{"id":4887,"date":"2020-01-10T03:14:29","date_gmt":"2020-01-10T03:14:29","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=4887"},"modified":"2024-09-04T14:45:29","modified_gmt":"2024-09-04T14:45:29","slug":"resolucao-comentada-gravitacao-universal-2018-2019","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/vestibulares-recentes\/mecanica\/gravitacao-2018-2019\/resolucao-comentada-gravitacao-universal-2018-2019\/","title":{"rendered":"Resolu\u00e7\u00e3o Comentada \u2013 Gravita\u00e7\u00e3o Universal \u2013 2018-2019"},"content":{"rendered":"

Resolu\u00e7\u00e3o Comentada \u2013 Gravita\u00e7\u00e3o Universal \u2013 2018-2019<\/span><\/span><\/span><\/p>\n

01-<\/span><\/span><\/span><\/p>\n

Se voc\u00ea\u00a0<\/b><\/span><\/span><\/span>n\u00e3o domina o assunto\u00a0<\/b><\/span><\/span><\/span>veja a seguir a teoria sobre\u00a0<\/b><\/span><\/span><\/span>gravidade artificial por rota\u00e7\u00e3o\u00a0<\/b><\/span><\/span><\/span>que poder\u00e1 ser \u00fatil no futuro.<\/b><\/span><\/span><\/span><\/p>\n

Gravidade artificial por rota\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span><\/span>nave pode ser constitu\u00edda<\/b><\/span><\/span><\/span>\u00a0de modo que\u00a0<\/b><\/span><\/span><\/span>origine um sistema que forne\u00e7a um ambiente de formato circular que esteja constantemente\u00a0<\/b><\/span><\/span><\/span>em\u00a0<\/b><\/span><\/span><\/span>movimento de rota\u00e7\u00e3o,\u00a0<\/b><\/span><\/span><\/span>girando com\u00a0<\/b><\/span><\/span><\/span>velocidade angular constante em torno de um\u00a0<\/b><\/span><\/span><\/span>ponto (eixo central)\u00a0<\/b><\/span><\/span><\/span>fixo.<\/b><\/span><\/span><\/span><\/p>\n

Pode ter a\u00a0<\/b><\/span><\/span><\/span>forma de forma de um cilindro (figura 1), um anel (figura 2) ou outra qualquer\u00a0<\/b><\/span><\/span><\/span>desde que<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

constitua uma estrutura\u00a0comprida\u00a0<\/b><\/span><\/span><\/span>que\u00a0<\/b><\/span><\/span><\/span>gire em torno de um ponto ou eixo fixo,\u00a0<\/b><\/span><\/span><\/span>numa r<\/b><\/span><\/span><\/span>ota\u00e7\u00e3o constante,<\/b><\/span><\/span><\/span>\u00a0de modo a\u00a0<\/b><\/span><\/span><\/span>simular a gravidade em sua superf\u00edcie interna\u00a0<\/b><\/span><\/span><\/span>gra\u00e7as \u00e0\u00a0<\/b><\/span><\/span><\/span>acelera\u00e7\u00e3o centr\u00edpeta\u00a0<\/b><\/span><\/span><\/span>gerada por esse\u00a0<\/b><\/span><\/span><\/span>movimento circular,\u00a0<\/b><\/span><\/span><\/span>fazendo com que os\u00a0<\/b><\/span><\/span><\/span>astronautas fiquem de p\u00e9 no ch\u00e3o da nave, como se estivessem na Terra.<\/b><\/span><\/span><\/span><\/p>\n

Essa\u00a0<\/b><\/span><\/span><\/span>simula\u00e7\u00e3o da \u201cgravidade\u201d<\/b><\/span><\/span><\/span>\u00a0ocorre, pois\u00a0<\/b><\/span><\/span><\/span>todo corpo em movimento circular tende a se afastar do centro e, no caso, \u201ccolando\u201d nas paredes internas do cilindro (nave).<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

O\u00a0<\/b><\/span><\/span><\/span>\u201cpeso aparente\u201d do astronauta\u00a0\u00e9 percebido rea\u00e7\u00e3o normal\u00a0N\u00a0<\/b><\/span><\/span><\/span>das\u00a0<\/b><\/span><\/span><\/span>paredes da nave sobre ele,\u00a0<\/b><\/span><\/span><\/span>que \u00e9 a\u00a0<\/b><\/span><\/span><\/span>pr\u00f3pria for\u00e7a resultante centr\u00edpeta de intensidade N = Fc= m.W2R,\u00a0<\/b><\/span><\/span><\/span>que deve ser\u00a0<\/b><\/span><\/span><\/span>igual ao\u00a0peso P do astronauta na Terra\u00a0onde g = 10m\/s2.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

