêndice A. </div><div class="t m0 x2 h3 ydf ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ye0 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 yfa ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 ye1 ff1 fs1 fc2 sc0 ls1 ws1"> <span class="_b blank"> </span> </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x15 yfb w5 hc" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bg8.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>8 </div><div class="t m0 x2 h4 yfc ff2 fs1 fc2 sc0 ls1 wse">2.1<span class="ff8 ls22 ws1"> </span><span class="ws1">Posição </span></div><div class="t m0 x2 h3 yfd ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd yfe ff1 fs1 fc2 sc0 ls1 ws1">A posição <span class="_12 blank"> </span>de uma partíc<span class="_4 blank"></span>ula em movimento <span class="_13 blank"> </span>(3D, 2D <span class="_12 blank"> </span>ou 1D), em <span class="_12 blank"> </span>qualquer instante <span class="ffb ls23">\ue750</span>, é </div><div class="t m0 x2 hd yff ff1 fs1 fc2 sc0 ls1 ws1">determinada <span class="_2 blank"></span>pelo <span class="_2 blank"></span>seu <span class="_2 blank"></span><span class="ff9">vetor <span class="_4 blank"></span>posição<span class="ff1"> <span class="_2 blank"></span><span class="ffb wsf">\ue74e<span class="_18 blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_2 blank"></span>(a <span class="_2 blank"></span>seta <span class="_4 blank"></span>que <span class="_2 blank"></span>vai <span class="_2 blank"></span>da <span class="_2 blank"></span>origem <span class="_2 blank"></span><span class="ffb ls24">\ue731<span class="ff1 ls1"> <span class="_4 blank"></span>de <span class="_2 blank"></span>um <span class="_4 blank"></span>sistema <span class="_2 blank"></span>de <span class="_2 blank"></span>coordenadas </span></span></span></span></span></span></div><div class="t m0 x2 hd y100 ff1 fs1 fc2 sc0 ls1 ws1">com o ponto <span class="ffb ls25">\ue732</span> ocupado pela partícula). </div><div class="t m0 x2 h3 y101 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y102 ff1 fs1 fc2 sc0 ls1 ws1">A <span class="_10 blank"> </span>posi<span class="_0 blank"> </span>ção <span class="_11 blank"> </span>de <span class="_10 blank"> </span>um<span class="_0 blank"> </span>a <span class="_11 blank"> </span>partícula <span class="_11 blank"> </span>em <span class="_11 blank"> </span>movimento <span class="_11 blank"> </span>(3<span class="_0 blank"> </span>D, <span class="_10 blank"> </span>2D <span class="_11 blank"> </span>ou<span class="_0 blank"> </span> <span class="_11 blank"> </span>1D), <span class="_11 blank"> </span>em </div><div class="t m0 x2 hd y103 ff1 fs1 fc2 sc0 ls1 ws1">qualquer <span class="_c blank"> </span>instante <span class="_d blank"> </span><span class="ffb ls23">\ue750</span>, <span class="_c blank"> </span>pode <span class="_d blank"> </span>ser <span class="_d blank"> </span>determinada <span class="_c blank"> </span>também<span class="_0 blank"> </span> <span class="_c blank"> </span>pela <span class="_d blank"> </span>sua <span class="_c blank"> </span><span class="ff9">posição<span class="_0 blank"> </span> </span></div><div class="t m0 x2 hd y104 ff9 fs1 fc2 sc0 ls1 wse">escalar<span class="ff1 ls26 ws1"> <span class="ffb ls27">\ue74f</span><span class="ls1"> <span class="_0 blank"> </span>(o <span class="_c blank"> </span>comprimento <span class="_0 blank"> </span>do <span class="_c blank"> </span>arco <span class="_0 blank"> </span>de <span class="_c blank"> </span>trajetória <span class="_0 blank"> </span>que<span class="_0 blank"> </span> <span class="_0 blank"> </span>vai <span class="_c blank"> </span>de <span class="_c blank"> </span>um <span class="_c blank"> </span>ponto </span></span></div><div class="t m0 x2 hd y105 ff1 fs1 fc2 sc0 ls1 ws1">de <span class="_c blank"> </span>origem <span class="_c blank"> </span><span class="ffb">\ue732</span></div><div class="t m0 x16 he y106 ffb fs7 fc2 sc0 ls28">\uebc8<span class="ff1 fs1 ls1 ws1 v2"> <span class="_c blank"> </span>até <span class="_c blank"> </span>o <span class="_c blank"> </span>ponto <span class="_d blank"> </span><span class="ffb ls25">\ue732</span> <span