<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/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg1.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">1 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y6 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y7 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y8 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y9 ff2 fs1 fc0 sc1 ls2 ws2"> </div><div class="t m0 x0 h4 ya ff3 fs2 fc2 sc0 ls2 ws2">Objetivos del <span class="blank _0"></span>capítulo </div><div class="t m0 x3 h5 yb ff4 fs1 fc3 sc0 ls2 ws0">\u2022<span class="ff3 ls0 ws2"> <span class="ff5 ls2">Estudiar <span class="blank _1"> </span>el <span class="blank _1"> </span>equil<span class="blank _0"></span>ibrio <span class="blank _1"> </span>de <span class="blank _1"> </span>un <span class="blank _1"> </span>sistema <span class="blank _1"> </span>de<span class="blank _0"></span> <span class="blank _1"> </span>fuerzas <span class="blank _1"> </span>concurrentes<span class="blank _0"></span> <span class="blank _1"> </span>en <span class="blank _1"> </span>un </span></span></div><div class="t m0 x4 h5 yc ff5 fs1 fc3 sc0 ls2 ws2">punto o sobre una<span class="blank _0"></span> partícula<span class="blank _0"></span>. </div><div class="t m0 x0 h5 yd ff5 fs1 fc3 sc0 ls2 ws2"> </div><div class="t m0 x3 h5 ye ff4 fs1 fc3 sc0 ls2 ws0">\u2022<span class="ff3 ls0 ws2"> <span class="ff5 ls2">Analizar <span class="blank _2"> </span>los <span class="blank _2"> </span>conceptos <span class="blank _2"> </span>de <span class="blank _2"> </span>fuerzas, <span class="blank _2"> </span>clases <span class="blank _2"> </span>de <span class="blank _2"> </span>fuerzas, <span class="blank _2"> </span>formas <span class="blank _3"> </span>de </span></span></div><div class="t m0 x4 h5 yf ff5 fs1 fc3 sc0 ls2 ws2">representación y<span class="blank _0"></span> unidades. </div><div class="t m0 x0 h5 y10 ff5 fs1 fc3 sc0 ls2 ws2"> </div><div class="t m0 x3 h5 y11 ff4 fs1 fc3 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff5 ls2">Determinar<span class="blank _0"></span> <span class="blank _4"> </span>la <span class="blank _1"> </span>resultante <span class="blank _1"> </span>de <span class="blank _4"> </span>dos <span class="blank _1"> </span>o <span class="blank _4"> </span>más <span class="blank _4"> </span>fuerza<span class="blank _0"></span>s, <span class="blank _1"> </span>mediante <span class="blank _4"> </span>la <span class="blank _1"> </span>ley <span class="blank _4"> </span>del </span></span></div><div class="t m0 x4 h5 y12 ff5 fs1 fc3 sc0 ls2 ws2">paralelogramo<span class="blank _0"></span> y la regla del pol<span class="blank _0"></span>ígono. </div><div class="t m0 x0 h5 y13 ff5 fs1 fc3 sc0 ls2 ws2"> </div><div class="t m0 x3 h5 y14 ff4 fs1 fc3 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff5 ls2">Descomponer<span class="blank _0"></span> <span class="blank _5"> </span>las <span class="blank _5"> </span>fu<span class="blank _0"></span>erzas <span class="blank _5"> </span>en <span class="blank _5"> </span>co<span class="blank _0"></span>mponentes <span class="blank _5"> </span>rec<span class="blank _0"></span>tangulares<span class="blank _0"></span> <span class="blank _5"> </span>y </span></span></div><div class="t m0 x4 h5 y15 ff5 fs1 fc3 sc0 ls2 ws2">sumarlas mediante<span class="blank _0"></span> el método<span class="blank _0"></span> de adición de c<span class="blank _0"></span>omponentes<span class="blank _0"></span>. </div><div class="t m0 x4 h5 y16 ff5 fs1 fc3 sc0 ls2 ws2"> </div><div class="t m0 x3 h5 y17 ff4 fs1 fc3 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff5 ls2">Aplicar <span class="blank _1"> </span>la<span class="blank _0"></span> <span class="blank _1"> </span>primera<span class="blank _0"></span> <span class="blank _1"> </span>ley de <span class="blank _1"> </span>Newton <span class="blank _1"> </span>para<span class="blank _0"></span> <span class="blank _1"> </span>el <span class="blank _1"> </span>equi<span class="blank _0"></span>librio <span class="blank _1"> </span>de <span class="blank _6"> </span>una <span class="blank _6"> </span>partícula </span></span></div><div class="t m0 x4 h5 y18 ff5 fs1 fc3 sc0 ls3 ws1">en<span class="ls2 ws2"> el plano y en<span class="blank _0"></span> el espacio. </span></div><div class="t m0 x4 h3 y19 ff2 fs1 fc3 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y1a ff2 fs1 fc0 sc0 ls2 ws2"> </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 x5 y1b w3 h6" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg2.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">2 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x0 h7 y1c ff6 fs2 fc3 sc0 ls2 ws2">2.1 INTRODUCCIÓ<span class="blank _0"></span>N </div><div class="t m0 x0 h3 y1d ff2 fs1 fc0 sc0 ls2 ws2">El <span class="blank _6"> </span>objetivo <span class="blank _6"> </span>básico del <span class="blank _6"> </span>presente capítulo, <span class="blank _6"> </span>como <span class="blank _6"> </span>ya <span class="blank _6"> </span>se <span class="blank _6"> </span>ha ex<span class="blank _6"> </span>presado, constituye el <span class="blank _1"> </span>análisi<span class="blank _0"></span>s </div><div class="t m0 x0 h3 y1e ff2 fs1 fc0 sc0 ls2 ws2">de equilibrio de un <span class="blank _0"></span>sistema de <span class="blank _0"></span>fuerzas concurrent<span class="blank _0"></span>es en un punto, o sob<span class="blank _0"></span>re una partíc<span class="blank _0"></span>ula. </div><div class="t m0 x0 h3 y1f ff2 fs1 fc0 sc0 ls2 ws2">En Mecánica <span class="blank _0"></span>el tér<span class="blank _0"></span>mino p<span class="blank _0"></span>artícula se <span class="blank _0"></span>utiliza par<span class="blank _0"></span>a referir<span class="blank _0"></span>se a <span class="blank _0"></span>un punto <span class="blank _0"></span>donde actúan una <span class="blank _0"></span>o </div><div class="t m0 x0 h3 y20 ff2 fs1 fc0 sc0 ls2 ws2">varias <span class="blank _7"> </span>fuerzas, <span class="blank _4"> </span>o <span class="blank _8"> </span>a <span class="blank _7"> </span>un <span class="blank _7"> </span>cuerpo <span class="blank _7"> </span>rígido<span class="blank _0"></span> <span class="blank _7"> </span>considerado <span class="blank _4"> </span>c<span class="blank _6"> </span>omo <span class="blank _7"> </span>una <span class="blank _7"> </span>masa <span class="blank _7"> </span>punt<span class="blank _0"></span>ual, <span class="blank _7"> </span>cuando <span class="blank _7"> </span>las </div><div class="t m0 x0 h3 y21 ff2 fs1 fc0 sc0 ls2 ws2">fuerzas <span class="blank _7"> </span>aplicadas <span class="blank _7"> </span>solo <span class="blank _7"> </span>tienden <span class="blank _7"> </span>a <span class="blank _7"> </span>producir <span class="blank _7"> </span>movimientos <span class="blank _7"> </span>de <span class="blank _7"> </span>traslación, <span class="blank _7"> </span>sin <span class="blank _7"> </span>presentarse </div><div class="t m0 x0 h3 y22 ff2 fs1 fc0 sc0 ls2 ws2">acciones de rotac<span class="blank _0"></span>ión. </div><div class="t m0 x0 h3 y23 ff2 fs1 fc0 sc0 ls2 ws2">Muchas <span class="blank _9"> </span>de <span class="blank _9"> </span>las <span class="blank _9"> </span>situacion<span class="blank _0"></span>es <span class="blank _9"> </span>de <span class="blank _9"> </span>equilibrio <span class="blank _9"> </span>en <span class="blank _9"> </span>ingeniería <span class="blank _9"> </span>están <span class="blank _9"> </span>relacionadas <span class="blank _9"> </span>con <span class="blank _9"> </span>la </div><div class="t m0 x0 h3 y24 ff2 fs1 fc0 sc0 ls2 ws2">interacción <span class="blank _1"> </span>de <span class="blank _4"> </span>elementos <span class="blank _1"> </span>que <span class="blank _1"> </span>i<span class="blank _6"> </span>mplican <span class="blank _1"> </span>fuerzas, <span class="blank _4"> </span>cuyas <span class="blank _1"> </span>líneas <span class="blank _4"> </span>de <span class="blank _1"> </span>acción <span class="blank _4"> </span>se <span class="blank _4"> </span>cortan <span class="blank _1"> </span>en <span class="blank _4"> </span>un </div><div class="t m0 x0 h3 y25 ff2 fs1 fc0 sc0 ls2 ws2">punto, <span class="blank _1"> </span>denominadas <span class="blank _6"> </span><span class="fc3 sc2">Fuerzas <span class="blank _1"> </span>Concurrentes</span>, <span class="blank _1"> </span>para <span class="blank _6"> </span>las<span class="blank _6"> </span> <span class="blank _1"> </span>cuales <span class="blank _1"> </span>realizar <span class="blank _6"> </span>la <span class="blank _1"> </span>s<span class="blank _6"> </span>umatoria <span class="blank _6"> </span>de <span class="blank _1"> </span>las </div><div class="t m0 x0 h3 y26 ff2 fs1 fc0 sc0 ls2 ws2">mismas <span class="blank _1"> </span>e <span class="blank _4"> </span>igualarlas <span class="blank _1"> </span>a <span class="blank _4"> </span>cero, <span class="blank _1"> </span>es <span class="blank _4"> </span>suficiente <span class="blank _1"> </span>para <span class="blank _1"> </span>su <span class="blank _4"> </span>análisis<span class="blank _6"> </span> <span class="blank _1"> </span>estático, <span class="blank _4"> </span>al <span class="blank _1"> </span>aplicar <span class="blank _4"> </span>la <span class="blank _4"> </span><span class="fc3 sc2">Primera<span class="blank _0"></span> </span></div><div class="t m0 x0 h3 y27 ff2 fs1 fc3 sc2 ls2 ws2">Ley de Newton<span class="fc0 sc0">. <span class="blank _0"></span>No ocurre lo m<span class="blank _0"></span>ismo, cuando<span class="blank _0"></span> se trata<span class="blank _0"></span> de fuerzas qu<span class="blank _0"></span>e actúan en <span class="blank _0"></span>dos o má<span class="blank _0"></span>s </span></div><div class="t m0 x0 h3 y28 ff2 fs1 fc0 sc0 ls2 ws2">puntos, <span class="blank _a"> </span>o <span class="blank _a"> </span>partículas, <span class="blank _a"> </span>diferentes<span class="blank _0"></span> <span class="blank _a"> </span>de <span class="blank _a"> </span>un <span class="blank _a"> </span>cuerpo <span class="blank _a"> </span>rígido, <span class="blank _a"> </span>las <span class="blank _a"> </span>cuales <span class="blank _a"> </span>no <span class="blank _a"> </span>se <span class="blank _a"> </span>considera<span class="blank _0"></span>n </div><div class="t m0 x0 h3 y29 ff2 fs1 fc0 sc0 ls2 ws2">concurrentes, por l<span class="blank _0"></span>o que requier<span class="blank _0"></span>en, además del men<span class="blank _0"></span>cionado análisis est<span class="blank _0"></span>ático de fuerz<span class="blank _0"></span>as, </div><div class="t m0 x0 h3 y2a ff2 fs1 fc0 sc0 ls2 ws2">obtener la s<span class="blank _6"> </span>umatoria de los <span class="blank _6"> </span>respectivos moment<span class="blank _0"></span>os e <span class="blank _6"> </span>igualarlos a <span class="blank _6"> </span>cero, para cumplir con </div><div class="t m0 x0 h3 y2b ff2 fs1 fc0 sc0 ls4 ws2">la <span class="fc3 sc2 ls2">Primera Ley de Newton<span class="blank _0"></span><span class="fc0 sc0 ls6">. <span class="ls2"> </span></span></span></div><div class="t m0 x0 h3 y2c ff2 fs1 fc0 sc0 ls2 ws2">Las <span class="blank _9"> </span>consideracione<span class="blank _0"></span>s <span class="blank _9"> </span>básicas <span class="blank _9"> </span>tenidas <span class="blank _9"> </span>en <span class="blank _9"> </span>cuenta <span class="blank _9"> </span>en <span class="blank _9"> </span>las <span class="blank _9"> </span>dos <span class="blank _9"> </span>situaciones <span class="blank _9"> </span>anteriores<span class="blank _0"></span> </div><div class="t m0 x0 h3 y2d ff2 fs1 fc0 sc0 ls2 ws2">determinan <span class="blank _8"> </span>la <span class="blank"> </span>d<span class="blank _0"></span>ivisión <span class="blank _8"> </span>entre <span class="blank _2"> </span>el <span class="blank _2"> </span>trata<span class="blank _0"></span>miento <span class="blank _2"> </span>dad<span class="blank _0"></span>o <span class="blank _2"> </span>al <span class="blank _8"> </span><span class="fc3 sc2">Equilibrio <span class="blank"> </span>d<span class="blank _0"></span>e <span class="blank _2"> </span>la <span class="blank _8"> </span>Partícula<span class="blank _6"> </span><span class="fc0 sc0">, <span class="blank _8"> </span>en <span class="blank"> </span>el<span class="blank _0"></span> </span></span></div><div class="t m0 x0 h3 y2e ff2 fs1 fc0 sc0 ls2 ws2">primer <span class="blank _0"></span>ca<span class="blank _0"></span>so, <span class="blank _0"></span>el <span class="blank _b"></span>cual <span class="blank _b"></span>será <span class="blank _0"></span>desarr<span class="blank _0"></span>ollado <span class="blank _b"></span>en <span class="blank _b"></span>es<span class="blank _6"> </span>te <span class="blank _b"></span>capítulo, <span class="blank _b"></span>o <span class="blank _0"></span>al <span class="blank _0"></span><span class="fc3 sc2">Equilibrio <span class="blank _b"></span>de <span class="blank _0"></span>Cuerpos <span class="blank _b"></span>Rígidos<span class="fc0 sc0 ls7">, </span></span></div><div class="t m0 x0 h3 y2f ff2 fs1 fc0 sc0 ls2 ws2">en el segundo, q<span class="blank _0"></span>uedando su estudio para <span class="blank _0"></span>un capítulo poster<span class="blank _0"></span>ior. </div><div class="t m0 x0 h7 y30 ff6 fs2 fc3 sc0 ls2 ws2">2.2 GENERALID<span class="blank _0"></span>ADES SOBRE LA<span class="blank _0"></span>S FUERZAS </div><div class="t m0 x0 h3 y31 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y32 ff2 fs1 fc0 sc0 ls2 ws2">Una <span class="blank _6"> </span>fuerza <span class="blank _6"> </span>se <span class="blank _6"> </span>puede <span class="blank _6"> </span>definir c<span class="blank _6"> </span>omo <span class="blank _6"> </span>la <span class="blank _6"> </span>acción <span class="blank _6"> </span>de <span class="blank _6"> </span>un <span class="blank _6"> </span>cuerpo <span class="blank _6"> </span>sobre <span class="blank _6"> </span>otro. <span class="blank _6"> </span>Las <span class="blank _6"> </span>fuerzas <span class="blank _6"> </span>que <span class="blank _6"> </span>se </div><div class="t m0 x0 h3 y33 ff2 fs1 fc0 sc0 ls2 ws2">ejercen <span class="blank _9"> </span>entre <span class="blank _a"> </span>s<span class="blank _6"> </span>í <span class="blank _9"> </span>los <span class="blank _c"> </span>cuerpos <span class="blank _c"> </span>en <span class="blank _9"> </span>la <span class="blank _c"> </span>naturaleza <span class="blank _9"> </span>responden <span class="blank _a"> </span>a <span class="blank _9"> </span>las <span class="blank _9"> </span>cuatro <span class="blank _c"> </span>s<span class="blank _6"> </span>iguientes<span class="blank _0"></span> </div><div class="t m0 x0 h3 y34 ff2 fs1 fc0 sc0 ls2 ws2">interacciones b<span class="blank _0"></span>ásicas: </div><div class="t m0 x3 h3 y35 ff4 fs1 fc0 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff2 fc3 sc2 ls2">Interacción <span class="blank _4"> </span>Gravitatoria<span class="fc0 sc0">: <span class="blank _1"> </span>ejercidas <span class="blank _4"> </span>por <span class="blank _4"> </span>los <span class="blank _4"> </span>cuerpos <span class="blank _1"> </span>entre <span class="blank _4"> </span>sí <span class="blank _4"> </span>como <span class="blank _4"> </span>consecuencia </span></span></span></div><div class="t m0 x4 h3 y36 ff2 fs1 fc0 sc0 ls2 ws2">de <span class="blank _1"> </span>poseer <span class="blank _6"> </span>masa. <span class="blank _1"> </span>El <span class="blank _1"> </span>peso <span class="blank _1"> </span>de <span class="blank _1"> </span>un <span class="blank _1"> </span>cuerpo <span class="blank _1"> </span>es <span class="blank _1"> </span>el <span class="blank _1"> </span>resultado <span class="blank _6"> </span>de <span class="blank _1"> </span>la <span class="blank _1"> </span>fuerza <span class="blank _1"> </span>gravitacional </div><div class="t m0 x4 h3 y37 ff2 fs1 fc0 sc0 ls2 ws2">ejercida por la tierra.