{"id":3256,"date":"2017-09-27T23:04:01","date_gmt":"2017-09-27T23:04:01","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=3256"},"modified":"2024-06-29T23:50:35","modified_gmt":"2024-06-29T23:50:35","slug":"gravitacao-2013-2014","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/vestibulares-recentes\/mecanica\/gravitacao-2013-2014\/","title":{"rendered":"Gravita\u00e7\u00e3o 2013-2014"},"content":{"rendered":"

GRAVITA\u00c7\u00c3O<\/span><\/span><\/span><\/p>\n

2014 e 2013<\/span><\/span><\/span><\/p>\n

Gravita\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/p>\n

01-(FUVEST-SP-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

H\u00e1\u00a0um\u00a0ponto\u00a0no\u00a0segmento\u00a0de\u00a0reta\u00a0unindo\u00a0o\u00a0Sol\u00a0\u00e0\u00a0Terra,\u00a0denominado\u00a0\u201cPonto\u00a0de\u00a0Lagrange\u00a0L1\u201d.\u00a0Um\u00a0<\/b><\/span><\/span><\/span><\/p>\n

sat\u00e9lite\u00a0artificial\u00a0colocado\u00a0nesse\u00a0ponto,\u00a0em\u00a0\u00f3rbita\u00a0ao\u00a0redor\u00a0do\u00a0Sol,\u00a0permanecer\u00e1\u00a0sempre\u00a0na\u00a0mesma\u00a0posi\u00e7\u00e3o\u00a0relativa\u00a0entre\u00a0o\u00a0Sol\u00a0e\u00a0a\u00a0Terra.\u00a0Nessa situa\u00e7\u00e3o, ilustrada na figura abaixo, a velocidade angular orbital W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0do <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

orbital W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0do sat\u00e9lite em torno do Sol ser\u00e1 igual \u00e0 da Terra, W<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Para essa condi\u00e7\u00e3o, determine<\/b><\/span><\/span><\/span><\/p>\n

a) W<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0em fun\u00e7\u00e3o da constante gravitacional G, da massa M<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0do Sol e da dist\u00e2ncia R entre a Terra e o Sol;<\/b><\/span><\/span><\/span><\/p>\n

b) o\u00a0valor\u00a0de<\/b><\/span><\/span><\/span>\uf020<\/b><\/span><\/span><\/span> W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0em\u00a0rad\/s;<\/b><\/span><\/span><\/span><\/p>\n

c)a\u00a0express\u00e3o\u00a0do\u00a0m\u00f3dulo\u00a0F<\/b><\/span><\/span><\/span>r<\/b><\/span><\/span><\/sub><\/span>\u00a0da\u00a0for\u00e7a\u00a0gravitacional\u00a0resultante\u00a0que\u00a0age\u00a0sobre\u00a0o\u00a0sat\u00e9lite,\u00a0em\u00a0fun\u00e7\u00e3o\u00a0de\u00a0G,\u00a0M<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>,\u00a0M<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>,\u00a0m,\u00a0R\u00a0e\u00a0d,\u00a0sendo\u00a0M<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0e\u00a0m,\u00a0respectivamente,\u00a0as\u00a0massas\u00a0da\u00a0Terra\u00a0e\u00a0do\u00a0sat\u00e9lite\u00a0e\u00a0d\u00a0a\u00a0dist\u00e2ncia\u00a0entre\u00a0a\u00a0Terra\u00a0e\u00a0o\u00a0sat\u00e9lite.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

02-(FUVEST-SP-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Uma esta\u00e7\u00e3o espacial foi projetada com formato cil\u00edndrico, de raio R igual a100m, como ilustra a figura.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Para simular o efeito gravitacional e permitir que as pessoas caminhem na parte interna da casca cil\u00edndrica, a esta\u00e7\u00e3o gira em torno de seu eixo, com velocidade angular constante Z. As pessoas ter\u00e3o sensa\u00e7\u00e3o de peso, como se estivessem na Terra, se a velocidade Z for de, aproximadamente, Dado: acelera\u00e7\u00e3o gravitacional na superf\u00edcie da Terra \u2013 g=10m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span><\/p>\n

a) 0,1rad\/s b) 0,3rad\/s c) 1rad\/s d) 3rad\/s e) 10rad\/s<\/b><\/span><\/span><\/span><\/p>\n

