{"id":2510,"date":"2016-10-18T19:34:26","date_gmt":"2016-10-18T19:34:26","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2510"},"modified":"2024-08-21T14:24:11","modified_gmt":"2024-08-21T14:24:11","slug":"introducao-a-teoria-da-relatividade","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/fisica-moderna\/introducao-a-teoria-da-relatividade\/","title":{"rendered":"Teoria da Relatividade"},"content":{"rendered":"

Introdu\u00e7\u00e3o \u00e0 Teoria da Relatividade<\/b><\/span><\/span><\/span><\/p>\n

Breve Hist\u00f3rico<\/b><\/span><\/span><\/span><\/p>\n

Albert Einstein <\/b><\/span><\/span><\/span>(1879-1955), pelos seus <\/b><\/span><\/span><\/span>feitos cient\u00edficos que inovaram radicalmente os caminhos <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

tecnol\u00f3gicos da humanidade, <\/b><\/span><\/span><\/span>colaborou de forma extraordin\u00e1ria <\/b><\/span><\/span><\/span>para o desenvolvimento da ci\u00eancia, para a qualidade de vida\u00a0 de todos os habitantes do planeta Terra, alterando a vis\u00e3o dos cientistas nas \u00e1reas da f\u00edsica das part\u00edculas, astronomia, astrof\u00edsica, cosmologia, filosofia e outros<\/b><\/span><\/span><\/span><\/p>\n

\"\"conceitos relacionados ao universo, quando, aos 26 anos de idade, em 1905, encaminhou para os Anais da F\u00edsica um artigo que revolucionaria os conceitos tradicionais de espa\u00e7o e tempo \u201c A Teoria Especial da Relatividade\u201d. \u00a0<\/b><\/span><\/span><\/span><\/p>\n

Posteriormente, em 1916 ele <\/b><\/span><\/span><\/span>publica a Teoria Geral da Relatividade e no ano seguinte um artigo que serviu de base para o raio laser referente \u00e0 emiss\u00e3o estimulada da luz e um segundo artigo que \u00e9 a base da cosmologia atual sobre a estrutura do Universo.<\/b><\/span><\/span><\/span><\/p>\n

Conceito de referencial inercial<\/b><\/span><\/span><\/span><\/p>\n

Considere um <\/b><\/span><\/span><\/span>vag\u00e3o em movimento retil\u00edneo uniforme (MRU) <\/b><\/span><\/span><\/span>e uma <\/b><\/span><\/span><\/span>bola colocada sobre uma mesa, ambas no interior do vag\u00e3o. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>primeira lei de Newton \u201cPrinc\u00edpio da In\u00e9rcia<\/b><\/span><\/span><\/span>\u201d afirma que\u00a0<\/b><\/span><\/span><\/span>qualquer corpo em <\/b><\/span><\/span><\/span>repouso <\/b><\/span><\/span><\/span>ou em <\/b><\/span><\/span><\/span>movimento retil\u00edneo uniforme<\/b><\/span><\/span><\/span> tende a manter esses estados, desde que nenhuma for\u00e7a atue sobre ele <\/b><\/span><\/span><\/span>(for\u00e7a resultante sobre ele nula).\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Nesse caso, <\/b><\/span><\/span><\/span>um referencial no interior do vag\u00e3o<\/b><\/span><\/span><\/span>\u00a0\u00e9 inercial<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>pois em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o a ele as leis da f\u00edsica <\/b><\/span><\/span><\/span>(no caso, princ\u00edpio da in\u00e9rcia) <\/b><\/span><\/span><\/span>s\u00e3o v\u00e1lidos, j\u00e1 que a bola em rela\u00e7\u00e3o a esse referencial estar\u00e1 em repouso (primeira figura).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se o <\/b><\/span><\/span><\/span>vag\u00e3o for freado, acelerado ou efetuar uma curva (segunda figura), a bola ser\u00e1 deslocada <\/b><\/span><\/span><\/span>sobre a mesa, <\/b><\/span><\/span><\/span>saindo da sua posi\u00e7\u00e3o de equil\u00edbrio <\/b><\/span><\/span><\/span>e sobre ela <\/b><\/span><\/span><\/span>n\u00e3o surgiu nenhuma for\u00e7a de intera\u00e7\u00e3o, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>nenhuma for\u00e7a externa agiu empurrando ou puxando a bola. <\/b><\/span><\/span><\/span><\/p>\n

Assim, nesse caso, o <\/b><\/span><\/span><\/span>princ\u00edpio da in\u00e9rcia n\u00e3o \u00e9 v\u00e1lido para esse referencial <\/b><\/span><\/span><\/span>que tamb\u00e9m est\u00e1 <\/b><\/span><\/span><\/span>colocado no interior do vag\u00e3o<\/b><\/span><\/span><\/span> e ele <\/b><\/span><\/span><\/span>n\u00e3o \u00e9 um referencial inercial \u00e9 um referencial n\u00e3o inercial. <\/b><\/span><\/span><\/span>Portanto, <\/b><\/span><\/span><\/span>num referencial n\u00e3o inercial, os corpos est\u00e3o sujeitos a pseudo-for\u00e7as (for\u00e7as de in\u00e9rcia) que, em princ\u00edpio, n\u00e3o podem ser atribu\u00eddas a qualquer agente direto.<\/b><\/span><\/span><\/span><\/p>\n

Um <\/b><\/span><\/span><\/span>referencial<\/b><\/span><\/span><\/span> \u00e9 denominado <\/b><\/span><\/span><\/span>referencial inercial se nele a primeira lei de Newton (ou qualquer outra lei f\u00edsica) \u00e9 v\u00e1lida.<\/b><\/span><\/span><\/span><\/p>\n

Referenciais inercais s\u00e3o referenciais que se movem, uns em rela\u00e7\u00e3o aos outros, com velocidade constante<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

\u00a0<\/span><\/p>\n

Conceito de Postulado<\/b><\/span><\/span><\/span><\/p>\n

Um <\/b><\/span><\/span><\/span>postulado na Teoria F\u00edsica <\/b><\/span><\/span><\/span>tem o <\/b><\/span><\/span><\/span>mesmo papel que um axioma tem na Matem\u00e1tica.<\/b><\/span><\/span><\/span><\/p>\n

\u00c9 uma <\/b><\/span><\/span><\/span>afirma\u00e7\u00e3o fundamental que n\u00e3o pode ser demonstrado logicamente. <\/b><\/span><\/span><\/span><\/p>\n

Em <\/b><\/span><\/span><\/span>F\u00edsica, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>postulado<\/b><\/span><\/span><\/span>, \u00e9 o resultado da <\/b><\/span><\/span><\/span>generaliza\u00e7\u00e3o dos fatos experimentais.\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Postulados da Relatividade Especial<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>teoria da relatividade especial \u00e9 constru\u00edda a partir do postulado do princ\u00edpio da relatividade de Einstein e do postulado da velocidade da luz:<\/b><\/span><\/span><\/span><\/p>\n