<span class="blank _0"></span> </div><div class="t m0 x3 h3 y38 ff4 fs1 fc0 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff2 fc3 sc2 ls2">Interacción <span class="blank _b"></span>Electromagnética<span class="fc4 sc0 ls8">: <span class="blank _b"></span><span class="fc0 ls2">s<span class="blank _6"> </span>e <span class="blank _b"></span>manifiestan <span class="blank _b"></span>de do<span class="blank _0"></span>s <span class="blank _b"></span>formas: <span class="blank _0"></span>entre <span class="blank _b"></span>partículas <span class="blank _b"></span>con </span></span></span></span></div><div class="t m0 x4 h3 y39 ff2 fs1 fc0 sc0 ls2 ws2">cargas <span class="blank _d"> </span>eléctricas <span class="blank _d"> </span>en <span class="blank _e"> </span>reposo <span class="blank _d"> </span>o <span class="blank _d"> </span>electrostáticas, <span class="blank _e"> </span>o <span class="blank _d"> </span>entre <span class="blank _d"> </span>partículas <span class="blank _d"> </span>con <span class="blank _d"> </span>cargas </div><div class="t m0 x4 h3 y3a ff2 fs1 fc0 sc0 ls2 ws2">eléctricas en movi<span class="blank _0"></span>miento o ma<span class="blank _0"></span>gnéticas. </div><div class="t m0 x0 h3 y3b ff2 fs1 fc0 sc0 ls5 ws2"> <span class="ff4 ls2 ws0 v1">\u2022</span><span class="ff3 ls1 v1"> </span><span class="fc3 sc2 ls2 v1">Interacción <span class="blank _7"> </span>Nuclear <span class="blank _7"> </span>Fuerte<span class="blank _6"> </span></span><span class="ls2 v1">: <span class="blank _7"> </span>son <span class="blank _7"> </span>las<span class="blank _6"> </span> <span class="blank _7"> </span>fuerzas <span class="blank _8"> </span>que <span class="blank _7"> </span>mantienen <span class="blank _7"> </span>los <span class="blank _7"> </span>protones <span class="blank _8"> </span>y <span class="blank _7"> </span>los </span></div><div class="t m0 x4 h3 y3c ff2 fs1 fc0 sc0 ls2 ws2">neutrones junt<span class="blank _0"></span>os en el núcleo del áto<span class="blank _0"></span>mo. </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="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y3d w3 h8" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg3.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">3 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x3 h3 y3e ff4 fs1 fc0 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff2 fc3 sc2 ls2">Interacción <span class="blank _7"> </span>Nuclear <span class="blank _8"> </span>Débil<span class="fc0 sc0">: <span class="blank _8"> </span>fuerzas <span class="blank _7"> </span>entre <span class="blank _8"> </span>partícula<span class="blank _0"></span>s <span class="blank _7"> </span>de <span class="blank _8"> </span>menor <span class="blank _8"> </span>tamaño <span class="blank _7"> </span>relativo </span></span></span></div><div class="t m0 x4 h3 y3f ff2 fs1 fc0 sc0 ls2 ws2">como electrones y<span class="blank _0"></span> positron<span class="blank _0"></span>es, etc. </div><div class="t m0 x0 h3 y40 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y41 ff2 fs1 fc0 sc0 ls2 ws2">Las <span class="blank _d"> </span>c<span class="blank _6"> </span>lases <span class="blank _d"> </span>de <span class="blank _a"> </span>fuerzas <span class="blank _d"> </span>que <span class="blank _a"> </span>son <span class="blank _d"> </span>objetos <span class="blank _a"> </span>de <span class="blank _d"> </span>es<span class="blank _6"> </span>tudio <span class="blank _d"> </span>en <span class="blank _a"> </span>la <span class="blank _d"> </span>Mecánica <span class="blank _a"> </span>Clásica <span class="blank _d"> </span>son <span class="blank _a"> </span>las </div><div class="t m0 x0 h3 y42 ff2 fs1 fc0 sc0 ls2 ws2">relacionadas <span class="blank _7"> </span>con <span class="blank _7"> </span>las <span class="blank _7"> </span>de <span class="blank _7"> </span>interacción <span class="blank _7"> </span>g<span class="blank _6"> </span>ravitatoria<span class="blank _0"></span>s, <span class="blank _7"> </span>como <span class="blank _7"> </span>el <span class="blank _7"> </span>peso <span class="blank _8"> </span>de <span class="blank _7"> </span>los <span class="blank _7"> </span>cuerpos, <span class="blank _7"> </span>cuyas </div><div class="t m0 x0 h3 y43 ff2 fs1 fc0 sc0 ls2 ws2">acciones <span class="blank _0"></span>se <span class="blank _0"></span>manifiestan <span class="blank _b"></span>a distancia <span class="blank _b"></span>y las <span class="blank _0"></span>fuerzas d<span class="blank _0"></span>e <span class="blank _0"></span>contacto, <span class="blank _b"></span>c<span class="blank _6"> </span>omo <span class="blank _0"></span>las <span class="blank _0"></span>fuerzas <span class="blank _b"></span>de empuje </div><div class="t m0 x0 h3 y44 ff2 fs1 fc0 sc0 ls2 ws2">entre <span class="blank _4"> </span>sólidos, <span class="blank _1"> </span>líquidos <span class="blank _1"> </span>y <span class="blank _4"> </span>gases, <span class="blank _4"> </span>las <span class="blank _4"> </span>fuerzas<span class="blank _0"></span> <span class="blank _4"> </span>de <span class="blank _1"> </span>fricción <span class="blank _4"> </span>y <span class="blank _4"> </span>las <span class="blank _4"> </span>fuerzas <span class="blank _1"> </span>elásticas, <span class="blank _1"> </span>las <span class="blank _4"> </span>cuales </div><div class="t m0 x0 h3 y45 ff2 fs1 fc0 sc0 ls2 ws2">actúan <span class="blank _0"></span>en <span class="blank _b"></span>las <span class="blank _0"></span>cercanías <span class="blank _b"></span>entre <span class="blank _0"></span>los <span class="blank _0"></span>cuerpos, <span class="blank _b"></span>considerándose <span class="blank _b"></span>éstas <span class="blank _0"></span>dentro <span class="blank _b"></span>de <span class="blank _0"></span>la <span class="blank _0"></span>clasificación<span class="blank _0"></span> </div><div class="t m0 x0 h3 y46 ff2 fs1 fc0 sc0 ls2 ws2">de las de Intera<span class="blank _0"></span>cción Electromagnét<span class="blank _0"></span>ica. </div><div class="t m0 x0 h3 y47 ff2 fs1 fc0 sc0 ls2 ws2">Las <span class="blank _0"></span>fuerzas <span class="blank _0"></span>entre <span class="blank _b"></span>los cuer<span class="blank _0"></span>pos pr<span class="blank _0"></span>oducen <span class="blank _b"></span>dos efect<span class="blank _0"></span>os <span class="blank _b"></span>que son <span class="blank _b"></span>es<span class="blank _6"> </span>tudiado<span class="blank _0"></span>s en <span class="blank _b"></span>Mecánica: <span class="blank _b"></span>uno </div><div class="t m0 x0 h3 y48 ff2 fs1 fc0 sc0 ls2 ws2">externo, <span class="blank _b"></span>que <span class="blank _0"></span>se <span class="blank _b"></span>manifiesta <span class="blank _b"></span>en el <span class="blank _b"></span>cambio <span class="blank _b"></span>del e<span class="blank _0"></span>stado <span class="blank _b"></span>de <span class="blank _0"></span>reposo <span class="blank _b"></span>o d<span class="blank _0"></span>e <span class="blank _b"></span>movimiento <span class="blank _b"></span>del cu<span class="blank _0"></span>erpo </div><div class="t m0 x0 h3 y49 ff2 fs1 fc0 sc0 ls2 ws2">sobre <span class="blank _1"> </span>el <span class="blank _1"> </span>cual <span class="blank _1"> </span>actúan <span class="blank _1"> </span>y <span class="blank _1"> </span>otro <span class="blank _1"> </span>i<span class="blank _6"> </span>nterno, <span class="blank _1"> </span>que <span class="blank _1"> </span>tiende <span class="blank _1"> </span>a <span class="blank _1"> </span>deformarlo. <span class="blank _6"> </span>Como <span class="blank _1"> </span>s<span class="blank _1"> </span>e <span class="blank _1"> </span>ha <span class="blank _1"> </span>expresado, <span class="blank _1"> </span>el </div><div class="t m0 x0 h3 y4a ff2 fs1 fc0 sc0 ls2 ws2">análisis del <span class="blank _6"> </span>primero <span class="blank _6"> </span>es c<span class="blank _6"> </span>ontemplado en <span class="blank _6"> </span>la <span class="blank _6"> </span><span class="fc3 sc2">Mecánica <span class="blank _6"> </span>de <span class="blank _6"> </span>los <span class="blank _6"> </span>Cuerpos <span class="blank _6"> </span>Rígidos</span>, <span class="blank _6"> </span>mientras el </div><div class="t m0 x0 h3 y4b ff2 fs1 fc0 sc0 ls2 ws2">segundo, se estud<span class="blank _0"></span>ia en la <span class="fc3 sc2">Mecánica de los Cu<span class="blank _0"></span>erpos Deformables<span class="fc0 sc0">. </span></span></div><div class="t m0 x0 h7 y4c ff6 fs2 fc3 sc0 ls2 ws2">2.3 CANTIDAD<span class="blank _0"></span>ES ESCALAR<span class="blank _0"></span>ES Y VECTOR<span class="blank _0"></span>IALES </div><div class="t m0 x0 h3 y4d ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y4e ff2 fs1 fc0 sc0 ls2 ws2">Las <span class="blank _1"> </span>cantidades <span class="blank _6"> </span>físicas <span class="blank _6"> </span>como <span class="blank _1"> </span>el <span class="blank _1"> </span>tiempo, <span class="blank _6"> </span>la <span class="blank _1"> </span>masa, <span class="blank _1"> </span>el <span class="blank _1"> </span>volumen, <span class="blank _6"> </span>la <span class="blank _1"> </span>temperatura <span class="blank _6"> </span>y <span class="blank _1"> </span>la <span class="blank _1"> </span>energía </div><div class="t m0 x0 h3 y4f ff2 fs1 fc0 sc0 ls2 ws2">que <span class="blank _4"> </span>pueden <span class="blank _4"> </span>expresarse <span class="blank _4"> </span>completament<span class="blank _0"></span>e, <span class="blank _4"> </span>en <span class="blank _7"> </span>forma <span class="blank _1"> </span>matemática, <span class="blank _4"> </span>mediante <span class="blank _4"> </span>un <span class="blank _4"> </span>número <span class="blank _4"> </span>o </div><div class="t m0 x0 h3 y50 ff2 fs1 fc0 sc0 ls2 ws2">escalar, <span class="blank _1"> </span>se <span class="blank _6"> </span>les<span class="blank _6"> </span> <span class="blank _1"> </span>denominan <span class="blank _6"> </span>cantidades <span class="blank _1"> </span>escalares. <span class="blank _6"> </span>Estas <span class="blank _1"> </span>se <span class="blank _1"> </span>caracterizan <span class="blank _6"> </span>porque <span class="blank _1"> </span>obedecen </div><div class="t m0 x0 h3 y51 ff2 fs1 fc0 sc0 ls2 ws2">las <span class="blank _b"></span>reglas <span class="blank _b"></span>de <span class="blank _0"></span>la <span class="blank _b"></span>adición <span class="blank _b"></span>del <span class="blank _b"></span>álgebra <span class="blank _b"></span>ordinaria. <span class="blank _b"></span>O <span class="blank _0"></span>sea <span class="blank _b"></span>que <span class="blank _b"></span>resulta <span class="blank _0"></span>válido <span class="blank _b"></span>sumar, <span class="blank _b"></span>por <span class="blank _b"></span>ejemplo, </div><div class="t m0 x0 h3 y30 ff2 fs1 fc0 sc0 ls2 ws2">un <span class="blank _6"> </span>tiempo <span class="blank _1"> </span>de <span class="blank _6"> </span>10 <span class="blank _6"> </span>segundos <span class="blank _6"> </span>más <span class="blank _6"> </span>un <span class="blank _1"> </span>tiempo <span class="blank _6"> </span>de <span class="blank _6"> </span>5 <span class="blank _1"> </span>segundos, para <span class="blank _1"> </span>obtener <span class="blank _6"> </span>un <span class="blank _1"> </span>ti<span class="blank _0"></span>empo <span class="blank _1"> </span>total<span class="blank _0"></span> </div><div class="t m0 x0 h3 y52 ff2 fs1 fc0 sc0 ls2 ws2">de 15 segundos.