{"id":1435,"date":"2015-10-13T03:35:24","date_gmt":"2015-10-13T03:35:24","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1435"},"modified":"2024-08-23T14:20:22","modified_gmt":"2024-08-23T14:20:22","slug":"exercicios-de-vestibulares-com-resolucao-comentada-sobre-a-lei-da-gravitacao-universal-de-newton","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/mecanica\/gravitacao\/lei-da-gravitacao-universal-de-newton\/exercicios-de-vestibulares-com-resolucao-comentada-sobre-a-lei-da-gravitacao-universal-de-newton\/","title":{"rendered":"Lei da Gravita\u00e7\u00e3o Universal de Newton – Resolu\u00e7\u00e3o"},"content":{"rendered":"

Exerc\u00edcios de vestibulares com resolu\u00e7\u00e3o comentada sobre a<\/b><\/span><\/span><\/span><\/p>\n

lei da Gravita\u00e7\u00e3o Universal de Newton<\/b><\/span><\/span><\/span><\/p>\n

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

01-(UFMG)<\/b><\/span><\/span><\/span> Tr\u00eas sat\u00e9lites \u2013<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>I,<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>II<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>III<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u2013 movem-se em \u00f3rbitas circulares ao redor da Terra.<\/b><\/span><\/span><\/span><\/p>\n

O sat\u00e9lite<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>I<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>tem massa<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>e os sat\u00e9lites<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>II<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>III<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>t\u00eam, cada um, massa 2<\/b><\/span><\/span><\/span>m<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Os sat\u00e9lites<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>I<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>II<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>est\u00e3o em uma mesma \u00f3rbita de raio<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>r<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>e o raio da \u00f3rbita do sat\u00e9lite<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>III<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00e9 r\/2.<\/b><\/span><\/span><\/span><\/p>\n

:Sejam<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>I<\/b><\/i><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>, F<\/b><\/i><\/span><\/span><\/span>II<\/b><\/i><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>e F<\/b><\/i><\/span><\/span><\/span>III<\/b><\/i><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>m\u00f3dulos das for\u00e7as gravitacionais da Terra sobre, respectivamente, os sat\u00e9lites<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>I,<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>II<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>III<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Considerando-se essas informa\u00e7\u00f5es, \u00e9<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>CORRETO<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>afirmar que<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>=<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>II<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span><<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>III<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

B)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>=<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>II<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>><\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>III<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

C)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span><<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>II<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span><<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>III<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

D)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span><<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>II<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>=<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/i><\/span><\/span><\/span>III<\/b><\/span><\/span><\/sub><\/span><\/p>\n

E) F<\/b><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>=F<\/b><\/span><\/span><\/span>II<\/b><\/span><\/span><\/sub><\/span>=F<\/b><\/span><\/span><\/span>III<\/b><\/span><\/span><\/sub><\/span><\/p>\n

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

02-(PUC-SP)<\/b><\/span><\/span><\/span> A intensidade da for\u00e7a gravitacional com que a Terra atrai a Lua \u00e9 F. Se fossem duplicadas a massa da Terra e da Lua e se a dist\u00e2ncia que as separa fosse reduzida \u00e0 metade, a nova for\u00e7a seria:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

03-(FUVEST-SP)<\/b><\/span><\/span><\/span> No sistema solar, o planeta Saturno tem massa\u00a0 cerca de 100 vezes maior do que a da Terra e descreve uma \u00f3rbita, em torno do Sol, a uma dist\u00e2ncia m\u00e9dia 10 vezes maior do que a dist\u00e2ncia m\u00e9dia da Terra ao Sol (valores aproximados). A raz\u00e3o F<\/b><\/span><\/span><\/span>Sat<\/b><\/span><\/span><\/sub><\/span>\/F<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>entre a for\u00e7a gravitacional com que o Sol atrai saturno e a for\u00e7a gravitacional com que o Sol atrai a Terra \u00e9 de aproximadamente:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

04-(FUVEST-SP)<\/b><\/span><\/span><\/span> A raz\u00e3o entre\u00a0 as massas de um planeta e de um sat\u00e9lite \u00e9 81. Um foguete est\u00e1 a uma dist\u00e2ncia R do planeta e a uma dist\u00e2ncia r do sat\u00e9lite. Qual deve ser o valor da raz\u00e3o R\/r para que as duas for\u00e7as de atra\u00e7\u00e3o sobre o foguete se equilibrem?<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