class="_c blank"> </span>ocupado <span class="_c blank"> </span>pela <span class="_c blank"> </span>pa<span class="_0 blank"> </span>rtícula <span class="_c blank"> </span>ao <span class="_c blank"> </span>longo <span class="_c blank"> </span>de <span class="_c blank"> </span>sua<span class="_0 blank"> </span> </span></div><div class="t m0 x2 h3 y107 ff1 fs1 fc2 sc0 ls1 ws1">trajetória). </div><div class="t m0 x2 h3 y108 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hf y109 ff1 fs1 fc2 sc0 ls2b ws1">O <span class="ff9 ls1">vetor posição</span><span class="ls1d"> <span class="ffb ls1 wsf">\ue74e<span class="_18 blank"></span>\ue526<span class="ff1 ws1"> é uma função vetorial da variável escalar </span><span class="ls23">\ue750</span><span class="ff1 ws1">, ou seja, </span><span class="ws10">\ue74e<span class="_18 blank"></span>\ue526 \ued4c \ue74e<span class="_18 blank"></span>\ue526<span class="_0 blank"></span><span class="ls0 v3">\uf23a</span><span class="ls29">\ue750<span class="ls0 v3">\uf23b</span></span><span class="ff1 ws1">. </span></span></span></span></div><div class="t m0 x2 h3 yf3 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hf y10a ff1 fs1 fc2 sc0 ls1 ws1">A <span class="_4 blank"></span>posição escalar <span class="_4 blank"></span><span class="ffb ls27">\ue74f<span class="ff1 ls1"> é<span class="_4 blank"></span> uma funç<span class="_4 blank"></span>ão escalar<span class="_4 blank"></span> da <span class="_4 blank"></span>variável esc<span class="_4 blank"></span>alar <span class="ffb ls23">\ue750</span>, ou <span class="_2 blank"></span>seja, <span class="ffb ws11">\ue74f<span class="_e blank"> </span>\ued4c \ue74f<span class="_0 blank"></span><span class="ls0 v3">\uf23a</span><span class="ls29">\ue750<span class="ls0 v3">\uf23b</span></span></span>. A <span class="_2 blank"></span>fun<span class="_0 blank"> </span>ção <span class="ffb ws12">\ue74f \ued4c</span></span></span></div><div class="t m0 x2 hf y10b ffb fs1 fc2 sc0 ls27">\ue74f<span class="ls0 v3">\uf23a</span><span class="ls29">\ue750<span class="ls0 v3">\uf23b</span><span class="ff1 ls1 ws1"> é denominada de <span class="ff9">equação horária</span> do movimento. </span></span></div><div class="t m0 x2 h3 y10c ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y10d ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y10e ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h4 y10f ff1 fs1 fc0 sc0 ls2a ws1"> <span class="ff2 fc1 ls1"> </span></div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x2 y110 w6 h10" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bg9.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span>9 </div><div class="t m0 x2 h4 yfc ff2 fs1 fc2 sc0 ls1 wse">2.2<span class="ff8 ls22 ws1"> </span><span class="ws1">Velocidade </span></div><div class="t m0 x2 h3 yfd ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd yfe ff1 fs1 fc2 sc0 ls1 ws1">Considere <span class="_2 blank"></span>uma <span class="_2 blank"></span>partícula <span class="_7 blank"></span>que <span class="_2 blank"></span>no <span class="_2 blank"></span>instante <span class="_2 blank"></span><span class="ffb ls23">\ue750<span class="ff1 ls1"> <span class="_2 blank"></span>passa <span class="_2 blank"></span>pelo <span class="_2 blank"></span>ponto <span class="_2 blank"></span><span class="ffb ls25">\ue732<span class="ff1 ls1"> <span class="_2 blank"></span>definido </span></span></span></span></div><div class="t m0 x2 hd yff ff1 fs1 fc2 sc0 ls1 ws1">pelo <span class="_14 blank"> </span>vetor <span class="_17 blank"> </span>posição <span class="_17 blank"> </span><span class="ffb wsf">\ue74e<span class="_18 blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_14 blank"> </span>e <span class="_17 blank"> </span>que <span class="_17 blank"> </span>no <span class="_17 blank"> </span>instante <span class="_14 blank"> </span></span><span class="ws13">\ue750<span class="_19 blank"> </span>\ued45 \ue3bf\ue750<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_17 blank"> </span>passa <span class="_14 blank"> </span>pel<span class="_0 blank"> </span>o <span class="_17 blank"> </span>ponto <span class="_14 