Primeiro Postulado<\/b><\/span><\/span><\/span><\/p>\n

\u201cAs leis da f\u00edsica devem ser exatamente as mesmas se descritas por observadores em diferentes referenciais inerciais. N\u00e3o existe um referencial inercial privilegiado (referencial absoluto)\u201d. <\/b><\/span><\/span><\/span><\/p>\n

Esse <\/b><\/span><\/span><\/span>postulado afirma que n\u00e3o existe sistema de refer\u00eancia inercial preferencial <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>estudo de qualquer fen\u00f4meno f\u00edsico.<\/b><\/span><\/span><\/span><\/p>\n

Assim, o <\/b><\/span><\/span><\/span>princ\u00edpio da relatividade da mec\u00e2nica cl\u00e1ssica generaliza-se para todos os processos f\u00edsicos da Natureza, ou seja<\/b><\/span><\/span><\/span>, tanto as <\/b><\/span><\/span><\/span>leis da Mec\u00e2nica como as leis do Eletromagnetismo devem ter a mesma forma em qualquer referencial.<\/b><\/span><\/span><\/span><\/p>\n

Ent\u00e3o, por exemplo,<\/b><\/span><\/span><\/span> <\/b>observadores em referenciais inerciais diferentes<\/b><\/span><\/span><\/span> medem a <\/b><\/span><\/span><\/span>mesma acelera\u00e7\u00e3o para o movimento de uma part\u00edcula.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Segundo Postulado<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Postulado da velocidade da luz: \u201cA velocidade da luz no v\u00e1cuo tem o mesmo valor em todas as dire\u00e7\u00f5es e em todos os referenciais inerciais ( a <\/b><\/span><\/span><\/span>velocidade da luz \u00e9 independente da velocidade da fonte<\/b><\/span><\/span><\/span>)\u201d.<\/b><\/span><\/span><\/span><\/p>\n

Esta \u00e9 a velocidade m\u00e1xima com que qualquer tipo de informa\u00e7\u00e3o pode ser transmitida.<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>velocidade da luz n\u00e3o depende nem da velocidade do emissor<\/b><\/span><\/span><\/span> (fonte emissora da luz), <\/b><\/span><\/span><\/span>nem da velocidade do receptor (observador) do sinal luminoso.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Veja um exemplo:<\/b><\/span><\/span><\/span> <\/b>Suponha que, <\/b><\/span><\/span><\/span>no futuro, uma base avan\u00e7ada seja constru\u00edda em Marte. <\/b><\/span><\/span><\/span>Suponha, tamb\u00e9m, que <\/b><\/span><\/span><\/span>uma nave espacial est\u00e1 viajando em dire\u00e7\u00e3o a Terra, com velocidade constante igual \u00e0 metade da velocidade da luz. Quando essa nave passa por Marte, dois sinais de r\u00e1dio s\u00e3o emitidos em dire\u00e7\u00e3o \u00e0 Terra, <\/b><\/span><\/span><\/span> <\/b>um pela base e outro pela nave. <\/b><\/span><\/span><\/span>Ambos s\u00e3o <\/b><\/span><\/span><\/span>refletidos pela Terra e, posteriormente, detectados na base em Marte. Sejam t<\/b><\/span><\/span><\/span>b<\/b><\/span><\/span><\/sub><\/span>\u00a0e t<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span> os intervalos de tempo total de viagem dos sinais emitidos, respectivamente, pela base e pela nave, desde a emiss\u00e3o at\u00e9 a detec\u00e7\u00e3o de cada um deles pela base em Marte.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Como a <\/b><\/span><\/span><\/span>velocidade da luz (onda eletromagn\u00e9tica) \u00e9 3.10<\/b><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/sup><\/span>m\/s e independe do referencial, n\u00e3o importando de a fonte emissora estar em repouso ou em movimento, essa velocidade ser\u00e1 sempre a mesma e os tempos t<\/b><\/span><\/span><\/span>b<\/b><\/span><\/span><\/sub><\/span> e t<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span> ser\u00e3o iguais.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>velocidade da luz no v\u00e1cuo \u00e9 a velocidade m\u00e1xima poss\u00edvel de transmiss\u00e3o de intera\u00e7\u00e3o na <\/b><\/span><\/span><\/span>Natureza e <\/b><\/span><\/span><\/span>seu valor \u00e9 c=3,0.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>m\/s. Ela n\u00e3o depende do sistema de refer\u00eancia inercial adotado. Observe que, se V = c = \u0394S\/\u0394t \u00e9 constante para qualquer observador (referencial) ent\u00e3o espa\u00e7o (\u0394S) e tempo (\u0394t) podem assumir valores diferentes dependendo do observador (referencial), pois o quociente \u0394S\/\u0394t \u00e9 constante.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Dilata\u00e7\u00e3o do tempo<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Ao discutir o <\/b><\/span><\/span><\/span>conceito de tempo,<\/b><\/span><\/span><\/span> <\/b>Einstein<\/b><\/span><\/span><\/span> mostrou que a <\/b><\/span><\/span><\/span>simultaneidade<\/b><\/span><\/span><\/span> (fatos que ocorrem em diferentes locais e ao mesmo tempo) <\/b><\/span><\/span><\/span>\u00e9 algo relativo.<\/b><\/span><\/span><\/span><\/p>\n

Assim, o que \u00e9 <\/b><\/span><\/span><\/span>simult\u00e2neo para um observador poder\u00e1 n\u00e3o ser simult\u00e2neo para outro observador que se move em rela\u00e7\u00e3o ao primeiro.<\/b><\/span><\/span><\/span><\/p>\n

Em outras palavras, a <\/b><\/span><\/span><\/span>\u00fanica raz\u00e3o pela qual todos n\u00f3s sentimos espa\u00e7o e tempo da mesma forma deve-se ao fato de todos n\u00f3s estarmos nos movendo a uma mesma velocidade, uns em rela\u00e7\u00e3o aos outros. <\/b><\/span><\/span><\/span><\/p>\n

Contudo, quando os <\/b><\/span><\/span><\/span>observadores se locomovem <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>velocidades extremamente diferentes<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span><\/p>\n

o <\/b><\/span><\/span><\/span>tempo entre eles n\u00e3o ser\u00e1 mais simult\u00e2neo, mas diferente para cada um deles.<\/b><\/span><\/span><\/span><\/p>\n

Einstein<\/b><\/span><\/span><\/span> mostrou que a <\/b><\/span><\/span><\/span>maneira como a mec\u00e2nica cl\u00e1ssica de Newton abordava alguns conceitos n\u00e3o era v\u00e1lida para algumas situa\u00e7\u00f5es.<\/b><\/span><\/span><\/span><\/p>\n