05-(UF-PB)<\/b><\/span><\/span><\/span> A lei da Gravita\u00e7\u00e3o Universal de Newton expressa como a for\u00e7a\u00a0 de atra\u00e7\u00e3o entre dois corpos, de massas m e M, varia com a dist\u00e2ncia d entre eles. Considere um planeta de massa 8,1.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>kg em \u00f3rbita el\u00edptica em torno de seu sol. Considere que a dist\u00e2ncia entre o Sol e o ponto de m\u00e1xima aproxima\u00e7\u00e3o (peri\u00e9lio) seja d<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>=0,9.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>m e que a dist\u00e2ncia entre o Sol e o ponto de m\u00e1ximo afastamento (af\u00e9lio) seja d<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span>=1,0.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>m. No peri\u00e9lio, a for\u00e7a de atra\u00e7\u00e3o entre o Sol e o planeta \u00e9 de 1,4.10<\/b><\/span><\/span><\/span>23<\/b><\/span><\/span><\/sup><\/span>N.<\/b><\/span><\/span><\/span><\/p>\n

a) Desenhe, no\u00a0 seu caderno, a figura que mostra a trajet\u00f3ria do planeta em torno do Sol, e indique a(s) for\u00e7a(s) que atua(m) sobre o planeta quando ele se encontra no af\u00e9lio.<\/b><\/span><\/span><\/span><\/p>\n

b) Determine a massa do Sol em torno do qual gira o planeta.<\/b><\/span><\/span><\/span><\/p>\n

c)Determine a for\u00e7a de atra\u00e7\u00e3o entre o Sol e o planeta, quando este se encontra no af\u00e9lio.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Considere G=7,0.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>Nm<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/kg<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span><\/p>\n

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

06-(UNICAMP-SP)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observa\u00e7\u00f5es astron\u00f4micas indicam que as velocidades de rota\u00e7\u00e3o das estrelas em torno de gal\u00e1xias s\u00e3o incompat\u00edveis com a distribui\u00e7\u00e3o de massa vis\u00edvel das gal\u00e1xias, sugerindo que grande parte da mat\u00e9ria do Universo \u00e9 escura, isto \u00e9, mat\u00e9ria que n\u00e3o interage com a luz. O movimento de rota\u00e7\u00e3o das estrelas resulta da for\u00e7a de atra\u00e7\u00e3o gravitacional que as gal\u00e1xias exercem sobre elas.<\/b><\/span><\/span><\/span><\/p>\n

A curva no gr\u00e1fico abaixo mostra como a for\u00e7a gravitacional<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>F=<\/b><\/i><\/span><\/span><\/span>GMm\/r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>que uma gal\u00e1xia de massa<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>M<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>exerce sobre uma estrela externa \u00e0 gal\u00e1xia, deve variar em fun\u00e7\u00e3o da dist\u00e2ncia<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>r<\/b><\/i><\/span><\/span><\/span>da estrela em rela\u00e7\u00e3o ao centro da gal\u00e1xia, considerando-se<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/i><\/span><\/span><\/span>=1,0.10<\/b><\/span><\/span><\/span>30<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>kg<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>para a massa da estrela. A constante de gravita\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>G<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>vale<\/b><\/span><\/span><\/span><\/p>\n

10<\/b><\/span><\/span><\/span>\uf020<\/b><\/span><\/span><\/span>6,7.<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.F\/kg<\/b><\/span><\/span><\/span>-2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Determine a massa<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>M<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>da gal\u00e1xia.<\/b><\/span><\/span><\/span><\/p>\n

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

07-(ITA-SP)<\/b><\/span><\/span><\/span> Sabe-se que a atra\u00e7\u00e3o gravitacional da Lua sobre a camada de \u00e1gua \u00e9 a principal respons\u00e1vel pelo aparecimento das mar\u00e9s oce\u00e2nicas na Terra.\u00a0 Considere as seguintes afirmativas:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

I. As massa de \u00e1gua pr\u00f3ximas das regi\u00f5es A e B experimentam mar\u00e9s altas simultaneamente.<\/b><\/span><\/span><\/span><\/p>\n