03-(UNESP-SP-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Saturno\u00a0<\/b><\/span><\/span><\/span>\u00e9 o sexto planeta a partir do Sol e o segundo maior, em tamanho, do sistema solar. Hoje, s\u00e3o conhecidos mais de\u00a0<\/b><\/span><\/span><\/span>sessenta sat\u00e9lites naturais de Saturno<\/b><\/span><\/span><\/span>, sendo que o maior deles,\u00a0<\/b><\/span><\/span><\/span>Tit\u00e3,<\/b><\/span><\/span><\/span>\u00a0est\u00e1 a uma\u00a0<\/b><\/span><\/span><\/span>dist\u00e2ncia m\u00e9dia de 1 200 000 km de Saturno e tem um per\u00edodo de transla\u00e7\u00e3o de, aproximadamente,<\/b><\/span><\/span><\/span> <\/b>16 dias terrestres ao redor do planeta.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

T\u00e9tis\u00a0<\/b><\/span><\/span><\/span>\u00e9 outro dos maiores sat\u00e9lites de Saturno e est\u00e1 a uma\u00a0<\/b><\/span><\/span><\/span>dist\u00e2ncia m\u00e9dia de Saturno de 300 000 km.<\/b><\/span><\/span><\/span><\/p>\n

Considere:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O\u00a0<\/b><\/span><\/span><\/span>per\u00edodo\u00a0<\/b><\/span><\/span><\/span>aproximado de\u00a0<\/b><\/span><\/span><\/span>transla\u00e7\u00e3o de T\u00e9tis ao redor de Saturno<\/b><\/span><\/span><\/span>, em\u00a0<\/b><\/span><\/span><\/span>dias terrestres<\/b><\/span><\/span><\/span>, \u00e9<\/b><\/span><\/span><\/span><\/p>\n

(A) 4. (B) 2. (C) 6. (D) 8. (E) 10.<\/b><\/span><\/span><\/span><\/p>\n

04-(UNICAMP-SP-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u201c<\/span>As den\u00fancias de viola\u00e7\u00e3o de telefonemas e transmiss\u00e3o de dados de empresas e cidad\u00e3os brasileiros<\/b><\/span><\/span><\/span> <\/b>serviram para refor\u00e7ar a tese das For\u00e7as Armadas da necessidade de o Brasil dispor de <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

seu pr\u00f3prio<\/b><\/span><\/span><\/span> sat\u00e9lite geoestacion\u00e1rio<\/b><\/span><\/span><\/span>\u00a0de comunica\u00e7\u00e3o militar\u201d (<\/b><\/span><\/span><\/span>O Estado de S\u00e3o Paulo<\/b><\/i><\/span><\/span><\/span>, 15\/07\/2013). Uma\u00a0<\/b><\/span><\/span><\/span>\u00f3rbita geoestacion\u00e1ria<\/b><\/span><\/span><\/span>\u00a0\u00e9 caracterizada por estar no\u00a0<\/b><\/span><\/span><\/span>plano equatorial terrestre<\/b><\/span><\/span><\/span>, sendo que o sat\u00e9lite que a executa est\u00e1\u00a0<\/b><\/span><\/span><\/span>sempre acima do mesmo ponto no equador da superf\u00edcie terrestre<\/b><\/span><\/span><\/span>. Considere que a \u00f3rbita geoestacion\u00e1ria tem um\u00a0<\/b><\/span><\/span><\/span>raio r=42000km.<\/b><\/span><\/span><\/span><\/p>\n