Explicando a dilata\u00e7\u00e3o do tempo<\/b><\/span><\/span><\/span> com um <\/b><\/span><\/span><\/span>exemplo simples muito utilizado.<\/b><\/span><\/span><\/span><\/p>\n

Considere um <\/b><\/span><\/span><\/span>vag\u00e3o em <\/b><\/span><\/span><\/span>movimento retil\u00edneo e uniforme<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>velocidade constante<\/b><\/span><\/span><\/span> de intensidade V <\/b><\/span><\/span><\/span>em rela\u00e7\u00e3o a um <\/b><\/span><\/span><\/span>observador (O<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>) no solo. <\/b><\/span><\/span><\/span>No <\/b><\/span><\/span><\/span>interior do vag\u00e3o existe um sistema de <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

refer\u00eancia<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>inercial, observador O<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>raio de luz saindo do teto do vag\u00e3o atinge o ch\u00e3o, percorrendo em rela\u00e7\u00e3o ao vag\u00e3o <\/b><\/span><\/span><\/span>(ao <\/b><\/span><\/span><\/span>observador O<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>, dentro da vag\u00e3o,<\/b><\/span><\/span><\/span> figura <\/b><\/span><\/span><\/span>I) uma <\/b><\/span><\/span><\/span>dist\u00e2ncia h com velocidade da luz c num intervalo de tempo \u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>, tal que,\u00a0 V = c = h\/\u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>h = c.\u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Com o <\/b><\/span><\/span><\/span>vag\u00e3o em movimento <\/b><\/span><\/span><\/span>(velocidade constante V), <\/b><\/span><\/span><\/span>em rela\u00e7\u00e3o ao observador O<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>\u00a0no solo, <\/b><\/span><\/span><\/span>a luz percorre <\/b><\/span><\/span><\/span>uma dist\u00e2ncia d (figura II), maior que a observada por O<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>, sendo d = V.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 aplicando-se <\/b><\/span><\/span><\/span>Pit\u00e1goras <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>tri\u00e2ngulo ret\u00e2ngulo da figura II\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>d<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sup><\/span>= h<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0+ (V.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>, onde <\/b><\/span><\/span><\/span>V \u00e9 a velocidade do vag\u00e3o e c a velocidade da luz\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 observe <\/b><\/span><\/span><\/span>que d = c.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>\u00a0e que h = c.\u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.\u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0+ V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.\u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.\u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0 \"\"\u00a0 \u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= \u0394t<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>.( c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>\u0394t<\/b><\/span><\/span><\/span>s <\/b><\/span><\/span><\/sub><\/span>= \u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>\/\u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0 o <\/b><\/span><\/span><\/span>intervalo de tempo medido quando o observador est\u00e1 em <\/b><\/span><\/span><\/span>repouso (\u0394t<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>) no interior do vag\u00e3o<\/b><\/span><\/span><\/span> \u00e9 denominado <\/b><\/span><\/span><\/span>intervalo de tempo<\/b><\/span><\/span><\/span> <\/b>pr\u00f3prio<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>(\u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>)\u00a0<\/b><\/span><\/span><\/span>e o intervalo de tempo medido pelo observador que est\u00e1 <\/b><\/span><\/span><\/span>em repouso em rela\u00e7\u00e3o ao solo e fora do vag\u00e3o que est\u00e1 em movimento ser\u00e1 denominado de\u00a0<\/b><\/span><\/span><\/span>(\u0394t)<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Preste muita aten\u00e7\u00e3o no formul\u00e1rio abaixo<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe na equa\u00e7\u00e3o acima que:<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0Considerando a <\/b><\/span><\/span><\/span>velocidade V com que o vag\u00e3o se move muito pequena <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o \u00e0 velocidade da<\/b><\/span><\/span><\/span> <\/b>luz (3,0.10<\/b><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/sup><\/span>m\/s), a raz\u00e3o V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0ficar\u00e1 extremamente pequena <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>a express\u00e3o \u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0tender\u00e1 a 1 <\/b><\/span><\/span><\/span>fazendo com que <\/b><\/span><\/span><\/span>\u0394t = \u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Assim, para <\/b><\/span><\/span><\/span>velocidades compar\u00e1veis ao nosso dia a dia <\/b><\/span><\/span><\/span>os <\/b><\/span><\/span><\/span>efeitos<\/b><\/span><\/span><\/span> da <\/b><\/span><\/span><\/span>teoria da relatividade s\u00e3o insignificantes.<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0Por outro lado, se a <\/b><\/span><\/span><\/span>velocidade V do vag\u00e3o for se aproximando da velocidade da luz c, \u0394t<\/b><\/span><\/span><\/span> vai ficando <\/b><\/span><\/span><\/span>cada vez maior que \u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0e os efeitos relativ\u00edsticos v\u00e3o ficando cada vez maiores.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Veja um exerc\u00edcio exemplo:<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>nave Enterprise viaja de Netuno a Plut\u00e3o<\/b><\/span><\/span><\/span> a uma <\/b><\/span><\/span><\/span>velocidade constante v = 0,5c<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>onde c \u00e9 a<\/b><\/span><\/span><\/span>\"\"<\/p>\n

velocidade da luz no v\u00e1cuo<\/b><\/span><\/span><\/span>. No <\/b><\/span><\/span><\/span>referencial<\/b><\/span><\/span><\/span> <\/b>da espa\u00e7onave, o tempo transcorrido entre a partida de Netuno e a chegada \u00e0 Plut\u00e3o 2,5h = 150 min. Qual o tempo <\/b><\/span><\/span><\/span>transcorrido medido no <\/b><\/span><\/span><\/span>referencial de Netuno?<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

Contra\u00e7\u00e3o do espa\u00e7o (do comprimento)<\/b><\/span><\/span><\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>um vag\u00e3o em movimento retil\u00edneo e uniforme com velocidade constante de intensidade V<\/b><\/span><\/span><\/span> em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o a um observador (O<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>) no solo. <\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>interior do vag\u00e3o existe um sistema de refer\u00eancia inercial, observador O<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Coloque uma <\/b><\/span><\/span><\/span>barra de comprimento L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0em rela\u00e7\u00e3o a O<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/sub><\/span>\u00a0no interior do vag\u00e3o, orientada na dire\u00e7\u00e3o do movimento. <\/b><\/span><\/span><\/span><\/p>\n