blank"> </span></span></span>\ue732\ue522<span class="ff1 ws1"> </span></span></div><div class="t m0 x2 hd y100 ff1 fs1 fc2 sc0 ls1 ws1">definido pelo vetor posição <span class="ffb ws14">\ue74e<span class="_18 blank"></span>\ue526 <span class="fs7 ls2c v4">\uf1f1</span><span class="ff1 ws1">. </span></span></div><div class="t m0 x2 h3 y101 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y35 ffb fs1 fc2 sc0 ls1 ws14">\ue74e<span class="_18 blank"></span>\ue526 <span class="fs7 ls2d v4">\uf1f1</span><span class="ws13">\ued4c<span class="_19 blank"> </span>\ue74e<span class="_18 blank"></span>\ue526 \ued45 \ue3bf\ue74e<span class="_18 blank"></span>\ue526<span class="ff1 ws1"> </span></span></div><div class="t m0 x2 h3 y103 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y104 ff1 fs1 fc2 sc0 ls1 ws1">O vetor <span class="ffb wsf">\ue3bf\ue74e<span class="_18 blank"></span>\ue526<span class="ff1 ws1"> representa a variação na posição vetorial da partícula, em<span class="_0 blank"> </span> </span></span></div><div class="t m0 x2 h3 y111 ff1 fs1 fc2 sc0 ls1 ws1">intensidade, direção e sentido. </div><div class="t m0 x2 h3 y112 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y108 ff1 fs1 fc2 sc0 ls1 ws1">Define-se <span class="_15 blank"> </span>o <span class="_1a blank"> </span><span class="ff9">vetor <span class="_16 blank"> </span>velocidade <span class="_16 blank"> </span>média</span> <span class="_16 blank"> </span>(<span class="ffb wsf">\ue752<span class="_18 blank"></span>\ue526<span class="fs7 ws15 v5">\uebe0\ue0b1\uebd7\uebdc\uebd4 </span><span class="ff1 ls33 ws1">) <span class="_15 blank"> </span><span class="ls1">da <span class="_16 blank"> </span>partícula, <span class="_16 blank"> </span>no<span class="_0 blank"> </span> </span></span></span></div><div class="t m0 x2 hd y109 ff1 fs1 fc2 sc0 ls1 ws1">intervalo de tempo <span class="ffb wsf">\ue3bf\ue750</span>, como o quociente,<span class="_0 blank"> </span> </div><div class="t m0 x2 h3 yf3 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y113 ffb fs1 fc2 sc0 ls1 wsf">\ue752<span class="_18 blank"></span>\ue526<span class="_4 blank"></span><span class="fs7 ws16 v5">\uebe0\ue0b1\uebd7\uebdc\uebd4 <span class="fs1 ls2e v2">\ued4c</span><span class="ws17 v6">\ue3bf\uebe5</span></span></div><div class="t m0 x10 h11 y114 ffb fs7 fc2 sc0 ls1">\ue526</div><div class="t m0 x17 h11 y115 ffb fs7 fc2 sc0 ls1 ws18">\ue3bf\uebe7 <span class="ff1 fs1 ws1 v7"> </span></div><div class="t m0 x2 h3 y116 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y117 ff1 fs1 fc2 sc0 ls1 ws1">Define-se o <span class="ff9">vetor velocidade <span class="_0 blank"> </span>instantânea</span> da <span class="_0 blank"> </span>partícula, <span class="ff9">no instante <span class="_0 blank"> </span>de </span></div><div class="t m0 x2 hd y118 ff9 fs1 fc2 sc0 ls1 wse">tempo<span class="ff1 ws1"> <span class="ffb ls23">\ue750</span>, como, </span></div><div class="t m0 x2 h3 y119 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y11a ffb fs1 fc2 sc0 ls1 ws19">\ue752<span class="_18 blank"></span>\ue526 \ued4c<span class="_1b blank"> </span>\ue08e\ue08b\ue08f</div><div class="t m0 x18 h12 y11b ffb fs7 fc2 sc0 ls1 ws1a">\ue3bf\uebe7\ue55c\ueb34 <span class="ws17 v8">\ue3bf\uebe5</span></div><div class="t m0 x19 h11 y11c ffb fs7 fc2 sc0 ls1">\ue526</div><div class="t m0 x1a h13 y11d ffb fs7 fc2 sc0 ls1 ws18">\ue3bf\uebe7 <span class="ff1 fs1 ws1 v7"> <span class="_1c blank"> </span> <span class="_1d blank"> </span> <span class="_1d blank"> </span> <span class="_1d blank"> </span><span class="ffb ws11">\ue752<span class="_18 blank"></span>\ue526<span class="_e blank"> </span>\ued4c <span class="fs7 ws17 v9">\uebd7\uebe5</span></span></span></div><div class="t m0 x1b h11 y11c ffb fs7 fc2 sc0 ls1">\ue526</div><div class="t m0 x1c h11 y11d ffb fs7 fc2 sc0 ls34 ws1b">\uebd7\uebe7 <span class="ff1 fs1 ls1 ws1 v7"> </span></div><div class="t m0 x2 h3 y13 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y11e ff1 fs1 fc2 sc0 ls1 ws1">O vetor velocidade <span class="ffb wsf">\ue752<span class="_18 blank"></span>\ue526<span class="ff1 ws1"> é sempre tangente à trajetória da partícula.