II. As massas de \u00e1gua pr\u00f3ximas das regi\u00f5es A e B experimentam mar\u00e9s opostas, isto \u00e9, quando A tem mar\u00e9 alta, B tem mar\u00e9 baixa e vice-versa.<\/b><\/span><\/span><\/span><\/p>\n

III. Durante o intervalo de tempo de um dia ocorrem duas mar\u00e9s altas e duas mar\u00e9s baixas.<\/b><\/span><\/span><\/span><\/p>\n

Ent\u00e3o, est\u00e1(r\u00e3o) correta(s), apenas:<\/b><\/span><\/span><\/span><\/p>\n

a) a afirmativa I\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) a afirmativa II\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c) a afirmativa III\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) as afirmativas I e II\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e) as afirmativas I e III<\/b><\/span><\/span><\/span><\/p>\n

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

08-(UDESC-SC)<\/b><\/span><\/span><\/span>\u00a0 A mar\u00e9 \u00e9 o fen\u00f4meno natural de subida e descida do n\u00edvel das \u00e1guas, percebido principalmente nos oceanos, causado pela atra\u00e7\u00e3o gravitacional do Sol e da Lua. A ilustra\u00e7\u00e3o a seguir esquematiza a varia\u00e7\u00e3o do n\u00edvel das \u00e1guas ao longo de<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

uma rota\u00e7\u00e3o completa da Terra. Considere as seguintes proposi\u00e7\u00f5es sobre mar\u00e9, e assinale a alternativa incorreta.<\/b><\/span><\/span><\/span><\/p>\n

a) As mar\u00e9s de maior amplitude ocorrem pr\u00f3ximo das situa\u00e7\u00f5es de Lua Nova ou Lua Cheia, quando as for\u00e7as atrativas, devido ao Sol e \u00e0 Lua, se refor\u00e7am mutuamente.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) A influ\u00eancia da Lua \u00e9 maior do que a do Sol, pois, embora a sua massa seja muito menor do que a do Sol, esse fato \u00e9 compensado pela menor dist\u00e2ncia \u00e0 Terra.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c) A mar\u00e9 cheia \u00e9 vista por um observador quando a Lua passa por cima dele, ou quando a Lua passa por baixo dele.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) As massas de \u00e1gua que est\u00e3o mais pr\u00f3ximas da Lua ou do Sol sofrem atra\u00e7\u00e3o maior do que as massas de \u00e1gua que est\u00e3o mais afastadas, devido \u00e0 rota\u00e7\u00e3o da Terra.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e) As mar\u00e9s alta e baixa sucedem-se em intervalos de aproximadamente 6 horas.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

09-(CFT-SC)\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Sobre a trajet\u00f3ria el\u00edptica realizada pela Terra em torno do Sol, conforme ilustra\u00e7\u00e3o acima, \u00e9 correto afirmar que:<\/b><\/span><\/span><\/span><\/p>\n

a) a for\u00e7a pela qual a Terra atrai o Sol tem o mesmo m\u00f3dulo da for\u00e7a pela qual o Sol atrai a Terra.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) o sistema mostrado na figura representa o modelo geoc\u00eantrico.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c) o per\u00edodo de evolu\u00e7\u00e3o da Terra em torno do Sol \u00e9 de aproximadamente 24 horas.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) a velocidade de \u00f3rbita da Terra no ponto A \u00e9 maior do que no ponto C.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e) a velocidade de \u00f3rbita do planeta Terra independe da sua posi\u00e7\u00e3o em rela\u00e7\u00e3o ao Sol.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

10-(UFF-RJ)<\/b><\/span><\/span><\/span> Antoine de Saint-Exup\u00e9ry gostaria de ter come\u00e7ado a hist\u00f3ria do Pequeno Pr\u00edncipe dizendo:<\/b><\/span><\/span><\/span><\/p>\n

\u201cEra uma vez um pequeno pr\u00edncipe que habitava um planeta pouco maior que ele, e que tinha necessidade de um amigo \u2026\u201d<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Considerando que o raio m\u00e9dio da Terra \u00e9 um milh\u00e3o de vezes o raio m\u00e9dio do planeta do Pequeno Pr\u00edncipe, assinale a op\u00e7\u00e3o que indica a raz\u00e3o entre a densidade do planeta do Pequeno Pr\u00edncipe, \u03c1<\/b><\/span><\/span><\/span>P<\/b><\/span><\/span><\/sub><\/span>, e a densidade da Terra, \u03c1<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>, de modo que as acelera\u00e7\u00f5es da gravidade nas superf\u00edcies dos dois planetas sejam iguais.<\/b><\/span><\/span><\/span><\/p>\n