a) Calcule a\u00a0<\/b><\/span><\/span><\/span>acelera\u00e7\u00e3o centr\u00edpeta<\/b><\/span><\/span><\/span>\u00a0de um sat\u00e9lite em \u00f3rbita circular geoestacion\u00e1ria.<\/b><\/span><\/span><\/span><\/p>\n

b) A\u00a0<\/b><\/span><\/span><\/span>energia mec\u00e2nica<\/b><\/span><\/span><\/span>\u00a0de um sat\u00e9lite de\u00a0<\/b><\/span><\/span><\/span>massa\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/i><\/span><\/span><\/span>\u00a0<\/b><\/i><\/span><\/span><\/span>em \u00f3rbita circular em torno da terra \u00e9 dada por<\/b><\/span><\/span><\/span><\/p>\n

E= – GMm\/2r,<\/b><\/span><\/span><\/span>\u00a0em\u00a0<\/b><\/span><\/span><\/span>que\u00a0<\/b><\/span><\/span><\/span>r\u00a0<\/b><\/i><\/span><\/span><\/span>\u00e9 o raio da \u00f3rbita<\/b><\/span><\/span><\/span>,\u00a0<\/b><\/span><\/span><\/span>M=6.10<\/b><\/span><\/span><\/span>24<\/b><\/span><\/span><\/sup><\/span>\u00a0kg \u00e9 a massa da Terra e G=6,7.10<\/b><\/span><\/span><\/span>-11<\/b><\/span><\/span><\/sup><\/span>\u00a0Nm<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/kg<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

O\u00a0<\/b><\/span><\/span><\/span>raio de \u00f3rbita<\/b><\/span><\/span><\/span>\u00a0de\u00a0<\/b><\/span><\/span><\/span>sat\u00e9lites comuns<\/b><\/span><\/span><\/span>\u00a0de observa\u00e7\u00e3o (n\u00e3o geoestacion\u00e1rios) \u00e9 tipicamente de\u00a0<\/b><\/span><\/span><\/span>7000 km.<\/b><\/span><\/span><\/span><\/p>\n

Calcule a\u00a0<\/b><\/span><\/span><\/span>energia adicional<\/b><\/span><\/span><\/span>\u00a0necess\u00e1ria para colocar um sat\u00e9lite\u00a0<\/b><\/span><\/span><\/span>de 200 kg de massa<\/b><\/span><\/span><\/span>\u00a0em uma \u00f3rbita<\/b><\/span><\/span><\/span><\/p>\n

geoestacion\u00e1ria, em\u00a0<\/b><\/span><\/span><\/span>compara\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0a coloc\u00e1-lo em uma \u00f3rbita comum de observa\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

05-(PUC-MG-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Propriet\u00e1rios de antenas\u00a0<\/b><\/span><\/span><\/span>parab\u00f3licas de televis\u00e3o\u00a0<\/b><\/span><\/span><\/span>est\u00e3o acostumados a\u00a0<\/b><\/span><\/span><\/span>direcionar suas antenas para determinado ponto no c\u00e9u\u00a0<\/b><\/span><\/span><\/span>a fim de que\u00a0<\/b><\/span><\/span><\/span>possam receber o sinal das emissoras<\/b><\/span><\/span><\/span>. Ao se ajustar a orienta\u00e7\u00e3o de uma antena, apenas se est\u00e1 <\/b><\/span><\/span><\/span>apontando-a na dire\u00e7\u00e3o de um sat\u00e9lite retransmissor.<\/b><\/span><\/span><\/span><\/p>\n

\u00c9 CORRETO afirmar:<\/b><\/span><\/span><\/span><\/p>\n

a) Os sat\u00e9lites est\u00e3o em repouso em rela\u00e7\u00e3o \u00e0 Terra.<\/b><\/span><\/span><\/span><\/p>\n

b) Os sat\u00e9lites transmissores giram com velocidade angular maior que a da Terra.<\/b><\/span><\/span><\/span><\/p>\n

c) O raio da \u00f3rbita destes sat\u00e9lites \u00e9 menor que o raio da Terra.<\/b><\/span><\/span><\/span><\/p>\n

d) A velocidade linear dos sat\u00e9lites \u00e9 menor que a da superf\u00edcie da Terra.<\/b><\/span><\/span><\/span><\/p>\n