<span class="_0 blank"> </span> </span></span></div><div class="t m0 x2 h3 y11f ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y120 ff1 fs1 fc2 sc0 ls1 ws1">A <span class="_14 blank"> </span>intensidade <span class="_17 blank"> </span><span class="ffb ls2f">\ue752</span> <span class="_14 blank"> </span>do <span class="_14 blank"> </span>v<span class="_0 blank"> </span>etor <span class="_17 blank"> </span><span class="ffb wsf">\ue752<span class="_18 blank"></span>\ue526<span class="ff1 ls30 ws1"> <span class="ls35">é <span class="_17 blank"> </span><span class="ls1">chamada <span class="_14 blank"> </span>de<span class="_0 blank"> </span> <span class="_14 blank"> </span><span class="ff9">velocidade <span class="_17 blank"> </span>escalar</span> <span class="_14 blank"> </span>da <span class="_17 blank"> </span>partícula. <span class="_17 blank"> </span>Por <span class="_14 blank"> </span>definição, <span class="_17 blank"> </span>a </span></span></span></span></div><div class="t m0 x2 hd y121 ff1 fs1 fc2 sc0 ls1 ws1">intensidade <span class="ffb ls2f">\ue752</span> do vetor <span class="ffb wsf">\ue752<span class="_18 blank"></span>\ue526<span class="ff1 ws1"> é obtida por meio da determinação do módulo do vetor </span>\ue752<span class="_18 blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1">, isto é, </span></span></div><div class="t m0 x2 h3 y122 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hf y123 ffb fs1 fc2 sc0 ls1 ws1c">\ue752<span class="_e blank"> </span>\ued4c <span class="ls31 v3">\ue201</span><span class="wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="v3">\ue201</span><span class="ff1 ws1"> </span></span></div><div class="t m0 x2 h3 y124 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y125 ff1 fs1 fc2 sc0 ls2b ws1">A <span class="ls1">velocidade esca<span class="_4 blank"></span>lar <span class="ffb ls32">\ue752</span> da partícula <span class="_4 blank"></span>pode ser obtida substituindo-se o vetor <span class="ffb wsf">\ue3bf\ue74e<span class="_1e blank"></span>\ue526<span class="ff1 ws1"> pela intensidade </span></span></span></div><div class="t m0 x2 hd y126 ff1 fs1 fc2 sc0 ls1 ws1">desse vetor representada pelo seg<span class="_4 blank"></span>mento de reta <span class="_0 blank"> </span><span class="ffb wsf">\ue732\ue732\ue522</span>, isto é, </div><div class="t m0 x2 h3 y127 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y128 ffb fs1 fc2 sc0 ls1 ws1d">\ue752 \ued4c<span class="_1b blank"> </span>\ue08e\ue08b\ue08f</div><div class="t m0 x18 h12 y129 ffb fs7 fc2 sc0 ls1 ws1a">\ue3bf\uebe7\ue55c\ueb34 <span class="ls36 ws1e v8">\uebc9\uebc9</span><span class="v8">\uf1f1</span></div><div class="t m0 x17 h11 y12a ffb fs7 fc2 sc0 ls1 ws1f">\ue3bf\uebe7 <span class="ff1 fs1 ws1 v7"> </span></div><div class="t m0 x2 h3 y56 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y12b ff1 fs1 fc2 sc0 ls1 ws1">Mas, o <span class="_4 blank"></span>comprimento do seg<span class="_4 blank"></span>mento de reta <span class="ffb wsf">\ue732\ue732\ue522</span> se <span class="_4 blank"></span>aproxima do comprimento <span class="_4 blank"></span>do arco <span class="ffb wsf">\ue732\ue732\ue522</span> (<span class="ffb wsf">\ue3bf\ue74f<span class="_0 blank"></span></span>) à </div><div class="t m0 x2 hd y12c ff1 fs1 fc2 sc0 ls1 ws1">medida que <span class="ffb ws20">\ue3bf\ue750 \ue55c \ue372</span>. Assim, podemos escrever que, </div><div class="t m0 x2 h3 y12d ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y12e ffb fs1 fc2 sc0 ls1 ws1d">\ue752 \ued4c<span class="_1b blank"> </span>\ue08e\ue08b\ue08f</div><div class="t m0 x18 h12 y12f ffb fs7 fc2 sc0 ls1 ws1a">\ue3bf\uebe7\ue55c\ueb34 <span class="ls36 ws1e v8">\uebc9\uebc9</span><span class="v8">\uf1f1</span></div><div class="t m0 x17 h13 y130 ffb fs7 fc2 sc0 ls1 ws21">\ue3bf\uebe7 <span class="fs1 ws22 v7">\ued4c \ue08e\ue08b\ue08f</span></div><div class="t m0 x1d h12 y12f ffb fs7 fc2 sc0 ls1 ws23">\ue3bf\uebe7\ue55c\ueb34 <span class="ws17 v8">\ue3bf\uebe6</span></div><div class="t m0 x7 h13 y130 ffb fs7 fc2 sc0 ls1 ws17">\ue3bf\uebe7<span class="_0 blank"></span><span class="ff1 fs1 ws1 v7"> <span class="_1d blank"> </span> <span