Devido \u00e0 <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o do tempo, essa barra ter\u00e1 comprimento L em rela\u00e7\u00e3o a O<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>, depois <\/b><\/span><\/span><\/span>que o <\/b><\/span><\/span><\/span>vag\u00e3o<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>deslocou durante um intervalo de tempo \u0394t\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\/\u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 \u0394t<\/b><\/span><\/span><\/span>p <\/b><\/span><\/span><\/sub><\/span>= L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\/V\u00a0 \"\"\u00a0 V = L\/\u0394t\u00a0 \"\"\u00a0 \u0394t = L\/V\u00a0 \"\" \u0394t= \u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\/(\u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)\u00a0 \"\"\u00a0 \u0394t\/\u0394t<\/b><\/span><\/span><\/span>p <\/b><\/span><\/span><\/sub><\/span>= \u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sup><\/span>\u00a0\"\"\u00a0 (L\/V)\/(L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\/V) = \u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0 L\/L<\/b><\/span><\/span><\/span>p <\/b><\/span><\/span><\/sub><\/span>= \u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

L=L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>. \u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Preste muita aten\u00e7\u00e3o no formul\u00e1rio abaixo<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe na equa\u00e7\u00e3o acima que:<\/b><\/span><\/span><\/span><\/p>\n

\"\" o <\/b><\/span><\/span><\/span>efeito \u00e9 sentido <\/b><\/span><\/span><\/span>apenas na <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o do movimento.<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0As <\/b><\/span><\/span><\/span>dimens\u00f5es de um objeto<\/b><\/span><\/span><\/span> s\u00e3o <\/b><\/span><\/span><\/span>m\u00e1ximas quando medidas em repouso <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o ao observador. <\/b><\/span><\/span><\/span><\/p>\n

\"\" Quando o <\/b><\/span><\/span><\/span>objeto se move <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade V, <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o ao observador, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>resultado<\/b><\/span><\/span><\/span> da medida de sua <\/b><\/span><\/span><\/span>dimens\u00e3o paralela a dire\u00e7\u00e3o do movimento \u00e9 menor do que o valor obtido quando em repouso.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\"\" As <\/b><\/span><\/span><\/span>dimens\u00f5es do objeto, perpendiculares a dire\u00e7\u00e3o do movimento, n\u00e3o s\u00e3o afetadas.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\"\" No <\/b><\/span><\/span><\/span>cotidiano, valor da velocidade V \u00e9 desprez\u00edvel em rela\u00e7\u00e3o \u00e0 velocidade da luz c <\/b><\/span><\/span><\/span>e, nesse caso, a <\/b><\/span><\/span><\/span>raz\u00e3o V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00e9 muito pequena, tendendo a zero e pode ser desprezada.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Assim, <\/b><\/span><\/span><\/span>L = L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>. \u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 L = L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>. \u221a1 \u2013 0\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>L = L<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 que <\/b><\/span><\/span><\/span>est\u00e1 de acordo com a mec\u00e2nica\u00a0 de Newton (cl\u00e1ssica).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\"\" Com <\/b><\/span><\/span><\/span>velocidade da luz, ou velocidades pr\u00f3ximas a ela<\/b><\/span><\/span><\/span>, voc\u00ea pode <\/b><\/span><\/span><\/span>percorrer uma dist\u00e2ncia d num intervalo de tempo menor, devido \u00e0 contra\u00e7\u00e3o de seu comprimento.<\/b><\/span><\/span><\/span><\/p>\n

Assim, <\/b><\/span><\/span><\/span>\u00e9 poss\u00edvel atravessarmos o di\u00e2metro da Via L\u00e1ctea, <\/b><\/span><\/span><\/span>uma dist\u00e2ncia de <\/b><\/span><\/span><\/span>aproximadamente 100 anos-luz <\/b><\/span><\/span><\/span>(equivalente a 10<\/b><\/span><\/span><\/span>18<\/b><\/span><\/span><\/sup><\/span>m), em um <\/b><\/span><\/span><\/span>intervalo de tempo bem menor que 100 anos. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

Isso <\/b><\/span><\/span><\/span>pode ser explicado pelo fen\u00f4meno de contra\u00e7\u00e3o do comprimento, <\/b><\/span><\/span><\/span>como <\/b><\/span><\/span><\/span>visto pelo viajante<\/b><\/span><\/span><\/span>, ou ainda pelo <\/b><\/span><\/span><\/span>fen\u00f4meno de dilata\u00e7\u00e3o temporal, <\/b><\/span><\/span><\/span>como <\/b><\/span><\/span><\/span>observado por quem est\u00e1 em repouso em rela\u00e7\u00e3o \u00e0 gal\u00e1xia.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Veja um exerc\u00edcio exemplo:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Massa Relativ\u00edstica<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

A massa \u00e9 a medida da in\u00e9rcia de um corpo.<\/b><\/span><\/span><\/span> <\/b>Assim, <\/b><\/span><\/span><\/span>\u00e0<\/b><\/span><\/span><\/span> <\/b>medida que a velocidade de um corpo aumenta sua in\u00e9rcia tamb\u00e9m aumenta <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>quando a velocidade do corpo tende \u00e0 velocidade da luz <\/b><\/span><\/span><\/span>(a maior poss\u00edvel), <\/b><\/span><\/span><\/span>sua in\u00e9rcia\u00a0 e consequentemente sua massa tende ao infinito. <\/b><\/span><\/span><\/span><\/p>\n

Portanto, <\/b><\/span><\/span><\/span>al\u00e9m do espa\u00e7o e do tempo, na teoria da velocidade a massa tamb\u00e9m varia e essa varia\u00e7\u00e3o \u00e9 fornecida pela express\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Veja um exerc\u00edcio exemplo:<\/b><\/span><\/span><\/span><\/p>\n

Quando um <\/b><\/span><\/span><\/span>el\u00e9tron de massa m = 9,1.10<\/b><\/span><\/span><\/span>-31<\/b><\/span><\/span><\/sup><\/span> kg \u00e9 <\/b><\/span><\/span><\/span>acelerado at\u00e9 atingir <\/b><\/span><\/span><\/span>60% da velocidade da luz <\/b><\/span><\/span><\/span>(V = 0,6c), o que <\/b><\/span><\/span><\/span>acontecer\u00e1 com sua massa(m) em rela\u00e7\u00e3o \u00e0 sua massa em repouso (m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>)? <\/b><\/span><\/span><\/span>\"\"<\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Energia Relativ\u00edstica<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Como, na <\/b><\/span><\/span><\/span>teoria da relatividade, a massa relativ\u00edstica est\u00e1 associada com a velocidade, <\/b><\/span><\/span><\/span>essa <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o <\/b><\/span><\/span><\/span>faz com que a <\/b><\/span><\/span><\/span>teoria relativ\u00edstica implique tamb\u00e9m com a energia. <\/b><\/span><\/span><\/span><\/p>\n

Albert Einstein, Pr\u00eamio Nobel de F\u00edsica, <\/b><\/span><\/span><\/span>publicou, em 1905, cinco estudos em que definiu a <\/b><\/span><\/span><\/span>natureza da luz, revolucionou os conceitos de tempo e espa\u00e7o <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>formulou a mais conhecida das equa\u00e7\u00f5es<\/b><\/span><\/span><\/span><\/p>\n