06-(PUC-RJ-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um\u00a0<\/b><\/span><\/span><\/span>sat\u00e9lite de transmiss\u00e3o de dados<\/b><\/span><\/span><\/span>\u00a0\u00e9 posicionado estrategicamente\u00a0<\/b><\/span><\/span><\/span>sobre a cidade do Rio de<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Janeiro\u00a0<\/b><\/span><\/span><\/span>a uma altitude de 20.000 km. Sabendo que este sat\u00e9lite \u00e9\u00a0<\/b><\/span><\/span><\/span>geoestacion\u00e1rio<\/b><\/span><\/span><\/span>, i.e.,\u00a0<\/b><\/span><\/span><\/span>fica parado<\/b><\/span><\/span><\/span><\/p>\n

em rela\u00e7\u00e3o a uma localiza\u00e7\u00e3o geogr\u00e1fica no Rio de Janeiro<\/b><\/span><\/span><\/span>, calcule o\u00a0<\/b><\/span><\/span><\/span>per\u00edodo da \u00f3rbita\u00a0<\/b><\/span><\/span><\/span>deste sat\u00e9lite,\u00a0<\/b><\/span><\/span><\/span>em horas, em torno do eixo da terra<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

(A) 0 (B) 6 (C) 12 (D) 24 (E) 365<\/b><\/span><\/span><\/span><\/p>\n

07-(UDESC-SC-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um sat\u00e9lite est\u00e1 em uma \u00f3rbita circular em torno de um planeta de massa M e raio R a uma altitude H. Assinale a alternativa que representa a velocidade escalar adicional que o sat\u00e9lite precisa adquirir para escapar completamente do planeta.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

08-(UEFS-BA-014)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O\u00a0<\/b><\/span><\/span><\/span>raio m\u00e9dio da \u00f3rbita do planeta Marte \u00e9 cerca de\u00a0<\/b><\/span><\/span><\/span>quatro vezes\u00a0<\/b><\/span><\/span><\/span>o raio m\u00e9dio da \u00f3rbita do<\/b><\/span><\/span><\/span><\/p>\n

planeta Merc\u00fario<\/b><\/span><\/span><\/span>, no seu movimento de transla\u00e7\u00e3o em torno do Sol.<\/b><\/span><\/span><\/span><\/p>\n

Considerando-se o\u00a0<\/b><\/span><\/span><\/span>per\u00edodo de transla\u00e7\u00e3o de Merc\u00fario\u00a0<\/b><\/span><\/span><\/span>quatro vezes menor do que um ano<\/b><\/span><\/span><\/span><\/p>\n

na Terra<\/b><\/span><\/span><\/span>, o\u00a0<\/b><\/span><\/span><\/span>per\u00edodo de transla\u00e7\u00e3o de Marte em torno do Sol<\/b><\/span><\/span><\/span>, estimado em\u00a0<\/b><\/span><\/span><\/span>anos terrestres<\/b><\/span><\/span><\/span>,<\/b><\/span><\/span><\/span><\/p>\n

\u00e9 de, aproximadamente,<\/b><\/span><\/span><\/span><\/p>\n

A) 2,5 B) 2,0 C) 1,5 D) 0,6 E) 0,3<\/b><\/span><\/span><\/span><\/p>\n

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

Leis de Kepler<\/b><\/span><\/span><\/span><\/p>\n

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

28-(UFPE-PE-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um planeta realiza uma \u00f3rbita el\u00edptica com uma estrela em um dos focos. Em dois meses, o segmento de reta que liga a<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

estrela ao planeta varre uma \u00e1rea A no plano da \u00f3rbita do planeta. Em 32 meses tal segmento varre uma \u00e1rea igual a \u03b1A. Qual o valor de \u03b1?<\/b><\/span><\/span><\/span><\/p>\n