class="_1d blank"> </span><span class="ffb ws11">\ue752<span class="_e blank"> </span>\ued4c </span></span><span class="ls34 va">\uebd7\uebe6</span></div><div class="t m0 x1c h11 y130 ffb fs7 fc2 sc0 ls34 ws24">\uebd7\uebe7 <span class="ff1 fs1 ls1 ws1 v7"> </span></div><div class="t m0 x2 h3 y131 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y132 ff1 fs1 fc2 sc0 ls1 ws1">Ou <span class="_11 blank"> </span>seja, <span class="_12 blank"> </span>a <span class="_11 blank"> </span>velocidad<span class="_0 blank"> </span>e <span class="_11 blank"> </span>escalar <span class="_12 blank"> </span><span class="ffb ls2f">\ue752</span> <span class="_12 blank"> </span>também <span class="_12 blank"> </span>pode <span class="_11 blank"> </span>ser <span class="_12 blank"> </span>obtida <span class="_11 blank"> </span>derivando <span class="_12 blank"> </span><span class="ls35">a <span class="_12 blank"> </span></span>equação <span class="_11 blank"> </span>hor<span class="_0 blank"> </span>ária <span class="_11 blank"> </span>do<span class="_0 blank"> </span> </div><div class="t m0 x2 hd y133 ff1 fs1 fc2 sc0 ls1 ws1">movimento da partícula em relação a <span class="ffb ls23">\ue750</span>. </div><div class="t m0 x2 h3 y134 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y135 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y136 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y137 ff1 fs1 fc2 sc0 ls1 ws1"> <span class="_b blank"> </span> </div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x1a y138 w7 h14" alt="" src="https://files.passeidireto.com/a60c65c5-13ca-4550-a605-7408a8b8807b/bga.png"><div class="c x1 y1 w2 h0"><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">Prof.: Carlos Arthur Ca<span class="_0 blank"> </span>valcante<span class="_0 blank"> </span> <span class="_1 blank"> </span><span class="ls0 ws0">10</span> </div><div class="t m0 x2 h4 yfc ff2 fs1 fc2 sc0 ls1 wse">2.3<span class="ff8 ls22 ws1"> </span><span class="ws1">Aceleração </span></div><div class="t m0 x2 h3 yfd ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd yfe ff1 fs1 fc2 sc0 ls1 ws1">Considere <span class="_2 blank"></span>uma pa<span class="_4 blank"></span>rtícula <span class="_2 blank"></span>que no <span class="_2 blank"></span>instante <span class="_4 blank"></span><span class="ffb ls23">\ue750<span class="ff1 ls1"> <span class="_2 blank"></span>passa pe<span class="_4 blank"></span>lo <span class="_4 blank"></span>ponto <span class="_2 blank"></span><span class="ffb ls25">\ue732<span class="ff1 ls1"> com <span class="_2 blank"></span>um ve<span class="_4 blank"></span>tor </span></span></span></span></div><div class="t m0 x2 hd yff ff1 fs1 fc2 sc0 ls1 ws1">velocidade <span class="_d blank"> </span><span class="ffb wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_d blank"> </span>e <span class="_d blank"> </span>que <span class="_d blank"> </span>no <span class="_d blank"> </span>ins<span class="_0 blank"> </span>tante <span class="_d blank"> </span></span><span class="ws13">\ue750<span class="_13 blank"> </span>\ued45 \ue3bf<span class="_0 blank"></span>\ue750<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_d blank"> </span>passa <span class="_d blank"> </span>pelo <span class="_d blank"> </span>ponto <span class="_d blank"> </span></span></span>\ue732\ue522<span class="ff1 ws1"> <span class="_d blank"> </span>com <span class="_d blank"> </span>um <span class="_d blank"> </span>vetor </span></span></div><div class="t m0 x2 hd y100 ff1 fs1 fc2 sc0 ls1 ws1">velocidade <span class="ffb ws25">\ue752<span class="_1e blank"></span>\ue526 <span class="fs7 ls37 v4">\uf1f1</span><span class="ff1 ws1">. </span></span></div><div class="t m0 x2 h3 y101 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y35 ff1 fs1 fc2 sc0 ls1 ws1">Desenhamos os <span class="_1f blank"> </span>vetores <span class="_19 blank"> </span><span class="ffb wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_c blank"> </span><span class="ff1 ls38 ws1"> <span class="ls35">e <span class="_19 blank"> </span></span></span><span class="ws26">\ue752<span class="_1e blank"></span>\ue526 <span class="fs7 ls2c v4">\uf1f1</span><span