E = mc\u00b2.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Segundo a <\/b><\/span><\/span><\/span>Teoria da Relatividade Especial, formulada por Einstein, <\/b><\/span><\/span><\/span>essa rela\u00e7\u00e3o <\/b><\/span><\/span><\/span>E = mc\u00b2 <\/b><\/span><\/span><\/span>expressa a <\/b><\/span><\/span><\/span>possibilidade de a massa de um corpo ser convertida em energia e vice-versa.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

E<\/b><\/span><\/span><\/span> tamb\u00e9m \u00e9 chamada <\/b><\/span><\/span><\/span>energia pr\u00f3pria do corpo.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>energia do repouso <\/b><\/span><\/span><\/span>\u00e9 fornecida por <\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>=m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>, onde <\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00e9 a massa do repouso. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>energia cin\u00e9tica relativ\u00edstica <\/b><\/span><\/span><\/span>do corpo <\/b><\/span><\/span><\/span>corresponde \u00e0 diferen\u00e7a entre a energia pr\u00f3pria (E) <\/b><\/span><\/span><\/span>e a <\/b><\/span><\/span><\/span>energia do repouso (E<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>)\u00a0<\/b><\/span><\/span><\/span> \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>c <\/b><\/span><\/span><\/sub><\/span>= E \u2013 E<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>c <\/b><\/span><\/span><\/sub><\/span>= mc<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>c <\/b><\/span><\/span><\/sub><\/span>= (m \u2013 m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span>c.<\/b><\/span><\/span><\/span><\/p>\n

Na express\u00e3o <\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>c <\/b><\/span><\/span><\/sub><\/span>= (m \u2013 m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).c<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>como <\/b><\/span><\/span><\/span>c \u00e9 constante<\/b><\/span><\/span><\/span>, se a <\/b><\/span><\/span><\/span>energia cin\u00e9tica E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>\u00a0diminuir ou aumentar ocorrer\u00e1 <\/b><\/span><\/span><\/span>uma correspondente <\/b><\/span><\/span><\/span>diminui\u00e7\u00e3o ou aumento de massa do corpo.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Veja um exerc\u00edcio exemplo:<\/b><\/span><\/span><\/span><\/p>\n

Em <\/b><\/span><\/span><\/span>1905 Albert Einstein publica a Teoria da Relatividade<\/b><\/span><\/span><\/span>, com a qual o <\/b><\/span><\/span><\/span>conceito de energia<\/b><\/span><\/span><\/span> ganha um <\/b><\/span><\/span><\/span>novo significado <\/b><\/span><\/span><\/span>e esta <\/b><\/span><\/span><\/span>grandeza passa a ser expressa pela famosa equa\u00e7\u00e3o de Einstein, <\/b><\/span><\/span><\/span>que estabeleceu definitivamente <\/b><\/span><\/span><\/span>a equival\u00eancia entre a massa e a energia.<\/b><\/span><\/span><\/span><\/p>\n

Tal <\/b><\/span><\/span><\/span>equival\u00eancia \u00e9 <\/b><\/span><\/span><\/span>talvez o<\/b><\/span><\/span><\/span> resultado mais revolucion\u00e1rio <\/b><\/span><\/span><\/span>da<\/b><\/span><\/span><\/span> teoria da relatividade. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

Ela <\/b><\/span><\/span><\/span>simplesmente <\/b><\/span><\/span><\/span>nos diz que <\/b><\/span><\/span><\/span>massa pode ser convertida em energia e vice-versa.<\/b><\/span><\/span><\/span><\/p>\n

Sabendo-se que a <\/b><\/span><\/span><\/span>velocidade da luz no v\u00e1cuo 3 . 10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span> m\/s, <\/b><\/span><\/span><\/span>determine <\/b><\/span><\/span><\/span>a energia contida<\/b><\/span><\/span><\/span> em uma <\/b><\/span><\/span><\/span>massa de 1 gr\u00e3o de feij\u00e3o<\/b><\/span><\/span><\/span>, de aproximadamente <\/b><\/span><\/span><\/span>0,2 g<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Rela\u00e7\u00e3o entre velocidades relativas relativ\u00edsticas<\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>velocidade relativa (V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>para<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>dois corpos <\/b><\/span><\/span><\/span>deslocando-se em <\/b><\/span><\/span><\/span>sentidos opostos, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidades pr\u00f3ximas \u00e0 da luz <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>m\u00f3dulos u e v <\/b><\/span><\/span><\/span>em<\/b><\/span><\/span><\/span> <\/b>rela\u00e7\u00e3o a um referencial inercial<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>fornecida <\/b><\/span><\/span><\/span>pela<\/b><\/span><\/span><\/span> <\/b>f\u00f3rmula de Einstein ao lado.<\/b><\/span><\/span><\/span><\/p>\n

Esta <\/b><\/span><\/span><\/span>express\u00e3o \u00e9 a f\u00f3rmula de soma de velocidades <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>caso relativ\u00edstico. Observe<\/b><\/span><\/span><\/span> que:
\n<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span><\/p>\n

Para <\/b><\/span><\/span><\/span>velocidades pequenas <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o<\/b><\/span><\/span><\/span> \u00e0 <\/b><\/span><\/span><\/span>velocidade da luz, <\/b><\/span><\/span><\/span>o termo <\/b><\/span><\/span><\/span>u.V\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>tende a<\/b><\/span><\/span><\/span> <\/b>zero,<\/b><\/span><\/span><\/span> <\/b>e a <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o se resume <\/b><\/span><\/span><\/span>a j\u00e1 esperada <\/b><\/span><\/span><\/span>f\u00f3rmula cl\u00e1ssica \u00a0V<\/b><\/span><\/span><\/span>R <\/b><\/span><\/span><\/sub><\/span>= u + V.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Essa<\/b><\/span><\/span><\/span> f\u00f3rmula n\u00e3o permite <\/b><\/span><\/span><\/span>que a <\/b><\/span><\/span><\/span>velocidade relativa entre dois corpos supere a velocidade da luz.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Veja um exerc\u00edcio exemplo:<\/b><\/span><\/span><\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>duas naves espaciais, N<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> e N<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> que viajam em <\/b><\/span><\/span><\/span>sentidos contr\u00e1rios<\/b><\/span><\/span><\/span>, isto \u00e9, opostos, com <\/b><\/span><\/span><\/span>velocidades de 50% e 70%, <\/b><\/span><\/span><\/span>respectivamente, da <\/b><\/span><\/span><\/span>velocidade da luz. <\/b><\/span><\/span><\/span>Calcule a <\/b><\/span><\/span><\/span>velocidade relativa de uma nave em rela\u00e7\u00e3o \u00e0 outra.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> = (N<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> + N<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>)\/[1 +( N<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.N<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)] \"\" <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> = (0,5c + 0,7c)\/[1 +( 0,5c.0,7c\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)] = 1,2c\/ (1 + 0,35c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>) \"\"<\/b><\/span><\/span><\/span><\/p>\n