<span class="blank _0"></span> </div><div class="t m0 x0 h3 y53 ff2 fs1 fc0 sc0 ls2 ws2">En cambio, las e<span class="blank _0"></span>xpresiones como la vel<span class="blank _0"></span>ocidad, la ace<span class="blank _0"></span>leración, la cantidad de <span class="blank _0"></span>movimiento<span class="blank _0"></span> </div><div class="t m0 x0 h3 y54 ff2 fs1 fc0 sc0 ls2 ws2">y <span class="blank _1"> </span>la <span class="blank _1"> </span>fuerza, <span class="blank _4"> </span>las <span class="blank _6"> </span>c<span class="blank _6"> </span>uales <span class="blank _1"> </span>para <span class="blank _1"> </span>ser <span class="blank _4"> </span>definidas <span class="blank _1"> </span>plenam<span class="blank _0"></span>ente <span class="blank _1"> </span>requieren <span class="blank _1"> </span>de <span class="blank _1"> </span>una <span class="blank _1"> </span>magnitud <span class="blank _1"> </span>y <span class="blank _1"> </span>una </div><div class="t m0 x0 h3 y55 ff2 fs1 fc0 sc0 ls2 ws2">dirección, <span class="blank _6"> </span>o <span class="blank _6"> </span>más <span class="blank _1"> </span>de <span class="blank _6"> </span>un <span class="blank _6"> </span>escalar, <span class="blank _1"> </span>se <span class="blank _6"> </span>conocen <span class="blank _6"> </span>con <span class="blank _1"> </span>el <span class="blank _6"> </span>nombre <span class="blank _6"> </span>de <span class="blank _6"> </span>c<span class="blank _6"> </span>antidades <span class="blank _6"> </span>vect<span class="blank _0"></span>oriales<span class="blank _6"> </span>, <span class="blank _1"> </span>las </div><div class="t m0 x0 h3 y56 ff2 fs1 fc0 sc0 ls2 ws2">cuales <span class="blank _6"> </span>están <span class="blank _6"> </span>sujetas <span class="blank _6"> </span>a <span class="blank _6"> </span>reglas es<span class="blank _6"> </span>peciales para <span class="blank _6"> </span>la <span class="blank _1"> </span>adición, tal <span class="blank _6"> </span>como <span class="blank _6"> </span>la <span class="blank _1"> </span>denomin<span class="blank _0"></span>ada <span class="blank _1"> </span><span class="fc3 sc2">Ley <span class="blank _6"> </span>del </span></div><div class="t m0 x0 h3 y57 ff2 fs1 fc3 sc2 ls2 ws3">Paralelogramo<span class="fc0 sc0 ws2">, la cual <span class="blank _0"></span>será estudiada má<span class="blank _0"></span>s adelante. </span></div><div class="t m0 x0 h3 y18 ff2 fs1 fc0 sc0 ls2 ws2">Debido a que resulta erróneo confundi<span class="blank _0"></span>r cantidades escalares con vector<span class="blank _0"></span>iales, porque no </div><div class="t m0 x0 h3 y19 ff2 fs1 fc0 sc0 ls2 ws2">cumplen la<span class="blank _0"></span>s mis<span class="blank _0"></span>mas re<span class="blank _0"></span>glas de <span class="blank _0"></span>operaciones<span class="blank _0"></span>, es <span class="blank _0"></span>necesario <span class="blank _0"></span>recurrir <span class="blank _b"></span>a algún tipo <span class="blank _b"></span>especial de<span class="blank _0"></span> </div><div class="t m0 x0 h3 y1a ff2 fs1 fc0 sc0 ls2 ws2">escritura <span class="blank _6"> </span>con <span class="blank _1"> </span>el <span class="blank _6"> </span>fin <span class="blank _1"> </span>de <span class="blank _6"> </span>diferenciarlas. <span class="blank _6"> </span>Una <span class="blank _6"> </span>for<span class="blank _6"> </span>ma <span class="blank _6"> </span>c<span class="blank _6"> </span>omún, <span class="blank _6"> </span>la <span class="blank _1"> </span>cual <span class="blank _6"> </span>usaremos <span class="blank _6"> </span>en <span class="blank _1"> </span>este <span class="blank _6"> </span>texto, </div><div class="t m0 x0 h3 y58 ff2 fs1 fc0 sc0 ls2 ws2">consiste en indicar una cantidad vectorial med<span class="blank _0"></span>iante una letra mayúscula en negrilla con </div><div class="t m0 x0 h3 y59 ff2 fs1 fc0 sc0 ls2 ws2">una punta <span class="blank _0"></span>de <span class="blank _0"></span>flecha enc<span class="blank _0"></span>ima, ejemp<span class="blank _0"></span>lo <span class="ff7">\ued04</span></div></div><div class="c x1 y1 w4 h0"><div class="t m0 x6 h3 y5a ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7 y1 w5 h0"><div class="t m0 x8 h3 y5a ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7 y1 w6 h0"><div class="t m0 x8 h3 y5a ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x9 h3 y59 ff2 fs1 fc0 sc0 ls2 ws2">, mientra<span class="blank _0"></span>s que <span class="blank _b"></span>para expresar una<span class="blank _0"></span> cant<span class="blank _0"></span>idad es<span class="blank _0"></span>calar </div><div class="t m0 x0 h3 y5b ff2 fs1 fc0 sc0 ls2 ws2">se hará simplem<span class="blank _0"></span>ente mediante una letr<span class="blank _0"></span>a mayúscula, así: <span class="blank _0"></span>V. </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="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x5 y5c w3 h9" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg4.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">4 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x0 h7 y5d ff6 fs2 fc3 sc0 ls2 ws2">2.4 OPERACIO<span class="blank _0"></span>NES ENTRE ESCALAR<span class="blank _0"></span>ES Y V<span class="blank _0"></span>ECTORES </div><div class="t m0 x0 h3 y5e ff2 fs1 fc3 sc2 ls2 ws2"> </div><div class="t m0 x0 h3 y5f ff2 fs1 fc3 sc2 ls2 ws3">Definiciones<span class="fc0 sc0 ls8 ws2">: <span class="blank _1"> </span><span class="ls2">los <span class="blank _1"> </span>siguientes <span class="blank _6"> </span>términos <span class="blank _1"> </span>son <span class="blank _6"> </span>necesarios <span class="blank _1"> </span>para <span class="blank _1"> </span>establecer <span class="blank _6"> </span>operaciones <span class="blank _1"> </span>entre<span class="blank _0"></span> </span></span></div><div class="t m0 x0 h3 y60 ff2 fs1 fc0 sc0 ls2 ws2">escalares y vecto<span class="blank _0"></span>res: </div><div class="t m0 x3 h3 y61 ff4 fs1 fc0 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff2 ls2">Se <span class="blank _0"></span>define <span class="blank _0"></span>el <span class="blank _0"></span>vector <span class="ff7">\ued04</span></span></span></div></div><div class="c x1 y1 w7 h0"><div class="t m0 xa h3 y62 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xb y1 w8 h0"><div class="t m0 x8 h3 y62 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xb y1 w9 h0"><div class="t m0 x8 h3 y62 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 xc h3 y61 ff2 fs1 fc0 sc0 ls2 ws2"> <span class="blank _0"></span>de magnitud <span class="blank _b"></span>V y <span class="blank _b"></span>s<span class="blank _6"> </span>e indica <span class="blank _b"></span>su sentido <span class="blank _b"></span>m<span class="blank _6"> </span>ediante <span class="blank _0"></span>una <span class="blank _0"></span>punta de<span class="blank _0"></span> </div><div class="t m0 x4 h3 y63 ff7 fs1 fc0 sc0 ls2 ws3">\ue688\ue68e\ue687\ue685\ue68a\ue683\ue603\ue69b\ue603\ue695\ue697<span class="blank _0"></span>\ue603\ue686\ue68b\ue694\ue687\ue685\ue685\ue68b\ue6d7\ue690\ue603\ue685<span class="blank _0"></span>\ue691\ue690\ue603\ue687\ue68e\ue603\ue69e\ue690\ue689<span class="blank _0"></span>\ue697\ue68e\ue691\ue603\ue83d\ue603\ue693\ue697\ue687\ue603\ue688\ue691<span class="blank _0"></span>\ue694\ue68f\ue683\ue603\ue685\ue691\ue690\ue603<span class="blank _0"></span>\ue697\ue690\ue603\ue687\ue68c\ue687\ue603\ue686\ue687<span class="blank _0"></span>\ue603\ue694\ue687\ue688\ue687\ue694\ue687\ue690\ue685\ue68b\ue683\ue7e1<span class="blank _0"></span>\ue603\ue685\ue691\ue68f\ue691\ue603\ue695\ue687<span class="blank _0"></span>\ue603</div><div class="t m0 x4 h3 y64 ff2 fs1 fc0 sc0 ls2 ws2">muestra en la F<span class="blank _0"></span>igura 2.1 (a). </div><div class="t m0 x3 h3 y65 ff4 fs1 fc0 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff2 ls2">Dos <span class="blank _6"> </span>vectores <span class="ff7">\ued04</span></span></span></div></div><div class="c x1 y1 wa h0"><div class="t m0 xd h3 y66 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xe y1 wb h0"><div class="t m0 x8 h3 y66 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xe y1 wc h0"><div class="t m0 x8 h3 y66 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 xf h3 y65 ff7 fs1 fc0 sc0 ls2 ws3">\ue603<span class="ff2 ws2">son iguales <span class="blank _6"> </span>si <span class="blank _6"> </span>tienen <span class="blank _6"> </span>la <span class="blank _6"> </span>misma m<span class="blank _6"> </span>agnitud, la <span class="blank _6"> </span>misma <span class="blank _6"> </span>dirección y <span class="blank _1"> </span>el </span></div><div class="t m0 x4 h3 y67 ff2 fs1 fc0 sc0 ls2 ws2">mismo sentido, se<span class="blank _0"></span>gún se ilustra en la F<span class="blank _0"></span>igura 2.1 (b). </div><div class="t m0 x3 h3 y68 ff4 fs1 fc0 sc0 ls2 ws0">\u2022<span class="ff3 ls1 ws2"> <span class="ff2 ls2">El <span class="blank _6"> </span>vector <span class="blank _6"> </span>negativo <span class="ff7 ws3">\uf346\ue603\ued04\ue603</span></span></span></div></div><div class="c x1 y1 wd h0"><div class="t m0 x10 h3 y69 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x11 y1 we h0"><div class="t m0 x8 h3 y69 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x12 y1 we h0"><div class="t m0 x8 h3 y69 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x13 y1 wf h0"><div class="t m0 x1 h3 y69 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x14 h3 y68 ff7 fs1 fc0 sc0 ls2 ws3">\ue603<span class="ff2 ws2">de <span class="blank _6"> </span>un <span class="blank _6"> </span>vector <span class="blank _6"> </span></span>\ued04</div></div><div class="c x1 y1 w10 h0"><div class="t m0 x15 h3 y69 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x16 y1 w5 h0"><div class="t m0 x8 h3 y69 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x16 y1 w11 h0"><div class="t m0 x8 h3 y69 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x17 h3 y68 ff7 fs1 fc0 sc0 ls2 ws3">\ue7e1\ue603<span class="ff2 ws2">se define c<span class="blank _6"> </span>omo <span class="blank _6"> </span>aquel que <span class="blank _6"> </span>tiene <span class="blank _6"> </span>la <span class="blank _6"> </span>misma </span></div><div class="t m0 x4 h3 y6a ff2 fs1 fc0 sc0 ls2 ws2">magnitud, <span class="blank _4"> </span>la <span class="blank _7"> </span>misma <span class="blank _7"> </span>dirección <span class="blank _7"> </span>y <span class="blank _4"> </span>sentido <span class="blank _7"> </span>contrario <span class="blank _4"> </span>a <span class="blank _8"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w12 h0"><div class="t m0 x18 h3 y6b ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x19 y1 w5 h0"><div class="t m0 x8 h3 y6b ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x19 y1 w13 h0"><div class="t m0 x8 h3 y6b ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x1a h3 y6a ff2 fs1 fc0 sc0 ls6 ws2">, <span class="blank _7"> </span><span class="ls2">lo <span class="blank _7"> </span>cual <span class="blank _4"> </span>se <span class="blank _7"> </span>aprecia <span class="blank _7"> </span>en <span class="blank _4"> </span>la </span></div><div class="t m0 x4 h3 y6c ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.1 (c). </div><div class="t m0 x1b h3 y6d ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 y6e ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.1 </div><div class="t m0 x0 h3 y6f ff2 fs1 fc3 sc2 ls2 ws2">Producto <span class="blank _9"> </span>de <span class="blank _c"> </span>un <span class="blank _9"> </span>Escalar <span class="blank _9"> </span>por <span class="blank _9"> </span>un <span class="blank _c"> </span>V<span class="blank _6"> </span>ector: <span class="blank _9"> </span><span class="fc0 sc0">la <span class="blank _9"> </span>suma <span class="blank _9"> </span>de <span class="blank _9"> </span>dos <span class="blank _c"> </span>vectores <span class="blank _c"> </span>i<span class="blank _6"> </span>guales <span class="blank _9"> </span><span class="ff7">\ued04</span></span></div></div><div class="c x1 y1 w14 h0"><div class="t m0 x1d h3 y70 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x1e y1 w5 h0"><div class="t m0 x8 h3 y70 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x1e y1 w15 h0"><div class="t m0 x8 h3 y70 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x1f h3 y6f ff7 fs1 fc0 sc0 ls2 ws4">\uf345<span class="blank"> </span>\ued04</div></div><div class="c x1 y1 w16 h0"><div class="t m0 x20 h3 y70 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x21 y1 w5 h0"><div class="t m0 x8 h3 y70 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x21 y1 w17 h0"><div class="t m0 x8 h3 y70 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x22 h3 y6f ff2 fs1 fc0 sc0 ls7 ws2">, </div><div class="t m0 x0 h3 y71 ff2 fs1 fc0 sc0 ls2 ws2">corresponde <span class="blank _7"> </span>al <span class="blank _7"> </span>vector <span class="blank _8"> </span>2<span class="ff7">\ued04</span></div></div><div class="c x1 y1 w18 h0"><div class="t m0 x23 h3 y72 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x24 y1 wb h0"><div class="t m0 x8 h3 y72 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x24 y1 w19 h0"><div class="t m0 x8 h3 y72 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x25 h3 y71 ff7 fs1 fc0 sc0 ls6">\ue7e1<span class="ff2 ls2 ws2"> <span class="blank _7"> </span>de <span class="blank _8"> </span>magnitud <span class="blank _7"> </span>2V, <span class="blank _7"> </span>c<span class="blank _6"> </span>uya <span class="blank _7"> </span>dirección <span class="blank _8"> </span>y <span class="blank _7"> </span>sentido <span class="blank _7"> </span>es <span class="blank _8"> </span>la <span class="blank _8"> </span>misma <span class="blank _7"> </span>del </span></div><div class="t m0 x0 h3 y73 ff2 fs1 fc0 sc0 ls2 ws2">vector <span class="blank"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w1a h0"><div class="t m0 x4 h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x26 y1 w1b h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x26 y1 w1c h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x27 h3 y73 ff2 fs1 fc0 sc0 ls2 ws2">, <span class="blank"> </span>como <span class="blank"> </span>lo <span class="blank"> </span>muestra <span class="blank"> </span>la <span class="blank"> </span>Figura <span class="blank"> </span>2.2 <span class="blank"> </span>(a), <span class="blank"> </span>asimismo, <span class="blank"> </span>la <span class="blank"> </span>adición <span class="blank"> </span>de <span class="blank"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w1d h0"><div class="t m0 x28 h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x29 y1 w1e h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x29 y1 w1f h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x2a h3 y73 ff7 fs1 fc0 sc0 ls2 ws5">\uf345<span class="blank"> </span>\ued04</div></div><div class="c x1 y1 w20 h0"><div class="t m0 x2b h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2c y1 w1e h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2c y1 w21 h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x2d h3 y73 ff7 fs1 fc0 sc0 ls2 ws4">\uf345<span class="blank"> </span>\ued04</div></div><div class="c x1 y1 w22 h0"><div class="t m0 x2e h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2f y1 w5 h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2f y1 w23 h0"><div class="t m0 x8 h3 y74 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x30 h3 y73 ff2 fs1 fc0 sc1 ls9 ws2"> <span class="sc0 ls2">es </span></div><div class="t m0 x0 h3 y75 ff2 fs1 fc0 sc0 ls2 ws2">equivalente al ve<span class="blank _0"></span>ctor 3<span class="ff7">\ued04</span></div></div><div class="c x1 y1 w24 h0"><div class="t m0 xf h3 y76 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x31 y1 w5 h0"><div class="t m0 x8 h3 y76 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x31 y1 w25 h0"><div class="t m0 x8 h3 y76 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x32 h3 y75 ff7 fs1 fc0 sc0 ls2 ws3">\ue7e1\ue603<span class="ff2 ws2">de magnitu<span class="blank _0"></span>d 3V con dir<span class="blank _0"></span>ección y<span class="blank _0"></span> sentido igu<span class="blank _0"></span>al al vector <span class="ff7">\ued04</span></span></div></div><div class="c x1 y1 w26 h0"><div class="t m0 x33 h3 y76 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2d y1 w1e h0"><div class="t m0 x8 h3 y76 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2d y1 w27 h0"><div class="t m0 x8 h3 