class="ff1 ws1"> <span class="_1f blank"> </span>a p<span class="_0 blank"> </span>artir d<span class="_0 blank"> </span>e uma<span class="_0 blank"> </span> <span class="_19 blank"> </span>mesma <span class="_19 blank"> </span>ori<span class="_0 blank"> </span>gem <span class="_1f blank"> </span></span><span class="wsf">\ue731\ue522<span class="ff1 ls39 ws1"> <span class="ls21">e </span></span></span></span></span></div><div class="t m0 x2 h3 y103 ff1 fs1 fc2 sc0 ls1 ws1">constatamos que, </div><div class="t m0 x2 h3 y139 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y111 ffb fs1 fc2 sc0 ls1 ws25">\ue752<span class="_1e blank"></span>\ue526 <span class="fs7 ls2d v4">\uf1f1</span><span class="ws13">\ued4c<span class="_1f blank"> </span>\ue752<span class="_1e blank"></span>\ue526<span class="_19 blank"> </span>\ued45 \ue3bf\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> </span></span></div><div class="t m0 x2 h3 y112 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y108 ff1 fs1 fc2 sc0 ls1 ws1">O <span class="_14 blank"> </span>vetor <span class="_17 blank"> </span><span class="ffb wsf">\ue3bf<span class="_0 blank"></span>\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_17 blank"> </span>representa <span class="_17 blank"> </span>a <span class="_17 blank"> </span>variação <span class="_17 blank"> </span>da <span class="_14 blank"> </span>v<span class="_0 blank"> </span>elocidade <span class="_17 blank"> </span></span>\ue752<span class="_18 blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_17 blank"> </span>da <span class="_17 blank"> </span>partícula <span class="_17 blank"> </span>durante <span class="_14 blank"> </span>o<span class="_0 blank"> </span> </span></span></div><div class="t m0 x2 hd y109 ff1 fs1 fc2 sc0 ls1 ws1">intervalo <span class="_11 blank"> </span>de <span class="_11 blank"> </span>tempo <span class="_12 blank"> </span><span class="ffb wsf">\ue3bf\ue750<span class="_0 blank"></span></span>. <span class="_11 blank"> </span>Observar <span class="_11 blank"> </span>qu<span class="_0 blank"> </span>e <span class="_11 blank"> </span><span class="ffb wsf">\ue3bf<span class="_0 blank"></span>\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_12 blank"> </span>representa <span class="_11 blank"> </span>tanto <span class="_11 blank"> </span>a <span class="_11 blank"> </span>vari<span class="_0 blank"> </span>ação <span class="_11 blank"> </span>na </span></span></div><div class="t m0 x2 hd y76 ff1 fs1 fc2 sc0 ls1 ws1">direção do vetor ve<span class="_4 blank"></span>locidade <span class="ffb wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_c blank"> </span><span class="ff1 ws1">, quanto a varia<span class="_4 blank"></span>ção na velocidade<span class="_4 blank"></span> escalar <span class="ffb ls2f">\ue752</span> ou<span class="_0 blank"> </span> </span></span></div><div class="t m0 x2 hd y13a ff1 fs1 fc2 sc0 ls1 ws1">intensidade do vetor velocidade <span class="ffb wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1">. </span></span></div><div class="t m0 x2 h3 y10b ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y13b ff1 fs1 fc2 sc0 ls1 ws1">Define-se <span class="_c blank"> </span>o <span class="_14 blank"> </span><span class="ff9">vetor <span class="_c blank"> </span>aceler<span class="_0 blank"> </span>ação <span class="_d blank"> </span>média</span> <span class="_d blank"> </span>(<span class="ffb wsf">\ue73d<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="fs7 ws17 v5">\uebe0\ue0b1<span class="ls34 ws27">\uebd7\uebdc<span class="ls3a">\uebd4</span></span></span><span class="ff1 ls33 ws1">) <span class="_14 blank"> </span><span class="ls1">da <span class="_c blank"> </span>partícula, <span class="_d blank"> </span>no <span class="_d blank"> </span>intervalo <span class="_d blank"> </span>de </span></span></span></div><div class="t m0 x2 hd y13c ff1 fs1 fc2 sc0 ls1 ws1">tempo <span class="ffb wsf">\ue3bf\ue750</span>, como o quocient<span class="_0 blank"> </span>e, </div><div class="t m0 x2 h3 y13d ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y13e ffb fs1 fc2 sc0 ls1 wsf">\ue73d<span class="_1e blank"></span>\ue526<span class="fs7 ws28 