Observe ainda que\u00a0<\/b><\/span><\/span><\/span>sendo a velocidade angular W de rota\u00e7\u00e3o da nave constante<\/b><\/span><\/span><\/span>, a \u201cgravidade artificial\u00a0<\/b><\/span><\/span><\/span>g<\/b><\/span><\/span><\/span>\u201d \u00e9\u00a0<\/b><\/span><\/span><\/span>diretamente proporcional ao raio R,\u00a0<\/b><\/span><\/span><\/span>ou seja,\u00a0<\/b><\/span><\/span><\/span>\u00e0 medida que o tripulante vai se aproximando do centro do sistema rotat\u00f3rio, o raio R vai diminuindo o que provoca tamb\u00e9m uma diminui\u00e7\u00e3o da (gravidade artificial\u201d.<\/b><\/span><\/span><\/span><\/p>\n

Assim, no\u00a0<\/b><\/span><\/span><\/span>centro do sistema<\/b><\/span><\/span><\/span>\u00a0a \u201cgravidade artificial\u00a0<\/b><\/span><\/span><\/span>g\u201d \u00e9 zero\u00a0<\/b><\/span><\/span><\/span>e\u00a0<\/b><\/span><\/span><\/span>a\u00ed<\/b><\/span><\/span><\/span>\u00a0o tripulante\u00a0<\/b><\/span><\/span><\/span>flutua.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

02-<\/span><\/span><\/span><\/p>\n

(A) Falsa\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>N\u00e3o respeitam\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Quando as\u00a0<\/b><\/span><\/span><\/span>naves aceleram \u00e0 velocidade de dobra\u00a0<\/b><\/span><\/span><\/span>de forma quase\u00a0<\/b><\/span><\/span><\/span>instant\u00e2nea, est\u00e1 sendo contrariada a lei da conserva\u00e7\u00e3o da energia mec\u00e2nica\u00a0<\/b><\/span><\/span><\/span>que afirma que a\u00a0<\/b><\/span><\/span><\/span>energia se conserva, n\u00e3o pode ser criada nem destru\u00edda.\u00a0<\/b><\/span><\/span><\/span>De\u00a0<\/b><\/span><\/span><\/span>onde surgiu\u00a0<\/b><\/span><\/span><\/span>a\u00a0<\/b><\/span><\/span><\/span>energia\u00a0<\/b><\/span><\/span><\/span>que\u00a0<\/b><\/span><\/span><\/span>impulsionou a nave?<\/b><\/span><\/span><\/span><\/p>\n

Al\u00e9m disso, quando as\u00a0<\/b><\/span><\/span><\/span>naves aceleram instantaneamente\u00a0<\/b><\/span><\/span><\/span>com velocidades espantosas a f\u00edsica diz que\u00a0<\/b><\/span><\/span><\/span>a nave e a tripula\u00e7\u00e3o deveriam virar p\u00f3, devido \u00e0s implica\u00e7\u00f5es da in\u00e9rcia (1\u00aa Lei de Newton).\u00a0<\/b><\/span><\/span><\/span>\u201c<\/b><\/span><\/span><\/span>todo objeto que estiver parado tende a ficar parado e objetos que est\u00e3o em movimento tendem a continuar em movimento<\/b><\/i><\/span><\/span><\/span>\u201d.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Estando os\u00a0<\/b><\/span><\/span><\/span>tripulantes parados na nave\u00a0<\/b><\/span><\/span><\/span>e esta iria se mover com uma\u00a0<\/b><\/span><\/span><\/span>velocidade muito alta,\u00a0<\/b><\/span><\/span><\/span>seus\u00a0<\/b><\/span><\/span><\/span>corpos tenderiam a ficar parados\u00a0<\/b><\/span><\/span><\/span>e, assim, seriam\u00a0<\/b><\/span><\/span><\/span>arremessados para o fundo da nave e esmagados pela in\u00e9rcia.<\/b><\/span><\/span><\/span><\/p>\n

O\u00a0<\/b><\/span><\/span><\/span>mesmo ocorreria\u00a0<\/b><\/span><\/span><\/span>se estivessem em\u00a0<\/b><\/span><\/span><\/span>movimento com velocidades muito altas\u00a0<\/b><\/span><\/span><\/span>com a\u00a0<\/b><\/span><\/span><\/span>nave freando\u00a0<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/span>nstantaneamente<\/b><\/span><\/span><\/span>\u00a0e, assim, eles seriam\u00a0<\/b><\/span><\/span><\/span>arremessados para a frente da nave e esmagados pela in\u00e9rcia.<\/b><\/span><\/span><\/span><\/p>\n