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

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

\u00a0<\/span>11-(UFV-MG)<\/b><\/span><\/span><\/span>\u00a0 Seja F o m\u00f3dulo da for\u00e7a da gravidade que o Sol faz sobre um cometa, de massa<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

constante, cujo per\u00edodo orbital \u00e9 T (em anos). Dos gr\u00e1ficos adiante, aquele que representa CORRETAMENTE a varia\u00e7\u00e3o de F com o tempo t \u00e9:<\/b><\/span><\/span><\/span><\/p>\n

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

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

12-(UFPR-PR)<\/b><\/span><\/span><\/span> Neste ano, comemoram-se os 400 anos das primeiras descobertas astron\u00f4micas com a utiliza\u00e7\u00e3o de um telesc\u00f3pio, realizadas pelo cientista italiano Galileu Galilei. Al\u00e9m de revelar ao mundo que a Lua tem montanhas e crateras e que o Sol possui manchas, ele tamb\u00e9m foi o primeiro a<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0apontar um telesc\u00f3pio para o planeta J\u00fapiter e observar os seus quatro maiores sat\u00e9lites, posteriormente denominados de Io, Europa, Ganimedes e Calisto.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Supondo que as \u00f3rbitas desses sat\u00e9lites ao redor de J\u00fapiter sejam circulares, e com base nas informa\u00e7\u00f5es da tabela acima, assinale a alternativa correta. (Os valores da tabela foram arredondados por conveni\u00eancia)<\/b><\/span><\/span><\/span><\/p>\n

a) A for\u00e7a de atra\u00e7\u00e3o entre J\u00fapiter e Ganimedes \u00e9 maior do que entre J\u00fapiter e Io.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) Quanto maior a massa de um sat\u00e9lite, maior ser\u00e1 o seu per\u00edodo orbital.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c) A circunfer\u00eancia descrita pelo sat\u00e9lite Calisto \u00e9 quatro vezes maior que a circunfer\u00eancia descrita pelo sat\u00e9lite Europa.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) A maior velocidade angular \u00e9 a do sat\u00e9lite Calisto, por possuir maior per\u00edodo orbital.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e) O per\u00edodo orbital de Europa \u00e9 aproximadamente o dobro do per\u00edodo orbital de Io.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

13-(ETEC-SP)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A ma\u00e7\u00e3, alimento t\u00e3o apreciado, faz parte de uma famosa lenda ligada \u00e0 biografia de Sir Isaac<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Newton. Ele, j\u00e1 tendo em mente suas Leis do Movimento, teria elaborado a Lei da Gravita\u00e7\u00e3o Universal no momento em que, segundo a lenda, estando Newton ao p\u00e9 de uma macieira, uma ma\u00e7\u00e3 lhe teria ca\u00eddo sobre sua cabe\u00e7a.<\/b><\/span><\/span><\/span><\/p>\n

Pensando nisso, analise as afirma\u00e7\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

I. Uma\u00a0 ma\u00e7\u00e3\u00a0 pendurada\u00a0 em\u00a0 seu\u00a0 galho\u00a0 permanece\u00a0 em repouso,\u00a0 enquanto\u00a0 duas\u00a0 for\u00e7as de mesma intensidade, o seu peso e a for\u00e7a de tra\u00e7\u00e3o do cabinho que a prende ao galho, atuam na mesma dire\u00e7\u00e3o e em sentidos opostos, gerando sobre a ma\u00e7\u00e3 uma for\u00e7a resultante de intensidade nula.<\/b><\/span><\/span><\/span><\/p>\n

II. Uma ma\u00e7\u00e3 em queda cai mais r\u00e1pido quanto maior for a sua massa j\u00e1 que a for\u00e7a resultante, nesse caso chamada de peso da ma\u00e7\u00e3, \u00e9 calculada pelo produto de sua massa pela acelera\u00e7\u00e3o da gravidade.<\/b><\/span><\/span><\/span><\/p>\n