y76 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x34 h3 y75 ff7 fs1 fc0 sc0 ls2 ws3">\ue7e1\ue603<span class="ff2 ws2">como </span></div><div class="t m0 x0 h3 y77 ff2 fs1 fc0 sc0 ls2 ws2">se indica en la F<span class="blank _0"></span>igura 2.2 (b). </div><div class="t m0 x0 h3 y78 ff2 fs1 fc0 sc0 ls2 ws2">En <span class="blank _4"> </span>forma <span class="blank _7"> </span>general, <span class="blank _4"> </span>la <span class="blank _4"> </span>s<span class="blank _6"> </span>uma <span class="blank _4"> </span>de <span class="blank _7"> </span>k <span class="blank _4"> </span>vectores <span class="blank _4"> </span>iguales <span class="blank _7"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w28 h0"><div class="t m0 x35 h3 y79 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x36 y1 w5 h0"><div class="t m0 x8 h3 y79 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x36 y1 w29 h0"><div class="t m0 x8 h3 y79 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x37 h3 y78 ff7 fs1 fc0 sc0 ls2 ws3">\ue7e1\ue603<span class="ff2 ws2">se <span class="blank _4"> </span>representa <span class="blank _7"> </span>por <span class="blank _4"> </span>el <span class="blank _4"> </span>producto <span class="blank _7"> </span>k</span>\ued04</div></div><div class="c x1 y1 w2a h0"><div class="t m0 x38 h3 y79 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x20 y1 w5 h0"><div class="t m0 x8 h3 y79 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x39 y1 w2b h0"><div class="t m0 x8 h3 y79 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x21 h3 y78 ff7 fs1 fc0 sc0 ls2 ws3">\ue7e1\ue603<span class="ff2 ws2"> </span></div><div class="t m0 x0 h3 y7a ff2 fs1 fc0 sc0 ls2 ws2">como un <span class="blank _6"> </span>vector de mag<span class="blank _6"> </span>nitud kV con <span class="blank _6"> </span>la misma <span class="blank _6"> </span>dirección <span class="blank _6"> </span>y sentido de <span class="blank _6"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w2c h0"><div class="t m0 x3a h3 y7b ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3b y1 w5 h0"><div class="t m0 x8 h3 y7b ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3b y1 w2d h0"><div class="t m0 x8 h3 y7b ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x3c h3 y7a ff7 fs1 fc0 sc0 ls6">\ue7e1<span class="ff2 ls2 ws2"> c<span class="blank _6"> </span>omo se aprecia </span></div><div class="t m0 x0 h3 y7c ff2 fs1 fc0 sc0 ls2 ws2">en la Figura 2.2(c).<span class="blank _0"></span> </div><div class="t m0 x0 h3 y7d ff2 fs1 fc0 sc0 ls2 ws2">Debido <span class="blank _0"></span>a <span class="blank _b"></span>que el <span class="blank _b"></span>escalar <span class="blank _0"></span>k <span class="blank _b"></span>puede ser <span class="blank _b"></span>positivo <span class="blank _0"></span>o <span class="blank _b"></span>negativo, <span class="blank _b"></span>s<span class="blank _6"> </span>e <span class="blank _0"></span>puede <span class="blank _b"></span>afirmar <span class="blank _0"></span>que <span class="blank _b"></span>el producto<span class="blank _0"></span> </div><div class="t m0 x0 h3 y7e ff2 fs1 fc0 sc0 ls2 ws3">k<span class="ff7">\ued04</span></div></div><div class="c x1 y1 w2e h0"><div class="t m0 x3d h3 y7f ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3e y1 wb h0"><div class="t m0 x8 h3 y7f ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3e y1 w2f h0"><div class="t m0 x8 h3 y7f ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x3f h3 y7e ff2 fs1 fc0 sc0 ls2 ws2"> <span class="blank _1"> </span>resulta <span class="blank _6"> </span>s<span class="blank _6"> </span>er <span class="blank _1"> </span>un <span class="blank _6"> </span>vector <span class="blank _1"> </span>de <span class="blank _1"> </span>magnitud <span class="blank _6"> </span>kV <span class="blank _1"> </span>con <span class="blank _1"> </span>la <span class="blank _1"> </span>misma <span class="blank _1"> </span>direcc<span class="blank _0"></span>ión <span class="blank _1"> </span>y <span class="blank _1"> </span>sentido <span class="blank _6"> </span>de <span class="blank _4"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w30 h0"><div class="t m0 x2b h3 y7f ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x2c y1 w5 h0"><div class="t m0 x8 h3 y7f ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x33 y1 w31 h0"><div class="t m0 x8 h3 y7f ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x40 h3 y7e ff2 fs1 fc0 sc0 ls6">,<span class="sc1 lsa ws2"> </span><span class="ls2 ws2">si <span class="blank _1"> </span>k <span class="blank _6"> </span>es </span></div><div class="t m0 x0 h3 y80 ff2 fs1 fc0 sc0 ls2 ws2">positivo, <span class="blank _8"> </span>o <span class="blank _2"> </span>d<span class="blank _0"></span>e <span class="blank _8"> </span>la <span class="blank _2"> </span>misma <span class="blank _7"> </span>di<span class="blank _6"> </span>rección <span class="blank _8"> </span>y <span class="blank _8"> </span>sentido <span class="blank _8"> </span>contrario <span class="blank _8"> </span>a <span class="blank"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w32 h0"><div class="t m0 x41 h3 y81 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x42 y1 w5 h0"><div class="t m0 x8 h3 y81 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x42 y1 w33 h0"><div class="t m0 x8 h3 y81 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x43 h3 y80 ff2 fs1 fc0 sc0 ls2 ws2">, <span class="blank _8"> </span>s<span class="blank _6"> </span>i <span class="blank _8"> </span>k <span class="blank _2"> </span>es <span class="blank _8"> </span>negativo,<span class="blank _0"></span> <span class="blank _8"> </span>c<span class="blank _6"> </span>omo <span class="blank _8"> </span>se </div><div class="t m0 x0 h3 y82 ff2 fs1 fc0 sc0 ls2 ws2">muestra en la F<span class="blank _0"></span>igura 2.2 (d). </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="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x44 y83 w34 ha" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg5.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">5 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x1e h3 y84 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 y85 ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.2 </div><div class="t m0 x0 h3 y86 ff2 fs1 fc3 sc2 ls2 ws2">División de <span class="blank _6"> </span>un V<span class="blank _6"> </span>ector entre un <span class="blank _6"> </span>Escalar: <span class="blank _6"> </span><span class="fc0 sc0">La <span class="blank _6"> </span>división de un <span class="blank _6"> </span>vector <span class="ff7">\ued04</span></span></div></div><div class="c x1 y1 w35 h0"><div class="t m0 x45 h3 y87 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x46 y1 w5 h0"><div class="t m0 x8 h3 y87 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x46 y1 w36 h0"><div class="t m0 x8 h3 y87 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x47 h3 y86 ff2 fs1 fc0 sc0 ls2 ws2"> entre <span class="blank _6"> </span>un <span class="blank _6"> </span>escalar k, <span class="blank _6"> </span>es </div><div class="t m0 x0 h3 y88 ff2 fs1 fc0 sc0 ls2 ws2">equivalente <span class="blank _1"> </span>al <span class="blank _4"> </span>producto <span class="blank _4"> </span>de <span class="blank _4"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w37 h0"><div class="t m0 x48 h3 y89 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x10 y1 w5 h0"><div class="t m0 x8 h3 y89 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x49 y1 w38 h0"><div class="t m0 x8 h3 y89 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x11 h3 y88 ff2 fs1 fc0 sc0 ls2 ws2"> <span class="blank _4"> </span>por <span class="blank _4"> </span>el <span class="blank _1"> </span>i<span class="blank _6"> </span>nverso <span class="blank _1"> </span>de <span class="blank _4"> </span>k, <span class="blank _4"> </span>o <span class="blank _4"> </span>sea <span class="blank _4"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 wf h0"><div class="t m0 x4a h3 y89 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x4b y1 w1e h0"><div class="t m0 x8 h3 y89 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x4b y1 w39 h0"><div class="t m0 x8 h3 y89 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x4c h3 y88 ff2 fs1 fc0 sc0 ls2 ws2">/k <span class="blank _4"> </span>= <span class="blank _4"> </span>(1/k)<span class="ff7">\ued04</span></div></div><div class="c x1 y1 w3a h0"><div class="t m0 x3b h3 y89 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3c y1 w5 h0"><div class="t m0 x8 h3 y89 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3c y1 w3b h0"><div class="t m0 x8 h3 y89 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x4d h3 y88 ff2 fs1 fc0 sc0 ls2 ws2">, <span class="blank _4"> </span>por <span class="blank _4"> </span>lo <span class="blank _4"> </span>tanto, <span class="blank _1"> </span>s<span class="blank _6"> </span>e </div><div class="t m0 x0 h3 y8a ff2 fs1 fc0 sc0 ls2 ws2">cumplen las mismas reglas en cuanto <span class="blank _6"> </span>a dirección y s<span class="blank _6"> </span>entido dadas anteriormente para el </div><div class="t m0 x0 h3 y8b ff2 fs1 fc0 sc0 ls2 ws2">producto k<span class="ff7">\ued04</span></div></div><div class="c x1 y1 w3c h0"><div class="t m0 x4e h3 y8c ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x4f y1 wb h0"><div class="t m0 x8 h3 y8c ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x4f y1 w3d h0"><div class="t m0 x8 h3 y8c ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x50 h3 y8b ff2 fs1 fc0 sc0 ls6 ws2">. <span class="ls2"> </span></div><div class="t m0 x51 h3 y8d ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 y8e ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.3 </div><div class="t m0 x0 h3 y8f ff2 fs1 fc0 sc0 ls2 ws2">La relación <span class="blank _0"></span>entre el <span class="blank _0"></span>vector<span class="blank _0"></span> <span class="ff7">\ued04</span></div></div><div class="c x1 y1 w3e h0"><div class="t m0 xa h3 y90 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xb y1 w1e h0"><div class="t m0 x8 h3 y90 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x52 y1 w3f h0"><div class="t m0 x8 h3 y90 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 xc h3 y8f ff2 fs1 fc0 sc0 ls2 ws2"> y <span class="blank _0"></span>su magnitud, <span class="blank _0"></span>cuando <span class="blank _b"></span>s<span class="blank _6"> </span>e <span class="blank _0"></span>divide por <span class="blank _0"></span>un es<span class="blank _0"></span>calar k, <span class="blank _0"></span>se aprec<span class="blank _0"></span>ia </div><div class="t m0 x0 h3 y91 ff2 fs1 fc0 sc0 ls2 ws2">en <span class="blank _4"> </span>las<span class="blank _6"> </span> <span class="blank _4"> </span>Figuras <span class="blank _7"> </span>2.3, <span class="blank _4"> </span>al <span class="blank _7"> </span>comparar <span class="blank _4"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w40 h0"><div class="t m0 x53 h3 y92 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x54 y1 w5 h0"><div class="t m0 x8 h3 y92 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x54 y1 w41 h0"><div class="t m0 x8 h3 y92 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x55 h3 y91 ff2 fs1 fc0 sc0 ls2 ws2">, <span class="blank _7"> </span>como <span class="blank _4"> </span>se <span class="blank _7"> </span>mue<span class="blank _0"></span>stra <span class="blank _4"> </span>en <span class="blank _7"> </span>la <span class="blank _4"> </span>Fig<span class="blank _6"> </span>ura <span class="blank _4"> </span>2.3 <span class="blank _7"> </span>(a), <span class="blank _7"> </span><span class="lsd"> </span>si <span class="blank _4"> </span>k <span class="blank _7"> </span>= <span class="blank _7"> </span>1 <span class="blank _4"> </span>su </div><div class="t m0 x0 h3 y93 ff2 fs1 fc0 sc0 ls2 ws2">magnitud <span class="blank _6"> </span>es <span class="blank _1"> </span>igual, <span class="blank _6"> </span>aunque <span class="blank _6"> </span>si <span class="blank _1"> </span>k <span class="blank _6"> </span>>1 <span class="blank _1"> </span>su <span class="blank _6"> </span>magnitud <span class="blank _1"> </span>disminuy<span class="blank _0"></span>e, <span class="blank _1"> </span>como <span class="blank _6"> </span>se <span class="blank _6"> </span>i<span class="blank _6"> </span>lustra <span class="blank _6"> </span>en <span class="blank _4"> </span>la <span class="blank _6"> </span>Figura </div><div class="t m0 x0 h3 y94 ff2 fs1 fc0 sc0 ls2 ws2">2.3 <span class="blank _7"> </span>(b) <span class="blank _4"> </span>y <span class="blank _7"> </span>en <span class="blank _7"> </span>cambio <span class="blank _4"> </span>si <span class="blank _7"> </span>k <span class="blank _7"> </span>< <span class="blank _7"> </span>1, <span class="blank _4"> </span>como <span class="blank _7"> </span>se <span class="blank _7"> </span>observ<span class="blank _0"></span>a <span class="blank _7"> </span>en <span class="blank _4"> </span>la <span class="blank _7"> </span>Figura <span class="blank _7"> </span>2.3 <span class="blank _4"> </span>(c), <span class="blank _7"> </span>la <span class="blank _7"> </span>magn<span class="blank _0"></span>itud <span class="blank _7"> </span>de <span class="blank _7"> </span><span class="ff7">\ued04</span></div></div><div class="c x1 y1 w42 h0"><div class="t m0 x39 h3 y95 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x56 y1 w5 h0"><div class="t m0 x8 h3 y95 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x56 y1 w43 h0"><div class="t m0 x8 h3 y95 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x2 h3 y94 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y96 ff2 fs1 fc0 sc0 ls2 ws2">aumenta. </div><div class="t m0 x0 h3 y97 ff2 fs1 fc3 sc2 ls2 ws2">Vector <span class="blank _e"> </span>Unitario: <span class="blank _e"> </span><span class="fc0 sc0">El <span class="blank _e"> </span>cociente <span class="blank _e"> </span>de <span class="blank _e"> </span>dividir <span class="blank"> </span>un <span class="blank _d"> </span>vector <span class="blank _e"> </span><span class="ff7">\ued04</span></span></div></div><div class="c x1 y1 w44 h0"><div class="t m0 x57 h3 y98 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x58 y1 w1e h0"><div class="t m0 x8 h3 y98 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x58 y1 w45 h0"><div class="t m0 x8 h3 y98 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x59 h3 y97 ff7 fs1 fc0 sc0 ls2 ws3">\ue603<span class="ff2 ws2">entre <span class="blank"> </span>s<span class="blank _6"> </span>u <span class="blank _e"> </span>magnitud <span class="blank"> </span>V, <span class="blank _d"> </span>da <span class="blank _e"> </span>como </span></div><div class="t