(B) Falsa\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>N\u00e3o respeitam\u00a0<\/b><\/span><\/span><\/span>\u00a0Quando as naves se\u00a0<\/b><\/span><\/span><\/span>movimentam pelo espa\u00e7o,\u00a0ouvimos o som\u00a0gerado por seus motores, o que contradiz o fato de que o som n\u00e3o se propaga no v\u00e1cuo. O mesmo corre com as explos\u00f5es, tiros, etc.<\/b><\/span><\/span><\/span><\/p>\n

Quando\u00a0<\/b><\/span><\/span><\/span>armas\u00a0<\/b><\/span><\/span><\/span>s\u00e3o\u00a0<\/b><\/span><\/span><\/span>disparadas<\/b><\/span><\/span><\/span>\u00a0podemos\u00a0<\/b><\/span><\/span><\/span>acompanhar o\u00a0percurso\u00a0dos tiros<\/b><\/span><\/span><\/span>, sejam dos\u00a0<\/b><\/span><\/span><\/span>phasers<\/b><\/i><\/span><\/span><\/span>\u00a0de m\u00e3o da tripula\u00e7\u00e3o, sejam das naves (que inclusive disparam torpedos \u201cfot\u00f4nicos\u201d).<\/b><\/span><\/span><\/span><\/p>\n

A f\u00edsica diz que n\u00e3o conseguir\u00edamos acompanhar visualmente os \u2018proj\u00e9teis\u2019 luminosos<\/b><\/span><\/span><\/span><\/p>\n

(C) Falsa\u00a0\u00a0n\u00e3o desrespeitam<\/b><\/span><\/span><\/span>, pois se\u00a0<\/b><\/span><\/span><\/span>desrespeitassem os tripulantes ficariam flutuando\u00a0<\/b><\/span><\/span><\/span>no\u00a0<\/b><\/span><\/span><\/span>interior das naves<\/b><\/span><\/span><\/span>\u00a0o que n\u00e3o acontece, pois de\u00a0<\/b><\/span><\/span><\/span>alguma maneira no interior da nave existe gravidade artificial.<\/b><\/span><\/span><\/span><\/p>\n

(D) Correta\u00a0\u00a0desrespeitam,\u00a0<\/b><\/span><\/span><\/span>pois a\u00a0<\/b><\/span><\/span><\/span>maioria das naves tem formatos aerodin\u00e2micos diferentes independente da regi\u00e3o do espa\u00e7o onde se encontram.<\/b><\/span><\/span><\/span><\/p>\n

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

03-<\/span><\/span><\/span><\/p>\n

Se voc\u00ea n\u00e3o domina a teoria ela est\u00e1 a seguir:<\/b><\/span><\/span><\/span><\/p>\n

Velocidade orbital (de transla\u00e7\u00e3o) de um sat\u00e9lite<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

04-<\/b><\/span><\/span><\/span><\/p>\n

Sat\u00e9lites geoestacion\u00e1rios\u00a0 ou geosincr\u00f4nicos\u00a0<\/b><\/span><\/span><\/span><\/span>(sincronizados com o movimento de\u00a0<\/b><\/span><\/span><\/span><\/span>rota\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/span>\u00a0da Terra).<\/b><\/span><\/span><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span><\/span><\/span>maioria dos sat\u00e9lites de telecomunica\u00e7\u00f5es<\/b><\/span><\/span><\/span><\/span>\u00a0s\u00e3o\u00a0<\/b><\/span><\/span><\/span><\/span>sat\u00e9lites geoestacion\u00e1rios,<\/b><\/span><\/span><\/span><\/span>\u00a0pois se encontram\u00a0<\/b><\/span><\/span><\/span><\/span>parados em rela\u00e7\u00e3o a um ponto fixo sobre a Terra.<\/b><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

Seu\u00a0<\/b><\/span><\/span><\/span><\/span>per\u00edodo T \u00e9 o mesmo que o da Terra (24h)<\/b><\/span><\/span><\/span><\/span>,\u00a0o raio de sua \u00f3rbita \u00e9 de, aproximadamente 36000 km,\u00a0<\/b><\/span><\/span><\/span><\/span>tem a mesma velocidade angular (W) que a Terra<\/b><\/span><\/span><\/span><\/span>\u00a0e se encontram em \u00f3rbitas sobre a linha do equador.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

Acima da altura\u00a0<\/b><\/span><\/span><\/span>aproximada de 36000 km o\u00a0<\/b><\/span><\/span><\/span>per\u00edodo do sat\u00e9lite aumenta<\/b><\/span><\/span><\/span>\u00a0e\u00a0<\/b><\/span><\/span><\/span>abaixo desse valor, diminui.<\/b><\/span><\/span><\/span><\/p>\n