29-(UDESC-SC-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Analise as proposi\u00e7\u00f5es sobre o planeta Merc\u00fario, com base nas tr\u00eas leis de Kepler.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

I. A \u00f3rbita de Merc\u00fario \u00e9 circular, com o Sol localizado no centro da circunfer\u00eancia.<\/b><\/span><\/span><\/span><\/p>\n

II. A magnitude da velocidade de transla\u00e7\u00e3o de Merc\u00fario varia ao longo de sua trajet\u00f3ria.<\/b><\/span><\/span><\/span><\/p>\n

III. A magnitude da velocidade de transla\u00e7\u00e3o de Merc\u00fario \u00e9 constante em toda a sua trajet\u00f3ria.<\/b><\/span><\/span><\/span><\/p>\n

IV. O per\u00edodo de transla\u00e7\u00e3o de Merc\u00fario independe do raio de sua \u00f3rbita circular.<\/b><\/span><\/span><\/span><\/p>\n

Assinale a alternativa correta.<\/b><\/span><\/span><\/span><\/p>\n

A. ( ) Somente a afirmativa III \u00e9 verdadeira.<\/b><\/span><\/span><\/span><\/p>\n

B. ( ) Somente as afirmativas I e III s\u00e3o verdadeiras.<\/b><\/span><\/span><\/span><\/p>\n

C. ( ) Somente a afirmativa II \u00e9 verdadeira.<\/b><\/span><\/span><\/span><\/p>\n

D. ( ) Somente as afirmativa II e IV s\u00e3o verdadeiras.<\/b><\/span><\/span><\/span><\/p>\n

E. ( ) Somente as afirmativas I e IV s\u00e3o verdadeiras.<\/b><\/span><\/span><\/span><\/p>\n

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

30-(UFV-MG-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A figura abaixo ilustra a \u00f3rbita el\u00edptica de um planeta em torno do Sol, sendo X e Y as \u00e1reas descritas por uma linha imagin\u00e1ria que liga o planeta ao Sol.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Sabendo-se que, de acordo com a 2\u00aa Lei de Kepler (Lei das \u00c1reas), a linha que une o Sol ao planeta descreve \u00e1reas iguais em tempos iguais, \u00e9 CORRETO afirmar que a velocidade escalar m\u00e9dia do planeta entre os pontos 3 e 4 da figura \u00e9:<\/b><\/span><\/span><\/span><\/p>\n

a) menor que sua velocidade escalar m\u00e9dia entre os pontos 1 e 2, quaisquer que sejam as \u00e1reas X e Y.<\/b><\/span><\/span><\/span><\/p>\n

b) menor que sua velocidade escalar m\u00e9dia entre os pontos 1 e 2, se forem iguais as \u00e1reas X e Y.<\/b><\/span><\/span><\/span><\/p>\n

c) igual a sua velocidade escalar m\u00e9dia entre os pontos 1 e 2, quaisquer que sejam as \u00e1reas X e Y.<\/b><\/span><\/span><\/span><\/p>\n

d) igual a sua velocidade escalar m\u00e9dia entre os pontos 1 e 2, se forem iguais as \u00e1reas X e Y.<\/b><\/span><\/span><\/span><\/p>\n

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

Lei da Gravita\u00e7\u00e3o Universal<\/b><\/span><\/span><\/span><\/p>\n

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

16-(ENEM-MEC-012)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A caracter\u00edstica que permite identificar um planeta no c\u00e9u \u00e9 o seu movimento relativo \u00e0s estrelas fixas. Se observarmos a posi\u00e7\u00e3o de um planeta por v\u00e1rios dias, verificaremos que sua posi\u00e7\u00e3o em rela\u00e7\u00e3o \u00e0s estrelas fixas se modifica regularmente. A figura destaca o movimento de Marte observado em intervalos de 10 dias, registrado da Terra.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Qual a causa da forma da trajet\u00f3ria do planeta Marte registrada na figura?<\/b><\/span><\/span><\/span><\/p>\n