v5">\uebe0\ue0b1\uebd7\uebdc\uebd4 </span><span class="ls2e">\ued4c</span><span class="fs7 ws17 v9">\ue3bf\uebe9</span></div></div><div class="c x1 y1 w8 h0"><div class="t m0 x1e h11 y13f ffb fs7 fc2 sc0 ls1">\uf22c</div></div><div class="c x1f y1 w9 h0"><div class="t m0 x20 h11 y13f ffb fs7 fc2 sc0 ls1">\ue526</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x17 h11 y140 ffb fs7 fc2 sc0 ls1 ws18">\ue3bf\uebe7 <span class="ff1 fs1 ws1 v7"> </span></div><div class="t m0 x2 h3 y141 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y142 ff1 fs1 fc2 sc0 ls1 ws1">Define-se <span class="_2 blank"></span>o <span class="ffa">ve<span class="_4 blank"></span>tor <span class="_4 blank"></span>aceleração <span class="_2 blank"></span>in<span class="_0 blank"> </span>stantânea<span class="ff1"> <span class="_4 blank"></span>da <span class="_2 blank"></span>partícula no <span class="_2 blank"></span>instante <span class="_2 blank"></span>de tempo<span class="_4 blank"></span> </span></span></div><div class="t m0 x2 hd y143 ffb fs1 fc2 sc0 ls23">\ue750<span class="ff1 ls1 ws1"> como o vetor, </span></div><div class="t m0 x2 h3 y144 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y145 ffb fs1 fc2 sc0 ls1 ws29">\ue73d<span class="_1e blank"></span>\ue526 \ued4c<span class="_1a blank"> </span>\ue08e\ue08b\ue08f</div><div class="t m0 x18 h12 y146 ffb fs7 fc2 sc0 ls1 ws1a">\ue3bf\uebe7<span class="_0 blank"></span>\ue55c\ueb34 <span class="ws17 v8">\ue3bf\uebe9</span></div></div><div class="c x1 y1 wa h0"><div class="t m0 x19 h11 y147 ffb fs7 fc2 sc0 ls1">\uf22c</div></div><div class="c x1e y1 wb h0"><div class="t m0 x20 h11 y147 ffb fs7 fc2 sc0 ls1">\ue526</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x1a h13 y148 ffb fs7 fc2 sc0 ls1 ws2a">\ue3bf\uebe7 <span class="ff1 fs1 ws1 v7"> <span class="_20 blank"> </span> <span class="_1d blank"> </span> <span class="_1d blank"> </span><span class="ffb ws1c">\ue73d<span class="_1e blank"></span>\ue526<span class="_e blank"> </span>\ued4c <span class="fs7 ws17 v9">\uebd7\uebe9</span></span></span></div></div><div class="c x1 y1 wc h0"><div class="t m0 x21 h11 y147 ffb fs7 fc2 sc0 ls1">\uf22c</div></div><div class="c x22 y1 wd h0"><div class="t m0 x20 h11 y147 ffb fs7 fc2 sc0 ls1">\ue526</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x23 h11 y148 ffb fs7 fc2 sc0 ls34 ws1b">\uebd7\uebe7 <span class="ff1 fs1 ls1 ws1 v7"> </span></div><div class="t m0 x2 h3 y149 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y14a ff1 fs1 fc2 sc0 ls1 ws1">Observamos que <span class="_12 blank"> </span>o<span class="_0 blank"> </span> vetor aceleração <span class="ffb ws14">\ue73d<span class="_21 blank"></span>\ue526 <span class="ff1 ws1"> é <span class="_12 blank"> </span>tan<span class="_0 blank"> </span>gente à curva <span class="_12 blank"> </span>d<span class="_0 blank"> </span>escrita pela </span></span></div><div class="t m0 x2 hd y14b ff1 fs1 fc2 sc0 ls1 ws1">extremidade <span class="_14 blank"> </span>do <span class="_17 blank"> </span>vetor <span class="_10 blank"> </span><span class="ffb wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> <span class="_17 blank"> </span>(denominada <span class="_14 blank"> </span>de<span class="_0 blank"> </span> <span class="_17 blank"> </span>hodógrafa) <span class="_14 blank"> </span>quando<span class="_0 blank"> </span> <span class="_17 blank"> </span>este <span class="_14 blank"> </span>último <span class="_17 blank"> </span>é </span></span></div><div class="t m0 x2 hd y14c ff1 fs1 fc2 sc0 ls1 ws1">desenhado <span class="_14 blank"> </span>a <span class="_14 blank"> </span>partir <span class="_14 blank"> </span>da <span class="_14 blank"> </span>origem <span class="_14 blank"> </span>fixa <span class="_17 blank"> </span><span class="ffb wsf">\ue731\ue522</span> <span class="_14 blank"> </span>e <span class="_14 blank"> </span>que, <span class="_14 blank"> </span>em <span class="_14 blank"> </span>geral, <span class="_17 blank"> </span><span class="ffb ws14">\ue73d<span class="_21 blank"></span>\ue526 <span class="ff1 ls1e ws1"> <span class="ff9 ls1">não <span class="_14 blank"> </span>é<span class="ff1"> <span class="_14 