V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> = 1,2c\/1,35 \"\" <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> \u2248 0,9c.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Observa\u00e7\u00e3o: Se voc\u00ea utilizar a f\u00f3rmula da F\u00edsica Cl\u00e1ssica voc\u00ea obter\u00e1 V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span> = 0,5c + 0,7c = 1,2c, valor imposs\u00edvel j\u00e1 que a velocidade da luz no v\u00e1cuo n\u00e3o pode ser maior que c.<\/b><\/span><\/span><\/span><\/p>\n

Selecionei alguns exerc\u00edcios interessantes para que voc\u00ea possa conferir as resolu\u00e7\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

01-(UNESP-SP<\/b><\/span><\/span><\/span>) Institu\u00eddo pela <\/b><\/span><\/span><\/span>Organiza\u00e7\u00e3o das Na\u00e7\u00f5es Unidas, 2005 foi o Ano Mundial da F\u00edsica,<\/b><\/span><\/span><\/span> em que se <\/b><\/span><\/span><\/span>comemorou o centen\u00e1rio dos trabalhos revolucion\u00e1rios<\/b><\/span><\/span><\/span> publicados por <\/b><\/span><\/span><\/span>Albert Einstein, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>mais importante\u00a0 cientista do s\u00e9culo XX <\/b><\/span><\/span><\/span>(segundo a revista norte americana Time). <\/b><\/span><\/span><\/span><\/p>\n

Na <\/b><\/span><\/span><\/span>Teoria da Relatividade Especial, de Einstein, <\/b><\/span><\/span><\/span>objetos que se <\/b><\/span><\/span><\/span>movem<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>velocidade V<\/b><\/span><\/span><\/span> em rela\u00e7\u00e3o a um <\/b><\/span><\/span><\/span>referencial inercial tem o tempo dilatado por um fator \u03bb, <\/b><\/span><\/span><\/span>para um <\/b><\/span><\/span><\/span>observador em repouso <\/b><\/span><\/span><\/span>nesse referencial.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>tabela mostra valores de \u03bb <\/b><\/span><\/span><\/span>para diversos <\/b><\/span><\/span><\/span>m\u00f3dulos da velocidade V, <\/b><\/span><\/span><\/span>representados em <\/b><\/span><\/span><\/span>m\u00faltiplos\u00a0 da velocidade da luz, c (ou 3,0.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>ms).<\/b><\/span><\/span><\/span><\/p>\n

Segundo <\/b><\/span><\/span><\/span>esse modelo, <\/b><\/span><\/span><\/span>pede-se:<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>qual a <\/b><\/span><\/span><\/span>velocidade, em m\/s, <\/b><\/span><\/span><\/span>que deve ser <\/b><\/span><\/span><\/span>atingida pelo objeto<\/b><\/span><\/span><\/span> para que a <\/b><\/span><\/span><\/span>dilata\u00e7\u00e3o do tempo seja de apenas 0,5%?<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Comente <\/b><\/span><\/span><\/span>como esse resultado <\/b><\/span><\/span><\/span>explica <\/b><\/span><\/span><\/span>por que as pessoas n\u00e3o percebem <\/b><\/span><\/span><\/span>os <\/b><\/span><\/span><\/span>efeitos da dilata\u00e7\u00e3o do tempo no seu dia-a-dia.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>se para o <\/b><\/span><\/span><\/span>objeto passaram-se 10 minutos, quantos minutos se passaram para um observador no referencial inercial que v\u00ea o objeto se movimentando \u00e0 velocidade de 0,600c?<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>O <\/b><\/span><\/span><\/span>intervalo de tempo que sofre maior dilata\u00e7\u00e3o na express\u00e3o \u0394t = \u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\/\u221a1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00e9 <\/b><\/span><\/span><\/span>\u0394t<\/b><\/span><\/span><\/span> <\/b>e ele se <\/b><\/span><\/span><\/span>dilata de 0,5% desse valor \"\" \u0394t = \u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0+ (0,5\/100).\u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\" <\/b><\/span><\/span><\/span>\u0394t = 1,005.\u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\" 1,005 de aumento corresponde ao fator \u03bb \"\" <\/b><\/span><\/span><\/span>\u0394t = \u03bb.\u0394t<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Procurando na tabela\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 quando \u03bb = 1,005<\/b><\/span><\/span><\/span> \u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>v = 0,100c<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>v = 0,100.3,0.10<\/b><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/sup><\/span> \"\" <\/b><\/span><\/span><\/span>v = 3,0.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>m\/s.<\/b><\/span><\/span><\/span><\/p>\n

O<\/b><\/span><\/span><\/span>bserve que as velocidades no nosso cotidiano s\u00e3o insignificantes em rela\u00e7\u00e3o a <\/b><\/span><\/span><\/span>3.10<\/b><\/span><\/span><\/span>7 <\/b><\/span><\/span><\/sup><\/span>= 30.000.000m\/s.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>quando <\/b><\/span><\/span><\/span>v = 0,600c\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>\u03bb = 1,250c\u00a0 \"\" <\/b><\/span><\/span><\/span> <\/b>\u0394t =<\/b><\/span><\/span><\/span> <\/b>\u03bb.\u0394t<\/b><\/span><\/span><\/span>p <\/b><\/span><\/span><\/sub><\/span>= 1,250.10min\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394t = 12,5 min.<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

02-(UFC-CE)<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>figura ao lado <\/b><\/span><\/span><\/span>mostra uma <\/b><\/span><\/span><\/span>nave espacial em forma de cubo <\/b><\/span><\/span><\/span>que se <\/b><\/span><\/span><\/span>move no referencial S, <\/b><\/span><\/span><\/span>ao <\/b><\/span><\/span><\/span>longo <\/b><\/span><\/span><\/span><\/p>\n

do eixo x, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade v = 0,8c <\/b><\/span><\/span><\/span>(c \u00e9 a velocidade da luz no v\u00e1cuo). <\/b><\/span><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>volume da nave, medido<\/b><\/span><\/span><\/span> por um <\/b><\/span><\/span><\/span>astronauta em repouso dentro dela,<\/b><\/span><\/span><\/span><\/p>\n

\u00e9 V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Calcule o <\/b><\/span><\/span><\/span>volume da nave medido por um observador em repouso no referencial S.<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span><\/span>d for a aresta da nave, <\/b><\/span><\/span><\/span>medida <\/b><\/span><\/span><\/span>pelo astronauta, o volume medido pelo astronauta vale \"\"<\/b><\/span><\/span><\/span> V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> =<\/b><\/span><\/span><\/span><\/p>\n

d.d.d \"\"<\/b><\/span><\/span><\/span> V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> = d<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>observador em repouso no referencial S <\/b><\/span><\/span><\/span>observar\u00e1 uma <\/b><\/span><\/span><\/span>contra\u00e7\u00e3o da aresta da nave apenas na dire\u00e7\u00e3o do eixo x, onde ela se move.<\/b><\/span><\/span><\/span><\/p>\n