Sua\u00a0<\/b><\/span><\/span><\/span>velocidade escalar\u00a0<\/b><\/span><\/span><\/span>\u00e9 fornecida\u00a0<\/b><\/span><\/span><\/span>por V = 2\u03c0R\/T<\/b><\/span><\/span><\/span>, que\u00a0<\/b><\/span><\/span><\/span>n\u00e3o depende de sua m<\/b><\/span><\/span><\/span>assa e que, quanto\u00a0<\/b><\/span><\/span><\/span>mais afastado da Terra maior ser\u00e1 sua velocidade escalar.<\/b><\/span><\/span><\/span><\/p>\n

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

05-<\/span><\/span><\/span><\/p>\n

Segunda lei de Kepler (lei das \u00e1reas)<\/b><\/span><\/span><\/span><\/p>\n

\u201c\u00a0O\u00a0<\/b><\/span><\/span><\/span>segmento de reta imagin\u00e1rio<\/b><\/span><\/span><\/span>\u00a0que une o\u00a0<\/b><\/span><\/span><\/span>centro do Sol ao centro do planeta varre \u00e1reas iguais em per\u00edodos de tempo iguais\u201d\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

A figura abaixo representa um\u00a0<\/b><\/span><\/span><\/span>planeta em \u00f3rbita el\u00edptica ao redor do Sol.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

06-<\/span><\/span><\/span><\/p>\n

<\/p>\n

07- <\/span><\/span><\/span><\/p>\n

<\/p>\n

08-<\/span><\/span><\/span><\/p>\n

Express\u00e3o matem\u00e1tica da acelera\u00e7\u00e3o da gravidade<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

09-<\/b><\/span><\/span><\/span><\/p>\n

Observe que\u00a0<\/b><\/span><\/span><\/span>se trata de um movimento harm\u00f4nico simples (MHS), pois a gravidade exerce uma for\u00e7a restauradora a partir do centro de massa da esfera<\/b><\/span><\/span><\/span>, com isso o objeto pontual fica indo e voltando para os polos. No caso,\u00a0<\/b><\/span><\/span><\/span>a for\u00e7a das massas externas \u00e0 esfera n\u00e3o faz diferen\u00e7a<\/b><\/span><\/span><\/span>, por conta da Lei de Gauss aplicada para a gravita\u00e7\u00e3o. Dessa forma temos que\u00a0<\/b><\/span><\/span><\/span>a for\u00e7a gravitacional deve ser igual \u00e0 centr\u00edpeta,\u00a0<\/b><\/span><\/span><\/span>mas nesse caso n\u00e3o se trata de um movimento circular, e sim uma for\u00e7a que tenta manter o objeto no centro da esfera:<\/b><\/span><\/span><\/span><\/p>\n

FG\u00a0= FC<\/b><\/span><\/span><\/span><\/p>\n

Para a for\u00e7a gravitacional temos:<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

Considere d como o raio R da Terra.<\/b><\/span><\/span><\/span><\/p>\n

Para a centr\u00edpeta:<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

10-<\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

A alternativa correta \u00e9 a B.<\/b><\/span><\/span><\/span><\/p>\n

11-<\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

Logo, a\u00a0<\/b><\/span><\/span><\/span>alternativa correta \u00e9 a E<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

12-<\/span><\/span><\/span><\/p>\n

Observe atentamente o gr\u00e1fico:<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

R- E<\/b><\/span><\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Resolu\u00e7\u00e3o Comentada \u2013 Gravita\u00e7\u00e3o Universal \u2013 2018-2019 01- Se voc\u00ea\u00a0n\u00e3o domina o assunto\u00a0veja a seguir a teoria sobre\u00a0gravidade artificial por rota\u00e7\u00e3o\u00a0que poder\u00e1 ser \u00fatil no futuro. Gravidade artificial por rota\u00e7\u00e3o A\u00a0nave pode ser constitu\u00edda\u00a0de modo que\u00a0origine um sistema que forne\u00e7a um ambiente de formato circular que esteja constantemente\u00a0em\u00a0movimento de rota\u00e7\u00e3o,\u00a0girando com\u00a0velocidade angular constante em torno de um\u00a0ponto (eixo central)\u00a0fixo. Pode<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4885,"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-4887","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4887","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=4887"}],"version-history":[{"count":1,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4887\/revisions"}],"predecessor-version":[{"id":4888,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4887\/revisions\/4888"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4885"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=4887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}