a) A maior velocidade orbital da Terra faz com que, em certas \u00e9pocas, ela ultrapasse Marte.<\/b><\/span><\/span><\/span><\/p>\n

b) A presen\u00e7a de outras estrelas faz com que sua trajet\u00f3ria seja desviada por meio da atra\u00e7\u00e3o gravitacional.<\/b><\/span><\/span><\/span><\/p>\n

c) A \u00f3rbita de Marte, em torno do Sol, possui uma forma el\u00edptica mais acentuada que a dos demais planetas.<\/b><\/span><\/span><\/span><\/p>\n

d) A atra\u00e7\u00e3o gravitacional entre a Terra e Marte faz com que este planeta apresente uma \u00f3rbita irregular em torno do Sol.<\/b><\/span><\/span><\/span><\/p>\n

e) A proximidade de Marte com J\u00fapiter, em algumas \u00e9pocas do ano, faz com que a atra\u00e7\u00e3o gravitacional de J\u00fapiter interfira em seu movimento.<\/b><\/span><\/span><\/span><\/p>\n

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

SAT\u00c9LITES EM \u00d3RBITAS CIRCULARES<\/b><\/span><\/span><\/span><\/p>\n

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

18-(ESCOLA NAVAL-012-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dois pequenos sat\u00e9lites A e B, id\u00eanticos, descrevem \u00f3rbitas circulares ao redor da Terra. A <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

velocidade orbital do sat\u00e9lite A vale V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>m\/s. Sabendo que os raios orbitais dos sat\u00e9lites s\u00e3o relacionados por\u00a0 R<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=1.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>, a velocidade orbital do sat\u00e9lite B, em m\/s, vale<\/b><\/span><\/span><\/span><\/p>\n

a) 2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 b) 1.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 c) 4.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 d) 2.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\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 e) 1.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span><\/p>\n

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

\u00a0<\/span>19-(PUC-RJ-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A Lua leva 28 dias para dar uma volta completa ao redor da Terra. Aproximando a \u00f3rbita como <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

circular, sua dist\u00e2ncia ao centro da Terra \u00e9 de cerca de 380 mil quil\u00f4metros. A velocidade aproximada da Lua, em km\/s, \u00e9:<\/b><\/span><\/span><\/span><\/p>\n

(A) 13\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) 0,16\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 (C) 59\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 (D) 24\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 (E) 1,0<\/b><\/span><\/span><\/span><\/p>\n

20-(UFPR-PR-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dois sat\u00e9lites, denominados de S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0e S<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>, est\u00e3o orbitando um planeta P. Os dois sat\u00e9lites s\u00e3o esf\u00e9ricos e possuem tamanhos e massas iguais. O sat\u00e9lite S<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\u00a0possui uma \u00f3rbita perfeitamente circular e o sat\u00e9lite S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0uma \u00f3rbita el\u00edptica, sat\u00e9lite S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0uma \u00f3rbita el\u00edptica\u00a0conforme mostra a figura. Em rela\u00e7\u00e3o ao movimento desses dois sat\u00e9lites, ao longo de suas respectivas \u00f3rbitas, considere as seguintes afirmativas:<\/b><\/span><\/span><\/span><\/p>\n

1. Os m\u00f3dulos da for\u00e7a gravitacional entre o sat\u00e9lite S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0e o planeta P e entre o sat\u00e9lite S<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\u00a0e o planeta P s\u00e3o constantes.<\/b><\/span><\/span><\/span><\/p>\n

2. A energia potencial gravitacional entre o sat\u00e9lite S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0e o sat\u00e9lite S<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00e9 vari\u00e1vel.<\/b><\/span><\/span><\/span><\/p>\n

3. A energia cin\u00e9tica e a velocidade angular s\u00e3o constantes para ambos os sat\u00e9lites.<\/b><\/span><\/span><\/span><\/p>\n