Assim,<\/b><\/span><\/span><\/span> <\/b>a<\/b><\/span><\/span><\/span> nova aresta d\u2019\u00a0valer\u00e1 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>d\u2019 = d.\u221a(1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)\u00a0 \"\"<\/b><\/span><\/span><\/span> \u00a0d\u2019 = d.\u221a(1 \u2013 0,64c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>d\u2019 = 0,6d.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>observador em repouso no referencial S <\/b><\/span><\/span><\/span>ver\u00e1 o <\/b><\/span><\/span><\/span>novo volume da nave fornecido<\/b><\/span><\/span><\/span> por \"\"<\/b><\/span><\/span><\/span> V = d.d.d\u2019<\/b><\/span><\/span><\/span><\/p>\n

\"\" V = d.d.0,6d\u00a0 \"\"\u00a0 V = 0,6.d.d.d\u00a0 \"\" \u00a0<\/b><\/span><\/span><\/span>V = 0,6d<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span> = 0,6V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

03-(UPE)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>trem de comprimento igual a 100 m <\/b><\/span><\/span><\/span>viaja a uma <\/b><\/span><\/span><\/span>velocidade de 0,8 c, <\/b><\/span><\/span><\/span>onde <\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/span> \u00e9 a <\/b><\/span><\/span><\/span>velocidade da luz,<\/b><\/span><\/span><\/span> quando <\/b><\/span><\/span><\/span>atravessa<\/b><\/span><\/span><\/span> um t\u00fanel de <\/b><\/span><\/span><\/span>comprimento igual a 70 m<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Quando visto por um observador parado ao lado dos trilhos<\/b><\/span><\/span><\/span>, \u00e9 <\/b><\/span><\/span><\/span>CORRETO afirmar que o trem<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> n\u00e3o chega <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>ficar totalmente dentro do t\u00fanel, <\/b><\/span><\/span><\/span>restando um <\/b><\/span><\/span><\/span>espa\u00e7o de 12 m fora do t\u00fanel.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> fica totalmente dentro do t\u00fanel <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>sobra um espa\u00e7o de 10 m.<\/b><\/span><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/span> fica totalmente dentro do t\u00fanel <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>sobra um espa\u00e7o de 15 m.<\/b><\/span><\/span><\/span><\/p>\n

d)<\/b><\/span><\/span><\/span> n\u00e3o chega a ficar totalmente dentro do t\u00fanel, <\/b><\/span><\/span><\/span>restando um <\/b><\/span><\/span><\/span>espa\u00e7o de 5 m fora do t\u00fanel.<\/b><\/span><\/span><\/span><\/p>\n

e)<\/b><\/span><\/span><\/span> fica totalmente dentro do t\u00fanel<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>n\u00e3o resta nenhum espa\u00e7o.<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

L<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>= 100m\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = 0,8c\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/span> <\/b>=70m\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>para um <\/b><\/span><\/span><\/span>observador em repouso externo ao trem, <\/b><\/span><\/span><\/span>o\u00a0 <\/b><\/span><\/span><\/span>comprimento do trem <\/b><\/span><\/span><\/span>ser\u00e1<\/b><\/span><\/span><\/span> \u00a0\"\"\u00a0<\/b><\/span><\/span><\/span>L=L<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>.\u221a(1 \u2013 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>L=100. \u221a1 \u2013 (0,8c)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>L=100.06\u00a0 \"\"<\/b><\/span><\/span><\/span> <\/b>L=60m. <\/b><\/span><\/span><\/span><\/p>\n

Como o <\/b><\/span><\/span><\/span>comprimento do trem se reduz a 60m, para <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>observador parado ao lado dos trilhos, o trem<\/b><\/span><\/span><\/span><\/p>\n

ficar\u00e1 totalmente no interior do t\u00fanel de 70m sobrando (70 \u2013 60) = 10m. <\/b><\/span><\/span><\/span><\/p>\n

R- B<\/b><\/span><\/span><\/span><\/p>\n

04-(UFG-GO)<\/b><\/span><\/span><\/span> <\/b>Antipart\u00edculas, <\/b><\/span><\/span><\/span>raras na natureza, possuem <\/b><\/span><\/span><\/span>carga el\u00e9trica oposta \u00e0 de suas part\u00edculas<\/b><\/span><\/span><\/span><\/p>\n

correspondentes.<\/b><\/span><\/span><\/span> <\/b>\"\"<\/p>\n

Se <\/b><\/span><\/span><\/span>encontr\u00e1ssemos uma fonte de antipart\u00edculas, <\/b><\/span><\/span><\/span>poder\u00edamos <\/b><\/span><\/span><\/span>produzir<\/b><\/span><\/span><\/span> uma <\/b><\/span><\/span><\/span>grande quantidade de energia, permitindo que elas se aniquilassem<\/b><\/span><\/span><\/span> <\/b>com suas part\u00edculas. <\/b><\/span><\/span><\/span>Dessa forma, <\/b><\/span><\/span><\/span>calcule:<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>a <\/b><\/span><\/span><\/span>quantidade de energia <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>seria liberada se 2,0 gramas de antimat\u00e9ria fossem aniquiladas com 2,0 gramas de sua mat\u00e9ria (considere a velocidade da luz igual a 3,0.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>m\/s);<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>por <\/b><\/span><\/span><\/span>quanto tempo essa energia abasteceria <\/b><\/span><\/span><\/span>uma <\/b><\/span><\/span><\/span>cidade com um milh\u00e3o de habitantes,<\/b><\/span><\/span><\/span><\/p>\n

considerando que <\/b><\/span><\/span><\/span>uma pessoa consome, em m\u00e9dia, 100 kWh por m\u00eas.<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

a) Massas aniquiladas \"\" m =<\/b><\/span><\/span><\/span> (2g + 2g) = 4g <\/b><\/span><\/span><\/span>= 4.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>kg\u00a0 \"\" <\/b><\/span><\/span><\/span>f\u00f3rmula de <\/b><\/span><\/span><\/span>Einstein<\/b><\/span><\/span><\/span> da <\/b><\/span><\/span><\/span>equival\u00eancia entre<\/b><\/span><\/span><\/span> <\/b>massa e energia \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>E = m.c<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sup><\/span>= 4.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>.(3.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>E = 3,6.10<\/b><\/span><\/span><\/span>14<\/b><\/span><\/span><\/sup><\/span>J.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> Energia consumida <\/b><\/span><\/span><\/span>pela cidade de <\/b><\/span><\/span><\/span>um milh\u00e3o de habitantes (10<\/b><\/span><\/span><\/span>6 <\/b><\/span><\/span><\/sup><\/span>habitantes) com pot\u00eancia de P =<\/b><\/span><\/span><\/span><\/p>\n