m0 x0 h3 y99 ff2 fs1 fc0 sc0 ls2 ws2">resultado <span class="blank _1"> </span>lo <span class="blank _1"> </span>que <span class="blank _1"> </span>se <span class="blank _4"> </span>denomina </div><div class="t m1 x14 hb y99 ff2 fs3 fc0 sc0 ls2 ws2">vector <span class="blank _1"> </span>unitario,</div><div class="t m0 x5a h3 y99 ff2 fs1 fc0 sc0 ls2 ws2"> <span class="blank _1"> </span>mostrado <span class="blank _1"> </span>en <span class="blank _4"> </span>la <span class="blank _1"> </span>Figura <span class="blank _1"> </span>2.3 <span class="blank _4"> </span>(d), <span class="blank _6"> </span>el <span class="blank _4"> </span>cual <span class="blank _1"> </span>se </div><div class="t m0 x0 h3 y9a ff2 fs1 fc0 sc0 ls2 ws2">designa por <span class="ff7">\ued1d</span></div></div><div class="c x1 y1 w46 h0"><div class="t m0 x50 h3 y9b ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x5b y1 w47 h0"><div class="t m0 x8 h3 y9b ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x5b y1 w48 h0"><div class="t m0 x8 h3 y9b ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x5c h3 y9a ff2 fs1 fc0 sc0 ls2 ws2"> y se expre<span class="blank _0"></span>sa así: </div><div class="t m0 x5d h3 y82 ff7 fs1 fc0 sc0 ls2">\uee9b</div></div><div class="c x1 y1 w49 h0"><div class="t m0 x5d h3 y9c ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x5e y1 w4a h0"><div class="t m0 x8 h3 y9c ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x5f y1 w4b h0"><div class="t m0 x60 h3 y9c ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x61 hc y82 ff7 fs1 fc0 sc0 lsb">\uf34c<span class="ls2 v2">\uee82</span></div></div><div class="c x1 y1 w4c h0"><div class="t m0 x16 h3 y9d ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x62 y1 w4a h0"><div class="t m0 x8 h3 y9d ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x17 y1 w4d h0"><div class="t m0 x60 h3 y9d ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x16 hd y9e ff7 fs1 fc0 sc0 lsc">\ued38<span class="ls2 ws6 v3">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _0"></span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\udb80\udddb\ue974\ue7e4\ue973\udb80\udddc<span class="ff2 ws2"> </span></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"><img fetchpriority="low" loading="lazy" class="bi x5 y9f w3 he" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg6.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">6 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 ya0 ff2 fs1 fc0 sc0 ls2 ws2">El vector <span class="blank _0"></span>unitario <span class="ff7">\ued1d</span></div></div><div class="c x1 y1 w4e h0"><div class="t m0 x63 h3 ya1 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x64 y1 w4f h0"><div class="t m0 x8 h3 ya1 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x64 y1 w50 h0"><div class="t m0 x8 h3 ya1 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x65 h3 ya0 ff7 fs1 fc0 sc0 ls2 ws3">\ue603<span class="ff2 ws2">tiene la <span class="blank _0"></span>misma dire<span class="blank _0"></span>cción de <span class="ff7">\ued04</span></span></div></div><div class="c x1 y1 w51 h0"><div class="t m0 x66 h3 ya2 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x67 y1 w5 h0"><div class="t m0 x8 h3 ya2 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x67 y1 w52 h0"><div class="t m0 x8 h3 ya2 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x68 h3 ya0 ff2 fs1 fc0 sc0 ls2 ws2"> y <span class="blank _0"></span>su magnitud <span class="blank _0"></span>es V/V =1, <span class="blank _0"></span>por lo <span class="blank _0"></span>tanto, </div><div class="t m0 x0 h3 ya3 ff2 fs1 fc0 sc0 ls2 ws2">es <span class="blank _e"> </span>adimensiona<span class="blank _0"></span>l, <span class="blank _e"> </span>entonces <span class="blank"> </span>el <span class="blank _e"> </span>vector<span class="ff7 ws3">\ue603\ued04</span></div></div><div class="c x1 y1 w53 h0"><div class="t m0 x9 h3 ya4 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x1c y1 w5 h0"><div class="t m0 x8 h3 ya4 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x69 y1 w54 h0"><div class="t m0 x8 h3 ya4 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x6a h3 ya3 ff7 fs1 fc0 sc0 lse">\ue603<span class="ff2 ls2 ws2">se <span class="blank _e"> </span>puede <span class="blank"> </span>expresar <span class="blank _e"> </span>en <span class="blank"> </span>términos <span class="blank _e"> </span>de <span class="blank"> </span>su <span class="blank _e"> </span>vector </span></div><div class="t m0 x0 h3 ya5 ff2 fs1 fc0 sc0 ls2 ws2">unitario <span class="ff7">\ued1d</span></div></div><div class="c x1 y1 w55 h0"><div class="t m0 x6b h3 ya6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6c y1 w47 h0"><div class="t m0 x8 h3 ya6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6c y1 w56 h0"><div class="t m0 x8 h3 ya6 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x6d h3 ya5 ff2 fs1 fc0 sc0 ls2 ws2">, así: </div><div class="t m0 x5f h3 ya7 ff7 fs1 fc0 sc0 ls2">\uee82</div></div><div class="c x1 y1 w57 h0"><div class="t m0 x5f h3 ya8 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6e y1 w4a h0"><div class="t m0 x8 h3 ya8 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6f y1 w58 h0"><div class="t m0 x60 h3 ya8 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x70 h3 ya7 ff7 fs1 fc0 sc0 ls2 ws7">\uf34c<span class="blank"> </span>\uee9b</div></div><div class="c x1 y1 w59 h0"><div class="t m0 x17 h3 ya9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x71 y1 w4a h0"><div class="t m0 x8 h3 ya9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x72 y1 w5a h0"><div class="t m0 x60 h3 ya9 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x73 h3 ya7 ff7 fs1 fc0 sc0 lsf">\ued38<span class="ff2 ls2 ws2"> <span class="blank _0"></span> <span class="blank _0"></span> (2.2) </span></div><div class="t m0 x0 h7 yaa ff6 fs2 fc3 sc0 ls2 ws2">2.5 CARACTERÍS<span class="blank _0"></span>TICAS DE UNA FU<span class="blank _0"></span>ERZA </div><div class="t m0 x0 h3 yab ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 yac ff2 fs1 fc0 sc0 ls2 ws2">Una <span class="blank _6"> </span>fuerza se <span class="blank _1"> </span>repre<span class="blank _0"></span>senta <span class="blank _6"> </span>mediante una <span class="blank _6"> </span>cantidad <span class="blank _6"> </span>vectorial, <span class="blank _6"> </span>por tanto, <span class="blank _6"> </span>se <span class="blank _6"> </span>caracteriza <span class="blank _6"> </span>por </div><div class="t m0 x0 h3 yad ff2 fs1 fc0 sc0 ls2 ws2">poseer: punto de apl<span class="blank _0"></span>icación, ma<span class="blank _0"></span>gnitud, dirección <span class="blank _0"></span>y sentido. </div><div class="t m0 x0 h3 yae ff2 fs1 fc3 sc2 ls2 ws2">Punto de <span class="blank _6"> </span>Aplicación:<span class="fc0 sc0"> U<span class="blank _6"> </span>na fuerza <span class="ff7">\uee72</span></span></div></div><div class="c x1 y1 w5b h0"><div class="t m0 x53 h3 yaf ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x54 y1 w5c h0"><div class="t m0 x8 h3 yaf ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x74 y1 w5d h0"><div class="t m0 x60 h3 yaf ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x55 h3 yae ff2 fs1 fc0 sc0 ls2 ws2"> que <span class="blank _6"> </span>actúa sobre <span class="blank _6"> </span>una partícula <span class="blank _6"> </span>A, como se <span class="blank _6"> </span>muestra en </div><div class="t m0 x0 h3 yb0 ff2 fs1 fc0 sc0 ls2 ws2">la Figura 2.4 (a), tiene <span class="blank _0"></span>su punto de apli<span class="blank _0"></span>cación en la <span class="blank _0"></span>partícula mis<span class="blank _0"></span>ma. </div><div class="t m0 x75 h3 yb1 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 yb2 ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.4 </div><div class="t m0 x0 h3 yb3 ff2 fs1 fc3 sc2 ls2 ws3">Magnitud:<span class="fc0 sc0 ws2"> <span class="blank _1"> </span>La <span class="blank _1"> </span>magnitud <span class="blank _1"> </span>de <span class="blank _6"> </span>una <span class="blank _4"> </span>fuerza <span class="blank _6"> </span>es <span class="blank _1"> </span>la <span class="blank _1"> </span>medida <span class="blank _1"> </span>de <span class="blank _1"> </span>su <span class="blank _1"> </span>mayor <span class="blank _1"> </span>o <span class="blank _1"> </span>menor <span class="blank _1"> </span>capacidad <span class="blank _1"> </span>de </span></div><div class="t m0 x0 h3 y91 ff2 fs1 fc0 sc0 ls2 ws2">acción <span class="blank _7"> </span>y <span class="blank _7"> </span>está <span class="blank _7"> </span>ex<span class="blank _6"> </span>presada <span class="blank _7"> </span>en <span class="blank _7"> </span>forma <span class="blank _7"> </span>de <span class="blank _7"> </span>una <span class="blank _7"> </span>cantidad <span class="blank _7"> </span>escalar. <span class="blank _7"> </span>Sus <span class="blank _7"> </span>unidades <span class="blank _7"> </span>están <span class="blank _7"> </span>dadas </div><div class="t m0 x0 h3 yb4 ff2 fs1 fc0 sc0 ls2 ws2">básicamente <span class="blank _b"></span>como: <span class="blank _b"></span>newton <span class="blank _b"></span>(N), <span class="blank _b"></span>en <span class="blank _b"></span>el <span class="blank _b"></span>Sistema <span class="blank _b"></span>Internacional <span class="blank _b"></span>(SI) <span class="blank _b"></span>y <span class="blank _b"></span>libra <span class="blank _b"></span>(lb<span class="blank _0"></span>), <span class="blank _b"></span>en <span class="blank _b"></span>el <span class="blank _b"></span>Si<span class="blank _6"> </span>stema<span class="blank _0"></span> </div><div class="t m0 x0 h3 yb5 ff2 fs1 fc0 sc0 ls2 ws2">Usado en los Est<span class="blank _0"></span>ados Unidos o (<span class="blank _0"></span>SU). </div><div class="t m0 x0 h3 yb6 ff2 fs1 fc3 sc2 ls2 ws3">Dirección:</div><div class="t m1 x76 hb yb6 ff2 fs3 fc3 sc2 ls2 ws2"> </div><div class="t m0 x4e h3 yb6 ff7 fs1 fc0 sc0 ls2 ws8">\ue60f\ue683\ue603<span class="blank"> </span>\ue686\ue68b\ue694\ue687\ue685\ue685\ue68b\ue6d7\ue690\ue603\ue686\ue687\ue603<span class="blank"> </span>\ue697\ue690\ue683\ue603<span class="blank"> </span>\ue688\ue697\ue687\ue694\ue69c\ue683\ue603<span class="blank"> </span>\ue687\ue695\ue696\ue69e\ue603<span class="blank"> </span>\ue686\ue687\ue696\ue687\ue694\ue68f\ue68b<span class="blank _0"></span>\ue690\ue683\ue686\ue683\ue603<span class="blank"> </span>\ue692\ue691\ue694\ue603<span class="blank"> </span>\ue687\ue68e\ue603<span class="blank"> </span>\ue69e\ue690\ue689\ue697\ue68e\ue691\ue603\ue83d\ue603<span class="blank"> </span>\ue688\ue691\ue694\ue68f\ue683\ue686\ue691\ue603<span class="blank"> </span>\ue692\ue691\ue694\ue603<span class="blank"> </span>\ue695\ue697\ue603</div><div class="t m0 x0 h3 yb7 ff2 fs1 fc0 sc0 ls2 ws2">línea <span class="blank _0"></span>de <span class="blank _b"></span>acción, <span class="blank _0"></span>con <span class="blank _0"></span>un <span class="blank _b"></span>cierto <span class="blank _0"></span>eje <span class="blank _0"></span>de <span class="blank _b"></span>referencia, <span class="blank _0"></span>como <span class="blank _b"></span>se <span class="blank _0"></span>indica <span class="blank _0"></span>en <span class="blank _b"></span>la Figura <span class="blank _b"></span>2.4 <span class="blank _b"></span>(a), siendo </div><div class="t m0 x0 h3 yb8 ff2 fs1 fc0 sc0 ls2 ws2">su línea de acción una l<span class="blank _0"></span>ínea infin<span class="blank _0"></span>ita a lo largo de la c<span class="blank _0"></span>ual actúa la fuerza<span class="blank _0"></span>. </div><div class="t m0 x0 h3 yb9 ff2 fs1 fc3 sc2 ls2 ws3">Sentido:<span class="fc0 sc0 ws2"> Una <span class="blank _6"> </span>fuerza se <span class="blank _6"> </span>representa en forma g<span class="blank _6"> </span>ráfica mediante un <span class="blank _6"> </span>segmento de recta, <span class="blank _6"> </span>con </span></div><div class="t m0 x0 h3 yba ff2 fs1 fc0 sc0 ls2 ws2">una punta <span class="blank _6"> </span>de <span class="blank _6"> </span>flecha en <span class="blank _6"> </span>uno de <span class="blank _6"> </span>los <span class="blank _6"> </span>extremos para <span class="blank _6"> </span>indicar el<span class="blank _6"> </span> <span class="blank _6"> </span>sentido. <span class="blank _6"> </span>En la <span class="blank _6"> </span>Figura 2.4 <span class="blank _6"> </span>(a), </div><div class="t m0 x0 h3 ybb ff2 fs1 fc0 sc0 ls2 ws2">el sentido de la fuerz<span class="blank _0"></span>a es hacia arr<span class="blank _0"></span>iba y a la derecha. </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"><img fetchpriority="low" loading="lazy" class="bi x5 ybc w3 hf" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg7.