blank"> </span>tangente <span class="_14 blank"> </span>à </span></span></span></span></div><div class="t m0 x2 h3 y88 ff1 fs1 fc2 sc0 ls1 ws1">trajetória da partícula. </div><div class="t m0 x2 h3 y14d ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y14e ff1 fs1 fc2 sc0 ls1 ws1">Repetindo <span class="_2 blank"></span>uma constataçã<span class="_4 blank"></span>o <span class="_4 blank"></span>importante, <span class="_2 blank"></span>o vetor <span class="_2 blank"></span>aceleração <span class="ffb ws14">\ue73d<span class="_21 blank"></span>\ue526 <span class="ff1 ws1"> <span class="_2 blank"></span>representa <span class="_2 blank"></span>tanto </span></span></div><div class="t m0 x2 hd y14f ff1 fs1 fc2 sc0 ls1 ws1">a <span class="_2 blank"></span>variação <span class="_4 blank"></span>na <span class="_4 blank"></span><span class="ff9 wse">direção<span class="ff1 ws1"> <span class="_4 blank"></span>do ve<span class="_4 blank"></span>tor <span class="_4 blank"></span>velocidade <span class="ffb wsf">\ue752<span class="_21 blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1">, quanto <span class="_2 blank"></span>a <span class="_4 blank"></span>variação <span class="_2 blank"></span>na <span class="_4 blank"></span>velocidade </span></span></span></span></div><div class="t m0 x2 hd y150 ff1 fs1 fc2 sc0 ls1 ws1">escalar <span class="ffb ls2f">\ue752</span> (<span class="ff9 wse">intensidade</span> do vetor velocidade <span class="ffb wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ls33 ws2b">).<span class="_0 blank"> </span><span class="ls1 ws1"> </span></span></span></div><div class="t m0 x2 h3 y151 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 hd y152 ff1 fs1 fc2 sc0 ls1 ws1">Denomina-se <span class="_c blank"> </span>de <span class="_c blank"> </span>aceleraç<span class="_0 blank"> </span>ão <span class="_c blank"> </span>normal <span class="_d blank"> </span><span class="ffb ls3b">\ue73d<span class="fs7 ls3c v5">\uebe1</span></span> <span class="_c blank"> </span>a <span class="_d blank"> </span>componente <span class="_c blank"> </span>do <span class="_d blank"> </span>vetor <span class="_d blank"> </span>aceleração <span class="_c blank"> </span><span class="ffb ws14">\ue73d<span class="_1e blank"></span>\ue526 <span class="ff1 ws1"> <span class="_c blank"> </span>responsável <span class="_d blank"> </span>pela </span></span></div><div class="t m0 x2 hd y23 ff1 fs1 fc2 sc0 ls1 ws1">variação <span class="_12 blank"> </span>n<span class="ls35">a </span><span class="ff9 wse">direção</span> do <span class="_12 blank"> </span>vetor velocidade <span class="ffb wsf">\ue752<span class="_21 blank"></span>\ue526<span class="_c blank"> </span><span class="ff1 ws1"> <span class="_12 blank"> </span>e denomina-se <span class="_12 blank"> </span>de aceleração <span class="_12 blank"> </span>tangencial </span><span class="ls3b">\ue73d<span class="fs7 ls3d v5">\uebe7</span><span class="ff1 ls3e ws1"> <span class="ls21">a </span></span></span></span></div><div class="t m0 x2 hd y153 ff1 fs1 fc2 sc0 ls1 ws1">componente <span class="_2 blank"></span>do <span class="_2 blank"></span>vetor <span class="_7 blank"></span>aceleração <span class="_2 blank"></span><span class="ffb ws14">\ue73d<span class="_21 blank"></span>\ue526 <span class="ff1 ws1"> <span class="_2 blank"></span>responsável <span class="_2 blank"></span>pela <span class="_2 blank"></span>variação <span class="_2 blank"></span>na <span class="_2 blank"></span><span class="ff9 wse">intensidade<span class="ff1 ws1"> <span class="_2 blank"></span>do <span class="_2 blank"></span>vetor <span class="_2 blank"></span>velocidade </span></span></span></span></div><div class="t m0 x2 hd y154 ffb fs1 fc2 sc0 ls1 wsf">\ue752<span class="_1e blank"></span>\ue526<span class="_0 blank"></span><span class="ff1 ws1"> (velocidade escalar). </span></div><div class="t m0 x2 h3 y155 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h3 y156 ff1 fs1 fc2 sc0 ls1 ws1"> </div><div class="t m0 x2 h4 y157 ff1 fs1 fc0 sc0 ls2a ws1"> <span class="ff2 fc1 ls1"> </span></div></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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