III. A ma\u00e7\u00e3 em queda sofre uma a\u00e7\u00e3o do planeta Terra, denominada for\u00e7a peso, que tem dire\u00e7\u00e3o vertical e o sentido para baixo, e a ma\u00e7\u00e3, por sua vez, atrai a Terra com uma for\u00e7a de mesma intensidade e dire\u00e7\u00e3o,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 contudo o sentido \u00e9 para cima.<\/b><\/span><\/span><\/span><\/p>\n

\u00c9 correto o que se afirma em<\/b><\/span><\/span><\/span><\/p>\n

(A) I, apenas.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

(B) II, apenas.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

(C) I e III, apenas.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

(D) II e III, apenas.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

(E) I, II e III.<\/b><\/span><\/span><\/span><\/p>\n

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

14-(UERJ-RJ)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Na tirinha abaixo, o di\u00e1logo entre a ma\u00e7\u00e3, a bola e a Lua, que est\u00e3o sob a a\u00e7\u00e3o da Terra, faz alus\u00e3o a uma lei da F\u00edsica.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Aponte a constante f\u00edsica introduzida por essa lei.<\/b><\/span><\/span><\/span><\/p>\n

Indique a raz\u00e3o entre os valores dessa constante f\u00edsica para a intera\u00e7\u00e3o gravitacional Lua-Terra e para a intera\u00e7\u00e3o ma\u00e7\u00e3-Terra<\/b><\/span><\/span><\/span><\/p>\n

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

\u00a0<\/span>15-(UNICAMP-SP)<\/b><\/span><\/span><\/span><\/p>\n

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

Em setembro de 2010, J\u00fapiter atingiu a menor dist\u00e2ncia da Terra em muitos anos. As figuras abaixo<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0ilustram a situa\u00e7\u00e3o de maior afastamento e a de maior aproxima\u00e7\u00e3o dos planetas, considerando que suas \u00f3rbitas s\u00e3o circulares, que o raio da \u00f3rbita terrestre (R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>) mede 1,5.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>m e que o raio da \u00f3rbita de J\u00fapiter (R<\/b><\/span><\/span><\/span>J<\/b><\/span><\/span><\/sub><\/span>) equivale a 7,5.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>m.<\/b><\/span><\/span><\/span><\/p>\n

A for\u00e7a gravitacional entre dois corpos de massas\u00a0 m<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>e\u00a0 m<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>tem m\u00f3dulo F<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>= G.m<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.m<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>, em que\u00a0 r \u00e9 a dist\u00e2ncia entre eles e G=6,7.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>N.m<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/kg<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>. Sabendo que a massa de J\u00fapiter \u00e9 m<\/b><\/span><\/span><\/span>J<\/b><\/span><\/span><\/sub><\/span>=2,0.10<\/b><\/span><\/span><\/span>27<\/b><\/span><\/span><\/sup><\/span>kg e que a massa da Terra \u00e9 m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=6,0.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>kg, o m\u00f3dulo da for\u00e7a gravitacional entre J\u00fapiter e a Terra no momento de maior proximidade \u00e9<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

 <\/p>\n

Confira a resolu\u00e7\u00e3o comentada dos exerc\u00edcios<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Exerc\u00edcios de vestibulares com resolu\u00e7\u00e3o comentada sobre a lei da Gravita\u00e7\u00e3o Universal de Newton \u00a0 01-(UFMG) Tr\u00eas sat\u00e9lites \u2013\u00a0I,\u00a0II\u00a0e\u00a0III\u00a0\u2013 movem-se em \u00f3rbitas circulares ao redor da Terra. O sat\u00e9lite\u00a0I\u00a0tem massa\u00a0m\u00a0e os sat\u00e9lites\u00a0II\u00a0e\u00a0III\u00a0t\u00eam, cada um, massa 2m\u00a0. Os sat\u00e9lites\u00a0I\u00a0e\u00a0II\u00a0est\u00e3o em uma mesma \u00f3rbita de raio\u00a0r\u00a0e o raio da \u00f3rbita do sat\u00e9lite\u00a0III\u00a0\u00e9 r\/2. :Sejam\u00a0FI\u00a0, FII\u00a0e FIII\u00a0m\u00f3dulos das for\u00e7as gravitacionais da Terra sobre,<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1433,"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-1435","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1435","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=1435"}],"version-history":[{"count":4,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1435\/revisions"}],"predecessor-version":[{"id":10878,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1435\/revisions\/10878"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1433"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}