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">7 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 ybd ff2 fs1 fc0 sc0 ls2 ws2">Si <span class="blank"> </span>se <span class="blank"> </span>utiliza <span class="blank _2"> </span>una <span class="blank"> </span>escala <span class="blank _2"> </span>apropiada, <span class="blank"> </span>la <span class="blank _2"> </span>magnitud <span class="blank _2"> </span>de <span class="blank"> </span>una <span class="blank"> </span>fuer<span class="blank _0"></span>za <span class="blank"> </span>puede <span class="blank"> </span>ser<span class="blank _0"></span> <span class="blank"> </span>expresada </div><div class="t m0 x0 h3 ybe ff2 fs1 fc0 sc0 ls2 ws2">mediante <span class="blank _7"> </span>la <span class="blank _4"> </span>longitud <span class="blank _7"> </span>de <span class="blank _4"> </span>dicho <span class="blank _7"> </span>segmento. <span class="blank _7"> </span>Por <span class="blank _4"> </span>ejemplo, <span class="blank _4"> </span>si <span class="blank _7"> </span>se <span class="blank _7"> </span>define <span class="blank _7"> </span>una <span class="blank _4"> </span>escala <span class="blank _7"> </span>de <span class="blank _7"> </span>1cm </div><div class="t m0 x0 h3 ybf ff2 fs1 fc0 sc0 ls2 ws2">correspondiente a 10 N y <span class="blank _6"> </span>se desea di<span class="blank _6"> </span>bujar una fuerza de 60 <span class="blank _6"> </span>N, el s<span class="blank _6"> </span>egmento de recta que </div><div class="t m0 x0 h3 yc0 ff2 fs1 fc0 sc0 ls2 ws2">lo represente será de <span class="blank _0"></span>6 cm, lo cual <span class="blank _0"></span>se aprecia en la<span class="blank _0"></span>s Figuras 2.4 (b) <span class="blank _0"></span>y (c). </div><div class="t m0 x0 h7 yc1 ff6 fs2 fc3 sc0 ls2 ws2">2.6 LEY DEL PAR<span class="blank _0"></span>ALELOGRAMO </div><div class="t m0 x0 h3 y63 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 yc2 ff2 fs1 fc0 sc0 ls2 ws2">La <span class="blank _d"> </span>ley <span class="blank _d"> </span>del <span class="blank _d"> </span>paralelogramo <span class="blank _e"> </span>establece <span class="blank _d"> </span>que <span class="blank _d"> </span>dos <span class="blank _d"> </span>fuerzas <span class="blank _e"> </span><span class="ff7">\uee72</span></div></div><div class="c x1 y1 w5e h0"><div class="t m0 x77 h3 yc3 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x78 y1 w5c h0"><div class="t m0 x8 h3 yc3 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x78 y1 w5f h0"><div class="t m0 x60 h3 yc3 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x79 h10 yc4 ff7 fs4 fc0 sc0 ls10">\uf135<span class="fs1 ls2 ws3 v4">\ue603\ue69b\ue603\uee72</span></div></div><div class="c x1 y1 w60 h0"><div class="t m0 x18 h3 yc3 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x19 y1 w5c h0"><div class="t m0 x8 h3 yc3 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x19 y1 w61 h0"><div class="t m0 x60 h3 yc3 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x1a h10 yc4 ff7 fs4 fc0 sc0 ls11">\uf136<span class="fs1 ls2 ws3 v4">\ue603<span class="ff2 ws2">que <span class="blank _e"> </span>actúan <span class="blank _d"> </span>sobre <span class="blank _d"> </span>una </span></span></div><div class="t m0 x0 h3 yc5 ff2 fs1 fc0 sc0 ls2 ws2">partícula A se pueden <span class="blank _6"> </span>reemplazar por una sola fuerza <span class="blank _6"> </span><span class="ff7">\uee7e</span></div></div><div class="c x1 y1 w62 h0"><div class="t m0 x7a h3 yc6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7b y1 w63 h0"><div class="t m0 x8 h3 yc6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7c y1 w64 h0"><div class="t m0 x60 h3 yc6 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x7d h3 yc5 ff2 fs1 fc0 sc0 ls2 ws2"> denominada resultante, la cual </div><div class="t m0 x0 h3 yc7 ff2 fs1 fc0 sc0 ls2 ws2">produce <span class="blank _d"> </span>el <span class="blank _a"> </span>mismo <span class="blank _d"> </span>efecto <span class="blank _d"> </span>que <span class="blank _a"> </span>dichas <span class="blank _d"> </span>fuerzas <span class="blank _d"> </span>en <span class="blank _a"> </span>su <span class="blank _a"> </span>conjunto, <span class="blank _e"> </span>s<span class="blank _6"> </span>i <span class="blank _d"> </span>se <span class="blank _a"> </span>construye <span class="blank _d"> </span>con </div><div class="t m0 x0 h3 yc8 ff7 fs1 fc0 sc0 ls2">\uee72</div></div><div class="c x1 y1 w65 h0"><div class="t m0 x0 h3 yc9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7e y1 w5c h0"><div class="t m0 x8 h3 yc9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7e y1 w66 h0"><div class="t m0 x60 h3 yc9 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x3d h10 yca ff7 fs4 fc0 sc0 ls12">\uf135<span class="fs1 ls2 ws3 v4">\ue603\ue69b\ue603\uee72</span></div></div><div class="c x1 y1 w67 h0"><div class="t m0 x7f h3 yc9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x44 y1 w5c h0"><div class="t m0 x8 h3 yc9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x80 y1 w68 h0"><div class="t m0 x60 h3 yc9 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x81 h10 yca ff7 fs4 fc0 sc0 ls11">\uf136<span class="fs1 ls2 ws3 v4">\ue603<span class="ff2 ws2">un <span class="blank _6"> </span>paralelogramo <span class="blank _6"> </span>siendo <span class="blank _1"> </span><span class="ff7">\uee7e</span></span></span></div></div><div class="c x1 y1 w69 h0"><div class="t m0 x74 h3 yc9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x82 y1 w63 h0"><div class="t m0 x8 h3 yc9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x83 y1 w6a h0"><div class="t m0 x60 h3 yc9 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x84 h3 yc8 ff2 fs1 fc0 sc0 ls2 ws2"> <span class="blank _1"> </span>su <span class="blank _6"> </span>diagonal, <span class="blank _1"> </span>como <span class="blank _6"> </span>se <span class="blank _1"> </span>ilustra <span class="blank _6"> </span>en<span class="blank _6"> </span> <span class="blank _1"> </span>la <span class="blank _1"> </span>Figura <span class="blank _6"> </span>2.5 <span class="blank _1"> </span>(a). <span class="blank _6"> </span>Lo </div><div class="t m0 x0 h3 ycb ff2 fs1 fc0 sc0 ls2 ws2">anterior se expre<span class="blank _0"></span>sa así: </div><div class="t m0 x6 h3 ycc ff7 fs1 fc0 sc0 ls2">\uee7e</div></div><div class="c x1 y1 w6b h0"><div class="t m0 x6 h3 ycd ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7 y1 w63 h0"><div class="t m0 x8 h3 ycd ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x85 y1 w6c h0"><div class="t m0 x60 h3 ycd ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x69 h3 ycc ff7 fs1 fc0 sc0 ls2 ws7">\uf34c<span class="blank"> </span>\uee72</div></div><div class="c x1 y1 w57 h0"><div class="t m0 x5f h3 ycd ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6e y1 w5c h0"><div class="t m0 x8 h3 ycd ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6e y1 w6d h0"><div class="t m0 x60 h3 ycd ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x86 h10 yce ff7 fs4 fc0 sc0 ls13">\uf135<span class="fs1 ls2 ws9 v4">\uf345<span class="blank"> </span>\ue603<span class="blank"> </span>\uee72</span></div></div><div class="c x1 y1 w6e h0"><div class="t m0 x87 h3 ycd ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x66 y1 w5c h0"><div class="t m0 x8 h3 ycd ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x88 y1 w6f h0"><div class="t m0 x60 h3 ycd ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x89 h10 yce ff7 fs4 fc0 sc0 ls12">\uf136<span class="fs1 ls2 ws3 v4">\ue603\ue603<span class="ff2 ws2"> </span></span></div><div class="t m0 x8a h3 ycf ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 yd0 ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.5 </div><div class="t m0 x0 h3 yd1 ff2 fs1 fc0 sc0 ls2 ws2">Para <span class="blank _e"> </span>aplicar <span class="blank _e"> </span>la <span class="blank _e"> </span>ley <span class="blank _e"> </span>del <span class="blank _e"> </span>paralelogramo <span class="blank _e"> </span>se <span class="blank _d"> </span>dibujan<span class="blank _0"></span> <span class="blank _e"> </span>las <span class="blank _d"> </span>dos <span class="blank _e"> </span>fuerzas <span class="blank _e"> </span><span class="ff7">\uee72</span></div></div><div class="c x1 y1 w70 h0"><div class="t m0 x3b h3 yd2 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x3c y1 w5c h0"><div class="t m0 x8 h3 yd2 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x8b y1 w71 h0"><div class="t m0 x60 h3 yd2 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x8c h10 yd3 ff7 fs4 fc0 sc0 ls12">\uf135<span class="fs1 ls2 ws3 v4">\ue603\ue69b\ue603\uee72</span></div></div><div class="c x1 y1 w72 h0"><div class="t m0 x28 h3 yd2 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x29 y1 w5c h0"><div class="t m0 x8 h3 yd2 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x8d y1 w73 h0"><div class="t m0 x60 h3 yd2 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x8e h10 yd3 ff7 fs4 fc0 sc0 ls14">\uf136<span class="ff2 fs1 ls2 ws2 v4">, <span class="blank _e"> </span>a <span class="blank _e"> </span>escala, </span></div><div class="t m0 x0 h3 yd4 ff2 fs1 fc0 sc0 ls2 ws2">colocándolas <span class="blank _e"> </span>a <span class="blank _d"> </span>partir <span class="blank _e"> </span>de <span class="blank _e"> </span>un <span class="blank _d"> </span>mismo <span class="blank _d"> </span>punto <span class="blank _e"> </span>A, <span class="blank _d"> </span>se <span class="blank _d"> </span>trazan <span class="blank _d"> </span>después <span class="blank _e"> </span>líneas <span class="blank _e"> </span>paralelas <span class="blank _e"> </span>a </div><div class="t m0 x0 h3 yd5 ff7 fs1 fc0 sc0 ls2">\uee72</div></div><div class="c x1 y1 w65 h0"><div class="t m0 x0 h3 yd6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7e y1 w5c h0"><div class="t m0 x8 h3 yd6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7e y1 w66 h0"><div class="t m0 x60 h3 yd6 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x3d h10 yd7 ff7 fs4 fc0 sc0 ls12">\uf135<span class="fs1 ls2 ws3 v4">\ue603\ue69b\ue603\uee72</span></div></div><div class="c x1 y1 w67 h0"><div class="t m0 x7f h3 yd6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x44 y1 w5c h0"><div class="t m0 x8 h3 yd6 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x80 y1 w68 h0"><div class="t m0 x60 h3 yd6 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x81 h10 yd7 ff7 fs4 fc0 sc0 ls11">\uf136<span class="fs1 ls2 ws3 v4">\ue603<span class="ff2 ws2">para <span class="blank _b"></span>formar <span class="blank _0"></span>un <span class="blank _b"></span>paralelogramo, <span class="blank _0"></span>como <span class="blank _b"></span>lo muestra <span class="blank _b"></span>la <span class="blank _0"></span>Figura <span class="blank _b"></span>2.5 (b) <span class="blank _b"></span>y <span class="blank _0"></span>por <span class="blank _0"></span>último, <span class="blank _b"></span>se </span></span></div><div class="t m0 x0 h3 yd8 ff2 fs1 fc0 sc0 ls2 ws2">dibuja a <span class="ff7">\uee7e</span></div></div><div class="c x1 y1 w74 h0"><div class="t m0 x6b h3 yd9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x27 y1 w63 h0"><div class="t m0 x8 h3 yd9 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6c y1 w75 h0"><div class="t m0 x60 h3 yd9 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x6d h3 yd8 ff2 fs1 fc0 sc0 ls2 ws2"> al hacerla coinci<span class="blank _0"></span>dir con la diagonal<span class="blank _0"></span>. </div><div class="t m0 x0 h3 yda ff2 fs1 fc0 sc0 ls2 ws2">Una <span class="blank _0"></span>consecu<span class="blank _0"></span>encia <span class="blank _b"></span>de <span class="ls4">la <span class="blank _b"></span><span class="fc3 sc2 ls2">Ley <span class="blank _b"></span>del <span class="blank _0"></span>Paralelogramo</span></span></div><div class="t m1 x62 hb yda ff2 fs3 fc3 sc2 ls2 ws2"> </div><div class="t m0 x17 h3 yda ff2 fs1 fc0 sc0 ls2 ws2">es <span class="blank _b"></span>la <span class="blank _b"></span>denominada <span class="blank _0"></span><span class="fc3 sc2">Regla <span class="blank _b"></span>del <span class="blank _0"></span>Triángulo<span class="fc0 sc0">, <span class="blank _0"></span>que<span class="blank _0"></span> </span></span></div><div class="t m0 x0 h3 ydb ff2 fs1 fc0 sc0 ls2 ws2">consiste en <span class="blank _0"></span>dibujar <span class="blank _b"></span>las dos fuerza<span class="blank _0"></span>s, también <span class="blank _b"></span>a escala, una <span class="blank _0"></span>a <span class="blank _0"></span>continuación <span class="blank _0"></span>de <span class="blank _0"></span>la otra, <span class="blank _b"></span>como </div><div class="t m0 x0 h3 ydc ff2 fs1 fc0 sc0 ls2 ws2">se <span class="blank _7"> </span>indica <span class="blank _7"> </span>en <span class="blank _7"> </span>las <span class="blank _7"> </span>Figuras <span class="blank _7"> </span>2.6 <span class="blank _7"> </span>(a) <span class="blank _8"> </span>y <span class="blank _7"> </span>(b), <span class="blank _7"> </span>uniendo <span class="blank _7"> </span>después <span class="blank _7"> </span>el <span class="blank _7"> </span>inicio <span class="blank _7"> </span>de <span class="blank _7"> </span>la <span class="blank _8"> </span>primera <span class="blank _7"> </span>con <span class="blank _7"> </span>el </div><div class="t m0 x0 h3 ydd ff2 fs1 fc0 sc0 ls2 ws2">extremo <span class="blank"> </span>de <span class="blank"> </span>la <span class="blank"> </span>segunda, <span class="blank"> </span>para <span class="blank"> </span>obtener <span class="blank"> </span>de <span class="blank"> </span>esa <span class="blank"> </span>manera <span class="blank"> </span>la <span class="blank"> </span>resultante <span class="blank _e"> </span><span class="ff7">\uee7e</span></div></div><div class="c x1 y1 w76 h0"><div class="t m0 x4d h3 yde ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x8f y1 w63 h0"><div class="t m0 x8 h3 yde ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x75 y1 w77 h0"><div class="t m0 x60 h3 yde ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x90 h3 ydd ff2 fs1 fc0 sc0 ls2 ws2">, <span class="blank"> </span>al <span class="blank"> </span>formar <span class="blank"> </span>un </div><div class="t m0 x0 h3 ydf ff2 fs1 fc0 sc0 ls2 ws2">triángulo con la<span class="blank _0"></span>s tres fuerzas. </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 x5 ye0 w3 h11" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg8.