100×10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span> W \"\" E = n.P.\u0394t = <\/b><\/span><\/span><\/span>10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>x100x10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>x3600 = 36.10<\/b><\/span><\/span><\/span>13<\/b><\/span><\/span><\/sup><\/span> <\/b>= 3,6.10<\/b><\/span><\/span><\/span>14<\/b><\/span><\/span><\/sup><\/span> J<\/b><\/span><\/span><\/span><\/p>\n

R: 1 m\u00eas<\/b><\/span><\/span><\/span><\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span>Postulados da Relatividade Especial\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Velocidade relativa (V<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>para<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>dois corpos deslocando-se em sentidos opostos,<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>velocidades <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>m\u00f3dulo u e v <\/b><\/span><\/span><\/span>em<\/b><\/span><\/span><\/span> <\/b>rela\u00e7\u00e3o a um referencial inercial.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>energia cin\u00e9tica relativ\u00edstica<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>de um corpo corresponde \u00e0 <\/b><\/span><\/span><\/span>diferen\u00e7a entre a energia pr\u00f3pria (E) e a energia do repouso (E<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>)\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=E \u2013 E<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=mc<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>c<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=(m \u2013 m<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).c.<\/b><\/span><\/span><\/span><\/p>\n

Como c \u00e9 constante, se E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>\u00a0diminuir ou aumentar ocorrer\u00e1 uma correspondente diminui\u00e7\u00e3o ou aumento de massa do corpo.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

Pela <\/b><\/span><\/span><\/span>teoria da Relatividade Geral de Einstein,<\/b><\/span><\/span><\/span> quando <\/b><\/span><\/span><\/span>raios de luz <\/b><\/span><\/span><\/span>provenientes de um <\/b><\/span><\/span><\/span>corpo estelar, como estrelas ou gal\u00e1xias, <\/b><\/span><\/span><\/span>passam <\/b><\/span><\/span><\/span>muito pr\u00f3ximos de um objeto estelar de grande densidade de massa, esses raios de luz s\u00e3o desviados <\/b><\/span><\/span><\/span>para um <\/b><\/span><\/span><\/span>ponto de encontro oposto ao lado em que os raios incidem no objeto.<\/b><\/span><\/span><\/span><\/p>\n

Esse <\/b><\/span><\/span><\/span>encurvamento de um raio de luz em sentido oposto ao do corpo \u00e9 explicado pelo mesmo modo que um \u00edndice de refra\u00e7\u00e3o vari\u00e1vel encurva a luz em uma<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Miragem.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Assim, <\/b><\/span><\/span><\/span>por exemplo, <\/b><\/span><\/span><\/span>um <\/b><\/span><\/span><\/span>grupo de gal\u00e1xias de grande massa <\/b><\/span><\/span><\/span>tamb\u00e9m provoca <\/b><\/span><\/span><\/span>uma forte curvatura no espa\u00e7o-tempo, fazendo com que todos os raios luminosos que atravessem a regi\u00e3o sejam curvados, formando uma verdadeira<\/b><\/span><\/span><\/span>\u00a0lente c\u00f3smica<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

<\/h3>\n

\"\"<\/p>\n

Paradoxo dos g\u00eameos<\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Paradoxo,<\/span><\/span> no exemplo abaixo, pode ser definido como<\/span><\/span><\/span> aparente falta de l\u00f3gica.<\/span><\/span><\/h3>\n

O <\/b><\/span><\/span><\/span>paradoxo dos g\u00eameos <\/b><\/span><\/span><\/span>foi um <\/b><\/span><\/span><\/span>experimento mental proposto <\/b><\/span><\/span><\/span>para demonstrar a <\/b><\/span><\/span><\/span>teoria da dilata\u00e7\u00e3o do tempo, atualmente j\u00e1 comprovada experimentalmente.<\/b><\/span><\/span><\/span><\/p>\n

Considere dois irm\u00e3os<\/b><\/span><\/span><\/span> <\/b>g\u00eameos,<\/b><\/span><\/span><\/span> sendo que o <\/b><\/span><\/span><\/span>irm\u00e3o <\/b><\/span><\/span><\/span>g\u00eameo A<\/b><\/span><\/span><\/span> fica na Terra, <\/b><\/span><\/span><\/span>enquanto <\/b><\/span><\/span><\/span>o outro,<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>g\u00eameo B,<\/b><\/span><\/span><\/span> <\/b> utilizando uma <\/b><\/span><\/span><\/span>espa\u00e7onave, faz uma viagem espacial na qual viaja pr\u00f3ximo a velocidade da luz.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Por causa do <\/b><\/span><\/span><\/span>movimento do g\u00eameo B <\/b><\/span><\/span><\/span>(o que viaja pr\u00f3ximo a velocidade da luz) <\/b><\/span><\/span><\/span>seu tempo passa mais devagar dentro da espa\u00e7onave, <\/b><\/span><\/span><\/span>conforme \u00e9 visto pelo irm\u00e3o, <\/b><\/span><\/span><\/span>g\u00eameo A, que ficou na Terra.<\/b><\/span><\/span><\/span><\/p>\n

Quando o <\/b><\/span><\/span><\/span>g\u00eameo B retornar para a Terra verificar\u00e1 que seu irm\u00e3o, o g\u00eameo A, est\u00e1 mais velho.<\/b><\/span><\/span><\/span><\/p>\n

O efeito vale para qualquer pessoa.<\/b><\/span><\/span><\/span><\/p>\n

<\/a><\/p>\n

\"\"<\/p>\n

Se voc\u00ea quiser se aprofundar mais no assunto da Teoria da Relatividade seria aconselh\u00e1vel conferir as resolu\u00e7\u00f5es dos exerc\u00edcios que seleciomei, de n\u00fameros <\/span><\/span><\/span>03, 07,08,15, 17, 18, 26, 30, 36 e 48. <\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00f5es comentadas<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Introdu\u00e7\u00e3o \u00e0 Teoria da Relatividade Breve Hist\u00f3rico Albert Einstein (1879-1955), pelos seus feitos cient\u00edficos que inovaram radicalmente os caminhos tecnol\u00f3gicos da humanidade, colaborou de forma extraordin\u00e1ria para o desenvolvimento da ci\u00eancia, para a qualidade de vida\u00a0 de todos os habitantes do planeta Terra, alterando a vis\u00e3o dos cientistas nas \u00e1reas da f\u00edsica das part\u00edculas, astronomia, astrof\u00edsica, cosmologia, filosofia e outros<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":125,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-2510","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2510","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=2510"}],"version-history":[{"count":4,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2510\/revisions"}],"predecessor-version":[{"id":10726,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2510\/revisions\/10726"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/125"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}