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">8 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x1d h3 ye1 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 ye2 ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.6 </div><div class="t m0 x0 h3 ye3 ff2 fs1 fc0 sc0 ls2 ws2">Nótese <span class="blank _0"></span>que <span class="blank _0"></span>el re<span class="blank _0"></span>sultado <span class="blank _0"></span>obtenido <span class="blank _b"></span>es<span class="blank _6"> </span> <span class="blank _0"></span>el <span class="blank _0"></span>mismo, <span class="blank _0"></span>si <span class="blank _0"></span>el triáng<span class="blank _0"></span>ulo s<span class="blank _0"></span>e <span class="blank _0"></span>construye <span class="blank _0"></span>de <span class="blank _0"></span>dos <span class="blank _0"></span>formas:<span class="blank _0"></span> </div><div class="t m0 x0 h3 ye4 ff2 fs1 fc0 sc0 ls2 ws2">colocando <span class="blank _2"> </span><span class="ff7">\uee72</span></div></div><div class="c x1 y1 w78 h0"><div class="t m0 x4e h3 ye5 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x4f y1 w5c h0"><div class="t m0 x8 h3 ye5 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x91 y1 w79 h0"><div class="t m0 x60 h3 ye5 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x92 h10 ye6 ff7 fs4 fc0 sc0 ls11">\uf136<span class="ff2 fs1 ls2 ws2 v4"> <span class="blank"> </span>a <span class="blank _2"> </span>continuació<span class="blank _0"></span>n <span class="blank"> </span>de <span class="blank _2"> </span><span class="ff7">\uee72</span></span></div></div><div class="c x1 y1 w7a h0"><div class="t m0 x82 h3 ye5 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x93 y1 w5c h0"><div class="t m0 x8 h3 ye5 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x93 y1 w7b h0"><div class="t m0 x60 h3 ye5 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x94 h10 ye6 ff7 fs4 fc0 sc0 ls15">\uf135<span class="fs1 ls2 ws3 v4">\ue7e1\ue603<span class="ff2 ws2">como <span class="blank"> </span>l<span class="blank _0"></span>o <span class="blank"> </span>mue<span class="blank _0"></span>stra <span class="blank"> </span>l<span class="blank _0"></span>a <span class="blank"> </span>Figura <span class="blank _2"> </span>2.6 <span class="blank _2"> </span>(a), <span class="blank _2"> </span>o <span class="blank"> </span>v<span class="blank _0"></span>iceversa,<span class="blank _0"></span> </span></span></div><div class="t m0 x0 h3 ye7 ff7 fs1 fc0 sc0 ls2">\uee72</div></div><div class="c x1 y1 w65 h0"><div class="t m0 x0 h3 ye8 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7e y1 w5c h0"><div class="t m0 x8 h3 ye8 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7e y1 w66 h0"><div class="t m0 x60 h3 ye8 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x3d h10 ye9 ff7 fs4 fc0 sc0 ls12">\uf135<span class="fs1 ls2 ws3 v4">\ue603<span class="ff2 ws2">seguido de <span class="blank _1"> </span><span class="ff7">\uee72</span></span></span></div></div><div class="c x1 y1 w7c h0"><div class="t m0 x95 h3 ye8 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x96 y1 w5c h0"><div class="t m0 x8 h3 ye8 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x96 y1 w7d h0"><div class="t m0 x60 h3 ye8 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x97 h10 ye9 ff7 fs4 fc0 sc0 ls11">\uf136<span class="ff2 fs1 ls2 ws2 v4">, <span class="blank _6"> </span>como <span class="blank _6"> </span>s<span class="blank _6"> </span>e <span class="blank _6"> </span>aprecia <span class="blank _6"> </span>en <span class="blank _6"> </span>la <span class="blank _1"> </span>Figura <span class="blank _1"> </span>2.6 <span class="blank _6"> </span>(b), <span class="blank _6"> </span>lo <span class="blank _6"> </span>cua<span class="blank _6"> </span>l <span class="blank _6"> </span>comprueba <span class="blank _6"> </span>la <span class="blank _1"> </span>propi<span class="blank _0"></span>edad </span></div><div class="t m0 x0 h3 yea ff2 fs1 fc0 sc0 ls2 ws2">conmutativa de la ad<span class="blank _0"></span>ición de fuer<span class="blank _0"></span>zas, o sea: </div><div class="t m0 x98 h3 yeb ff7 fs1 fc0 sc0 ls2">\uee7e</div></div><div class="c x1 y1 w7e h0"><div class="t m0 x98 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x99 y1 w63 h0"><div class="t m0 x8 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x53 y1 w7f h0"><div class="t m0 x60 h3 yec ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x55 h3 yeb ff7 fs1 fc0 sc0 ls2 ws7">\uf34c<span class="blank"> </span>\uee72</div></div><div class="c x1 y1 w80 h0"><div class="t m0 x9a h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x6 y1 w5c h0"><div class="t m0 x8 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x9b y1 w81 h0"><div class="t m0 x60 h3 yec ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x7 h10 yed ff7 fs4 fc0 sc0 ls13">\uf135<span class="fs1 ls2 ws9 v4">\uf345<span class="blank"> </span>\ue603<span class="blank"> </span>\uee72</span></div></div><div class="c x1 y1 w82 h0"><div class="t m0 x6e h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x61 y1 w5c h0"><div class="t m0 x8 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x86 y1 w83 h0"><div class="t m0 x60 h3 yec ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x70 h10 yed ff7 fs4 fc0 sc0 ls16">\uf136<span class="fs1 ls2 wsa v4">\uf34c<span class="blank"> </span>\ue603<span class="blank"> </span>\uee72</span></div></div><div class="c x1 y1 w84 h0"><div class="t m0 x88 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x89 y1 w5c h0"><div class="t m0 x8 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x68 y1 w85 h0"><div class="t m0 x60 h3 yec ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x9c h10 yed ff7 fs4 fc0 sc0 ls13">\uf136<span class="fs1 ls2 ws4 v4">\uf345<span class="blank"> </span>\uee72</span></div></div><div class="c x1 y1 w86 h0"><div class="t m0 x58 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x7a y1 w5c h0"><div class="t m0 x8 h3 yec ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x59 y1 w87 h0"><div class="t m0 x60 h3 yec ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x7b h12 yed ff7 fs4 fc0 sc0 ls2">\uf135</div><div class="t m1 x9d hb yeb ff2 fs3 fc0 sc1 ls2 ws2"> </div><div class="t m0 x0 h7 yee ff6 fs2 fc3 sc0 ls2 ws2">2.7 LEY DE LOS S<span class="blank _0"></span>ENOS Y DE LO<span class="blank _0"></span>S COSENOS </div><div class="t m0 x0 h3 yef ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 y4f ff2 fs1 fc0 sc0 ls2 ws2">Dado <span class="blank _6"> </span>que <span class="blank _1"> </span>la <span class="blank _1"> </span><span class="fc3 sc2">Ley <span class="blank _6"> </span>del <span class="blank _6"> </span>Paralelog<span class="blank _6"> </span>ramo</span><span class="ls17"> </span>y <span class="blank _6"> </span>la <span class="blank _1"> </span>consecuente <span class="blank _6"> </span><span class="fc3 sc2">Reg<span class="blank _6"> </span>la <span class="blank _6"> </span>del <span class="blank _1"> </span>Triángulo</span>, <span class="blank _6"> </span>para <span class="blank _1"> </span>la <span class="blank _6"> </span>suma </div><div class="t m0 x0 h3 yf0 ff2 fs1 fc0 sc0 ls2 ws2">de <span class="blank _4"> </span>dos <span class="blank _4"> </span>fuerzas, <span class="blank _1"> </span>involucran <span class="blank _1"> </span>las <span class="blank _4"> </span>respectivas <span class="blank _1"> </span>magnitudes, <span class="blank _4"> </span>incluida <span class="blank _1"> </span>la <span class="blank _4"> </span>de <span class="blank _4"> </span>su <span class="blank _4"> </span>resultante, <span class="blank _1"> </span>las </div><div class="t m0 x0 h3 y51 ff2 fs1 fc0 sc0 ls2 ws2">cuales <span class="blank _0"></span>se pueden <span class="blank _0"></span>represe<span class="blank _0"></span>ntar med<span class="blank _0"></span>iante los <span class="blank _0"></span>lados <span class="blank _0"></span>de <span class="blank _0"></span>un trián<span class="blank _0"></span>gulo y <span class="blank _0"></span>sus c<span class="blank _0"></span>orrespondientes </div><div class="t m0 x0 h3 y30 ff2 fs1 fc0 sc0 ls2 ws2">ángulos internos, como <span class="blank _6"> </span>lo muestran <span class="blank _6"> </span>las Figuras 2.7 (a) <span class="blank _6"> </span>y <span class="blank _6"> </span>(b), entonces, <span class="blank _6"> </span>es <span class="blank _6"> </span>posible hallar </div><div class="t m0 x0 h3 yf1 ff2 fs1 fc0 sc0 ls2 ws2">las <span class="blank _6"> </span>magnitudes requeridas de <span class="blank _6"> </span>las <span class="blank _6"> </span>fuerzas, al <span class="blank _1"> </span>resolver las <span class="blank _6"> </span>relaciones entre <span class="blank _6"> </span>dichos <span class="blank _6"> </span>lados y </div><div class="t m0 x0 h3 yf2 ff2 fs1 fc0 sc0 ls2 ws2">ángulos, mediante la ap<span class="blank _0"></span>licación <span class="blank _0"></span>de la ley de los seno<span class="blank _0"></span>s y de los co<span class="blank _0"></span>senos. </div><div class="t m0 x9e h3 yf3 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 yf4 ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.7 </div><div class="t m0 x0 h3 yf5 ff2 fs1 fc0 sc0 ls2 ws2"> </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 x3d yf6 w88 h13" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bg9.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls2 ws2">9 <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="fc1">José Manuel<span class="blank _0"></span> Arroyo Andrad<span class="blank _0"></span>e UNIS<span class="blank _0"></span>UCRE<span class="fc0"> </span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x0 h3 ybd ff2 fs1 fc3 sc2 ls2 ws2">Ley de <span class="blank _0"></span>los Seno<span class="blank _0"></span>s: <span class="fc0 sc0">D<span class="blank _0"></span>ado el <span class="blank _0"></span>triángulo <span class="blank _b"></span>mostrado en <span class="blank _0"></span>la Fi<span class="blank _0"></span>gura 2.7<span class="blank _0"></span> (a) <span class="blank _0"></span>de <span class="blank _0"></span>lados <span class="blank _0"></span>a, b <span class="blank _0"></span>y <span class="blank _0"></span>c y <span class="blank _0"></span>cuyos </span></div><div class="t m0 x0 h3 ybe ff2 fs1 fc0 sc0 ls2 ws2">correspondiente<span class="blank _0"></span>s <span class="blank _7"> </span>ángulos <span class="blank _4"> </span>opuestos <span class="blank _7"> </span>son <span class="blank _7"> </span><span class="ff7 ls18">\ue83d</span><span class="ls6">, <span class="blank _7"> </span></span><span class="ff7 ws3">\ue83e</span><span class="ls19"> <span class="ls20">y <span class="blank _7"> </span></span></span><span class="ff7 ws3">\ue845</span>, <span class="blank _4"> </span>se <span class="blank _7"> </span>cumplen <span class="blank _7"> </span>las <span class="blank _4"> </span>siguientes <span class="blank _7"> </span>relaciones<span class="blank _0"></span> </div><div class="t m0 x0 h3 yf7 ff2 fs1 fc0 sc0 ls2 ws2">entre los lados y<span class="blank _0"></span> los senos d<span class="blank _0"></span>e los ángulos opue<span class="blank _0"></span>stos, así: </div><div class="t m0 x53 h3 yf8 ff7 fs1 fc0 sc0 ls2">\ued3d</div><div class="t m0 x9f h14 yf9 ff7 fs1 fc0 sc0 ls2 wsb">\ued4f\ued41\ued4a\ue603\uedd9<span class="blank"> </span><span class="wsc v3">\uf34c<span class="blank"> </span>\ue603<span class="blank _f"> </span></span><span class="v5">\ued3e</span></div><div class="t m0 x6a h14 yf9 ff7 fs1 fc0 sc0 ls2 wsd">\ued4f\ued41\ued4a\ue603\uedda<span class="blank"> </span><span class="wsa v3">\uf34c<span class="blank"> </span>\ue603<span class="blank _f"> </span></span><span class="v5">\ued3f</span></div><div class="t m0 x89 h15 yf9 ff7 fs1 fc0 sc0 ls2 wse">\ued4f\ued41\ued4a\ue603\uede0<span class="blank"> </span><span class="wsf v3">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _0"></span>\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\udb80\udddb\ue974\ue7e4\ue975\udb80\udddc\ue603\ue603<span class="ff2 ws2"> </span></span></div><div class="t m0 x0 h3 yfa ff2 fs1 fc3 sc2 ls2 ws2">Ley <span class="blank _b"></span>de lo<span class="blank _0"></span>s <span class="blank _0"></span>Cosenos:</div><div class="t m1 x65 hb yfa ff2 fs3 fc3 sc2 ls2 ws2"> </div><div class="t m0 xa0 h3 yfa ff2 fs1 fc0 sc0 ls2 ws2">El <span class="blank _b"></span>cuadrado <span class="blank _0"></span>de <span class="blank _b"></span>un <span class="blank _b"></span>lado <span class="blank _0"></span>cualquiera <span class="blank _b"></span>es <span class="blank _b"></span>igual <span class="blank _0"></span>a <span class="blank _b"></span>la <span class="blank _0"></span>suma <span class="blank _b"></span>de <span class="blank _0"></span>los <span class="blank _b"></span>cuadrados </div><div class="t m0 x0 h3 yfb ff2 fs1 fc0 sc0 ls2 ws2">de <span class="blank _8"> </span>los <span class="blank _7"> </span>otros <span class="blank _8"> </span>dos <span class="blank _8"> </span>lados, <span class="blank _7"> </span>menos <span class="blank _8"> </span>el <span class="blank _7"> </span>doble <span class="blank _8"> </span>de <span class="blank _7"> </span>s<span class="blank _6"> </span>u <span class="blank _8"> </span>pr<span class="blank _0"></span>oducto <span class="blank _8"> </span>por <span class="blank _7"> </span>el <span class="blank _8"> </span>coseno <span class="blank _7"> </span>del<span class="blank _6"> </span> <span class="blank _8"> </span>ángulo <span class="blank _8"> </span>que </div><div class="t m0 x0 h3 yfc ff2 fs1 fc0 sc0 ls2 ws2">forman. O sea, teniend<span class="blank _0"></span>o en cuenta la F<span class="blank _0"></span>igura 2.7 (a), <span class="blank _0"></span>se expresa así: </div><div class="t m0 xa1 h3 yfd ff7 fs1 fc0 sc0 ls1a">\ued3d<span class="fs4 ls16 v6">\uf136</span><span class="ls2 ws10">\uf34c<span class="blank _d"> </span>\ued3e<span class="blank"> </span><span class="fs4 ls13 v6">\uf136</span><span class="ws11">\uf345<span class="blank _3"> </span>\ued3f<span class="blank"> </span><span class="fs4 ls13 v6">\uf136</span><span class="ws4">\uf346<span class="blank"> </span>\ue603\ue974\ue684\ue685\ue603\ue685\ue691\ue695\ue603\ue83d\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _0"></span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="ff2 ws2">(2.4) </span></span></span></span></div><div class="t m0 x98 h3 yfe ff7 fs1 fc0 sc0 ls2 ws3">\ue684<span class="fs4 ls16 v6">\uf136</span><span class="ws12">\uf34c<span class="blank"> </span>\ue683<span class="fs4 ls13 v6">\uf136</span><span class="ws11">\uf345<span class="blank _3"> </span>\ued3f<span class="blank"> </span><span class="fs4 ls1b v6">\uf136</span><span class="ws4">\uf346<span class="blank"> </span>\ue603<span class="ls1c ws13">\ue974\ue683\ue685</span></span></span></span>\ue603\ue685\ue691\ue695\ue603\ue83e\ue603\ue603\ue603\ue603\ue603<span class="blank _0"></span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="ff2 ws2">(2.5)<span class="blank _0"></span> </span></div><div class="t m0 x98 h3 yff ff7 fs1 fc0 sc0 ls1d">\ue685<span class="fs4 ls1e v6">\uf136</span><span class="ls2 ws7">\uf34c<span class="blank"> </span>\ue683<span class="fs4 ls13 v6">\uf136</span><span class="ws4">\uf345<span class="blank"> </span>\ue684<span class="fs4 ls1b v6">\uf136</span>\uf346<span class="blank"> </span>\ue603</span></span><span class="ls1c ws13">\ue974\ue683\ue684</span><span class="ls2 ws3">\ue603\ue685\ue691\ue695\ue603\ue845\ue603\ue603\ue603<span class="blank _0"></span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="ff2 ws2">(2.6)<span class="blank _0"></span> </span></span></div><div class="t m0 x0 h3 y100 ff7 fs1 fc0 sc0 ls2 ws3">\ue616\ue68b\ue603\ue687\ue690\ue603\ue68e\ue683\ue603\ue694\ue687\ue68e\ue683\ue685\ue68b\ue6d7\ue690\ue603\udb80\udddb\ue974\ue7e4<span class="blank _0"></span>\ue978\udb80\udddc\ue603\ue695\ue687\ue603\ue694\ue687\ue687\ue68f\ue692\ue68e\ue683\ue69c\ue683\ue603\ue687\ue68e\ue603<span class="blank _0"></span>\ue69e\ue690\ue689\ue697\ue68e\ue691\ue603\ue845\ue603\ue692\ue691\ue694\ue603<span class="blank _0"></span>\ue687\ue68e\ue603\ue698\ue683\ue68e\ue691\ue694\ue603\ue686\ue687\ue603\ue97b\ue972<span class="blank _0"></span>\ue9b9\ue7e1\ue603\ue691\ue603\ue695\ue687\ue683\ue603\ue693\ue697\ue687\ue603<span class="blank _0"></span>\ue687\ue68e\ue603\ue696\ue694\ue68b\ue69e\ue690\ue689\ue697\ue68e\ue691\ue603</div><div class="t m0 x0 h3 y101 ff2 fs1 fc0 sc0 ls2 ws2">queda convertid<span class="blank _0"></span>o en rectán<span class="blank _0"></span>gulo, resulta la sigu<span class="blank _0"></span>iente expresión <span class="blank _0"></span>denominada Te<span class="blank _0"></span>orema de </div><div class="t m0 x0 h3 y102 ff2 fs1 fc0 sc0 ls2 ws2">Pitágoras: <span class="blank _10"> </span><span class="ff7 ls1d v7">\ue685<span class="fs4 ls1e v6">\uf136</span><span class="ls2 ws7">\uf34c<span class="blank"> </span>\ue683<span class="fs4 ls13 v6">\uf136</span><span class="ws4">\uf345<span class="blank"> </span>\ue684<span class="fs4 ls12 v6">\uf136</span></span></span></span><span class="v7"> <span class="blank _0"></span> <span class="blank _0"></span> (2.7) </span></div><div class="t m0 x0 h3 y103 ff2 fs1 fc0 sc0 ls1f ws2"> <span class="fs5 fc2 sc3 ls2 v8">2.7.1 EJEMPLO 2.1 </span></div><div class="t m0 x7f h3 y104 ff2 fs1 fc0 sc0 ls2 ws2">Dadas <span class="blank _4"> </span>dos <span class="blank _4"> </span>fuerzas <span class="blank _4"> </span><span class="ff7">\uee72</span></div></div><div class="c x1 y1 w89 h0"><div class="t m0 xa2 h3 y105 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xa3 y1 w5c h0"><div class="t m0 x8 h3 y105 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xa3 y1 w8a h0"><div class="t m0 x60 h3 y105 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x24 h10 y106 ff7 fs4 fc0 sc0 ls12">\uf135<span class="fs1 ls2 ws3 v4">\ue603\ue69b\ue603\uee72</span></div></div><div class="c x1 y1 w8b h0"><div class="t m0 x10 h3 y105 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x11 y1 w5c h0"><div class="t m0 x8 h3 y105 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x11 y1 w8c h0"><div class="t m0 x60 h3 y105 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x13 h10 y106 ff7 fs4 fc0 sc0 ls11">\uf136<span class="fs1 ls2 ws3 v4">\ue603<span class="ff2 ws2">de <span class="blank _4"> </span>magnitudes <span class="blank _4"> </span>respectiva<span class="blank _0"></span>s <span class="blank _4"> </span>80 <span class="blank _4"> </span>N <span class="blank _7"> </span>y <span class="blank _4"> </span>70 <span class="blank _4"> </span>N, <span class="blank _7"> </span>las <span class="blank _4"> </span>cuales </span></span></div><div class="t m0 x7f h3 y107 ff7 fs1 fc0 sc0 ls2 ws14">\ue688\ue691\ue694\ue68f\ue683\ue690\ue603<span class="blank"> </span>\ue687\ue690\ue696\ue694\ue687\ue603<span class="blank"> </span>\ue695\ue6c0\ue603<span class="blank"> </span>\ue697\ue690\ue603<span class="blank"> </span>\ue69e\ue690\ue689\ue697\ue68e<span class="blank _0"></span>\ue691\ue603<span class="blank"> </span>\ue841\ue603<span class="blank"> </span>\uf34c\ue603<span class="blank"> </span>\ue978\ue972\ue9b9\ue603<span class="blank"> </span>\ue685\ue691\ue68f\ue691\ue603<span class="blank"> </span>\ue695\ue687\ue603<span class="blank"> </span>\ue68b\ue690\ue686\ue68b\ue685\ue683\ue603<span class="blank"> </span>\ue687\ue690\ue603<span class="blank _4"> </span>\ue68e\ue683\ue603<span class="blank"> </span>\ue609\ue68b\ue689\ue697\ue694\ue683\ue603<span class="blank"> </span>\ue974\ue7e4\ue97a\ue7e1\ue603<span class="blank"> </span>\ue68a\ue683\ue68e\ue68e\ue683\ue694\ue603<span class="blank"> </span>\ue68e\ue683\ue603</div><div class="t m0 x7f h3 y108 ff2 fs1 fc0 sc0 ls2 ws2">magnitud R de la re<span class="blank _0"></span>sultante. </div><div class="t m0 x58 h3 y109 ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 y10a ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.8 </div><div class="t m0 x70 h3 y10b ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x70 h3 y10c ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x70 h3 y10d ff2 fs1 fc0 sc0 ls2 ws2"> </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 x3d y10e w88 h16" alt="" src="https://files.passeidireto.com/aa6fa3e4-c30a-4162-9054-f0a9b296ed34/bga.png"><div class="c x1 y1 w2 h0"><div class="t m0 x0 h2 y2 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y3 ff1 fs0 fc0 sc0 ls2 ws2"> </div><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls25 ws15">10<span class="ls2 ws2"> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _6"> </span><span class="fc1">José Manu<span class="blank _0"></span>el Arroyo And<span class="blank _0"></span>rade <span class="blank _0"></span>UNISUCRE<span class="fc0"> </span></span></span></div><div class="t m0 x2 h2 y5 ff1 fs0 fc1 sc0 ls2 ws2"> </div><div class="t m0 x3d h17 y10f ff2 fs5 fc2 sc3 ls2 ws2">2.7.1 EJEMPLO 2.1 (CONTINUACIÓN)<span class="blank _6"></span> </div><div class="t m0 x7f h3 y110 ff2 fs1 fc3 sc2 ls2 ws2">Solución </div><div class="t m0 x7f h3 y111 ff2 fs1 fc0 sc0 ls2 ws2">Se <span class="blank _a"> </span>traza <span class="blank _d"> </span>i<span class="blank _6"> </span>nicialmente <span class="blank _d"> </span>un <span class="blank _a"> </span>paralelogramo <span class="blank _d"> </span>con <span class="blank _a"> </span><span class="ff7">\uee72</span></div></div><div class="c x1 y1 w8d h0"><div class="t m0 xa4 h3 y112 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xa5 y1 w5c h0"><div class="t m0 x8 h3 y112 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xa5 y1 w8e h0"><div class="t m0 x60 h3 y112 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x7a h10 y113 ff7 fs4 fc0 sc0 ls12">\uf135<span class="fs1 ls2 ws3 v4">\ue603\ue69b\ue603\uee72</span></div></div><div class="c x1 y1 w8c h0"><div class="t m0 x4b h3 y112 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x79 y1 w5c h0"><div class="t m0 x8 h3 y112 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x4c y1 w8b h0"><div class="t m0 x60 h3 y112 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 xa6 h10 y113 ff7 fs4 fc0 sc0 ls11">\uf136<span class="fs1 ls2 ws3 v4">\ue603<span class="ff2 ws2">como <span class="blank _d"> </span>lados, <span class="blank _a"> </span>como <span class="blank _d"> </span>s<span class="blank _6"> </span>e </span></span></div><div class="t m0 x7f h3 y114 ff7 fs1 fc0 sc0 ls2 ws16">\ue68f\ue697\ue687\ue695\ue696\ue694\ue683\ue603<span class="blank"> </span>\ue687\ue690\ue603<span class="blank"> </span>\ue68e\ue683\ue603<span class="blank"> </span>\ue609\ue68b\ue689\ue697\ue694\ue683\ue603<span class="blank"> </span>\ue974\ue7e4\ue97b\ue603<span class="blank"> </span>\udb80\udddb\ue683\udb80\udddc\ue7e1\ue603<span class="blank"> </span>\ue687\ue690\ue603<span class="blank"> </span>\ue68e\ue683\ue603<span class="blank"> </span>\ue685\ue697\ue683\ue68e\ue603<span class="blank"> </span>\ue695\ue687\ue603<span class="blank"> </span>\ue691\ue684\ue695\ue687\ue694\ue698\ue683\ue603<span class="blank"> </span>\ue693<span class="blank _0"></span>\ue697\ue687\ue603<span class="blank"> </span>\ue68e\ue691\ue695\ue603<span class="blank"> </span>\ue69e\ue690\ue689\ue697\ue68e\ue691\ue695\ue603<span class="blank"> </span>\ue841\ue603<span class="blank"> </span>\ue69b\ue603<span class="blank"> </span>\ue840\ue7e1\ue603<span class="blank"> </span>\ue695\ue691\ue690\ue603</div><div class="t m0 x7f h3 y115 ff7 fs1 fc0 sc0 ls2 ws3">\ue685\ue691\ue694\ue694\ue687\ue695\ue692\ue691\ue690\ue686\ue68b\ue687\ue690\ue696\ue687<span class="blank _0"></span>\ue695\ue7e1\ue603\ue692\ue691\ue694\ue603\ue68e\ue691\ue603\ue696\ue683\ue690\ue696\ue691\ue603\ue695\ue691\ue690\ue603\ue68b\ue689\ue697\ue683\ue68e\ue687\ue695\ue7e1\ue603\ue691\ue603\ue695\ue687\ue683\ue603\ue693\ue697\ue687\ue603\ue841\ue603\uf34c\ue603<span class="blank _6"> </span>\ue840\ue603\uf34c\ue603\ue978\ue972\ue9b9\ue7e4\ue603\ue604\ue695\ue68b\ue68f\ue68b\ue695\ue68f\ue691\ue7e1\ue603\ue695\ue687\ue603</div><div class="t m0 x7f h3 y116 ff7 fs1 fc0 sc0 ls2 ws17">\ue686\ue687\ue686\ue697\ue685\ue687\ue603\ue693\ue697\ue687\ue603\ue68e\ue691\ue695\ue603\ue69e\ue690\ue689\ue697\ue68e\ue691\ue695\ue603\ue845\ue603\ue69b\ue603\ue840\ue603\ue695\ue691\ue690\ue603\ue695\ue697\ue692\ue68e\ue687\ue68f\ue687\ue690\ue696\ue683\ue694\ue68b\ue691\ue695\ue7e1\ue603\ue686<span class="blank _0"></span>\ue687\ue603\ue696\ue683\ue68e\ue603\ue688\ue691\ue694\ue68f\ue683\ue603\ue693\ue697\ue687\ue603\ue845\ue603\uf34c\ue603\ue973\ue97a\ue972\ue9b9\ue603<span class="blank"> </span><span class="ff2 ws2">- </span><span class="ls26">\ue840\ue603</span></div><div class="t m0 x7f h3 y117 ff2 fs1 fc0 sc0 ls2 ws2">= 180° - 60° = 120°. </div><div class="t m0 x7f h3 y118 ff2 fs1 fc0 sc0 ls2 ws2">Se <span class="blank _6"> </span>completa <span class="blank _6"> </span>el <span class="blank _6"> </span>paralelogramo al <span class="blank _1"> </span>dibu<span class="blank _0"></span>jar <span class="blank _6"> </span>a <span class="blank _1"> </span><span class="ff7">\uee7e</span></div></div><div class="c x1 y1 w8f h0"><div class="t m0 x72 h3 y119 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x73 y1 w63 h0"><div class="t m0 x8 h3 y119 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x66 y1 w90 h0"><div class="t m0 x60 h3 y119 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x67 h3 y118 ff2 fs1 fc0 sc0 ls2 ws2"> <span class="blank _6"> </span>como <span class="blank _6"> </span>la <span class="blank _6"> </span>diagonal <span class="blank _6"> </span>y <span class="blank _6"> </span>se <span class="blank _6"> </span>reemplazan </div><div class="t m0 x7f h3 y11a ff7 fs1 fc0 sc0 ls2 ws3">\ue68e\ue691\ue695\ue603\ue69e\ue690\ue689\ue697\ue68e\ue691\ue695\ue603\ue845\ue603\ue69b\ue603\ue840\ue7e1\ue603\ue692\ue691\ue694\ue603<span class="blank _0"></span>\ue695\ue697\ue695\ue603\ue698\ue683\ue68e\ue691\ue694\ue687\ue695\ue7e1\ue603\ue685\ue691<span class="blank _0"></span>\ue68f\ue691\ue603\ue695\ue687\ue603\ue68b\ue68e\ue697\ue695\ue696\ue694\ue683\ue603\ue687<span class="blank _0"></span>\ue690\ue603\ue68e\ue683\ue603\ue609\ue68b\ue689\ue697\ue694\ue683\ue603\ue974\ue7e4\ue97b\ue603\udb80\udddb\ue684\udb80\udddc\ue7e4<span class="ff2 ws2"> </span></div><div class="t m0 xa7 h3 y11b ff2 fs1 fc0 sc0 ls2 ws2"> </div><div class="t m0 x1c h3 y11c ff2 fs1 fc0 sc0 ls2 ws2">Figura 2.9 </div><div class="t m0 x7f h3 y11d ff2 fs1 fc0 sc0 ls2 ws2">Del <span class="blank _0"></span>paralelogram<span class="blank _0"></span>o <span class="blank _0"></span>anterior, <span class="blank _b"></span>se <span class="blank _0"></span>elabora <span class="blank _b"></span>un trián<span class="blank _0"></span>gulo <span class="blank _b"></span>de fuerzas, <span class="blank _b"></span>al trasladar <span class="blank _b"></span>a<span class="ff7 ws3">\ue603\uee72</span></div></div><div class="c x1 y1 w91 h0"><div class="t m0 x2d h3 y11e ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x34 y1 w5c h0"><div class="t m0 x8 h3 y11e ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x1d y1 w92 h0"><div class="t m0 x60 h3 y11e ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 x1e h10 y11f ff7 fs4 fc0 sc0 ls11">\uf136<span class="ff2 fs1 ls2 ws2 v4"> </span></div><div class="t m0 x7f h3 y120 ff2 fs1 fc0 sc0 ls2 ws2">a <span class="blank _1"> </span>c<span class="blank _6"> </span>ontinuación <span class="blank _1"> </span>de <span class="blank _1"> </span><span class="ff7 ws3">\ue603\uee72</span></div></div><div class="c x1 y1 w93 h0"><div class="t m0 xa2 h3 y121 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c x32 y1 w5c h0"><div class="t m0 x8 h3 y121 ff7 fs1 fc0 sc0 ls2">\udb80\uddcd</div></div><div class="c xa3 y1 w94 h0"><div class="t m0 x60 h3 y121 ff7 fs1 fc0 sc0 ls2">\ueb26</div></div><div class="c x1 y1 w2 h0"><div class="t m0 xa8 h10 y122 ff7 fs4 fc0 sc0 ls14">\uf135<span class="ff2 fs1 ls2 ws2 v4">, <span class="blank _1"> </span>como <span class="blank _1"> </span>s<span class="blank _6"> </span>e <span class="blank _1"> </span>muestra <span class="blank _1"> </span>en <span class="blank _4"> </span>la <span class="blank _1"> </span>Figura <span class="blank _1"> </span>2.9 <span class="blank _4"> </span>(c). <span class="blank _4"> </span>Se <span class="blank _1"> </span>sustituyen <span class="blank _1"> </span>los </span></div><div class="t m0 x7f h3 y123 ff7 fs1 fc0 sc0 ls2 ws3">\ue698\ue683\ue68e\ue691\ue694\ue687\ue695\ue603\ue686\ue687\ue603\ue68e\ue683\ue695\ue603\ue694\ue687\ue695\ue692\ue687\ue685\ue696\ue68b\ue698\ue683\ue695\ue603\ue68f\ue683\ue689\ue690\ue68b\ue696\ue697\ue686\ue687\ue695\ue603\ue69b\ue603\ue695\ue687\ue603\ue686\ue687\ue695\ue68b\ue689\ue690\ue683\ue690\ue603\ue68e\ue691\ue695\ue603\ue69e\ue690\ue689\ue697\ue68e\ue691\ue695\ue603\ue68b\ue690\ue696\ue687\ue694\ue690\ue691\ue695\ue603\ue83d\ue603\ue69b\ue603\ue83e\ue7e1\ue603</div><div class="t m0 x7f h3 y124 ff2 fs1 fc0 sc0 ls2 ws2">como se aprecia <span class="blank _0"></span>en la Figura 2.9 (d). </div><div class="t m0 x7f h3 y125 ff2 fs1 fc0 sc0 ls2 ws2">Se apli<span class="blank _0"></span>ca la <span class="blank _b"></span>ley de <span class="blank _0"></span>los c<span class="blank _0"></span>osenos, <span class="blank _0"></span>teniendo <span class="blank _b"></span>en cuenta <span class="blank _0"></span>que <span class="blank _b"></span>la magnitud <span class="blank _b"></span>R es <span class="blank _0"></span>opuesta </div><div class="t m0 x7f h3 y126 ff2 fs1 fc0 sc0 ls2 ws2">al ángulo de 120°, <span class="blank _0"></span>siendo este a la vez el án<span class="blank _0"></span>gulo entre las <span class="blank _0"></span>magnitudes 80 N y<span class="blank _0"></span> 70 </div><div class="t m0 x7f h3 y127 ff2 fs1 fc0 sc0 ls2 ws2">N, de acu<span class="blank _0"></span>erdo con <span class="blank _0"></span>la Figur<span class="blank _0"></span>a 2.9 <span class="blank _0"></span>(d) y<span class="blank _0"></span> al dar <span class="blank _0"></span>valores, c<span class="blank _0"></span>on referencia <span class="blank _0"></span>a la <span class="blank _0"></span>ecuación </div><div class="t m0 x7f h3 y128 ff2 fs1 fc0 sc0 ls2 ws2">(2.6), se tiene: </div><div class="t m0 x95 h18 y80 ff7 fs1 fc0 sc0 ls21">\ue615<span class="fs4 ls16 v6">\uf136</span><span class="ls22">\uf34c<span class="ls2 ws3 v9">\udb80\udddb</span><span class="ls1c">\ue97a\ue972<span class="ls2 ws3">\ue603\ue611<span class="v9">\udb80\udddc</span><span class="fs4 ls13 v6">\uf136</span><span class="ls23">\uf345</span><span class="v9">\udb80\udddb</span></span>\ue979\ue972<span class="ls2 ws3">\ue603\ue611<span class="v9">\udb80\udddc</span><span class="fs4 ls13 v6">\uf136</span><span class="ws4">\uf346<span class="blank"> </span>\ue974</span><span class="v9">\udb80\udddb</span></span>\ue97a\ue972<span class="ls2 ws3">\ue603\ue611<span class="v9">\udb80\udddc\udb80\udddb</span></span>\ue979\ue972<span class="ls2 ws3">\ue603\ue611<span class="ls24 v9">\udb80\udddc</span><span class="ws18">\ue685\ue691\ue695<span class="blank"> </span></span></span><span class="ws19">\ue973\ue974\ue972<span class="blank"> </span></span><span class="ls2 ws3">\ue9b9\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _0"></span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="fc3 ws1a">\uee7e<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="ls27 ws1b">\uf0da\uf0dc\uf0d9</span><span class="ws3">\ue603\uee7a<span class="ff2 sc2 ws2"> </span></span></span></span></span></span></div><div class="t m0 x70 h3 y129 ff2 fs1 fc0 sc0 ls2 ws2"> </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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