Assinale a alternativa correta.<\/b><\/span><\/span><\/span><\/p>\n

a) Somente a afirmativa 1 \u00e9 verdadeira. \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<\/b><\/span><\/span><\/span><\/p>\n

b) Somente a afirmativa 2 \u00e9 verdadeira.<\/b><\/span><\/span><\/span><\/p>\n

c) Somente a afirmativa 3 \u00e9 verdadeira. \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<\/b><\/span><\/span><\/span><\/p>\n

d) Somente as afirmativas 1 e 2 s\u00e3o verdadeiras.<\/b><\/span><\/span><\/span><\/p>\n

e) Somente as afirmativas 2 e 3 s\u00e3o verdadeiras.<\/b><\/span><\/span><\/span><\/p>\n

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

21-(UEL-PR-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A posi\u00e7\u00e3o m\u00e9dia de um sat\u00e9lite geoestacion\u00e1rio em rela\u00e7\u00e3o \u00e0 superf\u00edcie terrestre se mant\u00e9m devido \u00e0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a) sua velocidade angular ser igual \u00e0 velocidade angular da superf\u00edcie terrestre.<\/b><\/span><\/span><\/span><\/p>\n

b) sua velocidade tangencial ser igual \u00e0 velocidade tangencial da superf\u00edcie terrestre.<\/b><\/span><\/span><\/span><\/p>\n

c) sua acelera\u00e7\u00e3o centr\u00edpeta ser proporcional ao cubo da velocidade tangencial do sat\u00e9lite.<\/b><\/span><\/span><\/span><\/p>\n

d) for\u00e7a gravitacional terrestre ser igual \u00e0 velocidade angular do sat\u00e9lite.<\/b><\/span><\/span><\/span><\/p>\n

e) for\u00e7a gravitacional terrestre ser nula no espa\u00e7o, local em que a atmosfera \u00e9 rarefeita.<\/b><\/span><\/span><\/span><\/p>\n

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

Acelera\u00e7\u00e3o da gravidade<\/b><\/span><\/span><\/span><\/p>\n

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

18-(PUC-PR-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O planeta Y possui a mesma densidade \u201cd\u201d que a Terra, por\u00e9m seu raio \u00e9 tr\u00eas vezes maior. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Considere os planetas esf\u00e9ricos e desconsidere o efeito de rota\u00e7\u00e3o dos planetas. Sabendo que a acelera\u00e7\u00e3o da gravidade na Terra vale g, a gravidade do planeta Y (g<\/b><\/span><\/span><\/span>y<\/b><\/span><\/span><\/sub><\/span>) valer\u00e1:<\/b><\/span><\/span><\/span><\/p>\n

Dado: V=(4\/3) \u03c0.R\u00b3<\/b><\/span><\/span><\/span><\/p>\n

A) g\/27\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B) g\/9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 C) 9g\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 D) g\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 E) 3g<\/b><\/span><\/span><\/span><\/p>\n

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

19-(UFRGS-RS-013)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Em 6 de agosto de 2012, o jipe \u201cCuriosity \u201c pousou em \u00a0Marte. Em um dos mais espetaculares empreendimentos da era espacial, o ve\u00edculo foi colocado na superf\u00edcie do planeta vermelho com muita precis\u00e3o. Diferentemente das \u00a0miss\u00f5es anteriores, nesta, depois da usual descida bal\u00edstica na atmosfera do planeta e da diminui\u00e7\u00e3o da velocidade provocada por um enorme para quedas, o ve\u00edculo de quase \u00a0900 kg de massa, a partir de 20 m de altura, foi suave e lentamente baixado at\u00e9 o solo, suspenso por tr\u00eas cabos, por um tipo de guindaste voador estabilizado no ar por meio de 4 pares de foguetes direcionais. A ilustra\u00e7\u00e3o abaixo representa o evento.<\/b><\/span><\/span><\/span><\/p>\n

\"Gravita\u00e7\u00e3o\"<\/p>\n

O cabo ondulado que aparece na figura serve apenas para comunica\u00e7\u00e3o e transmiss\u00e3o de energia entre os m\u00f3dulos.<\/b><\/span><\/span><\/span><\/p>\n

Considerando as seguintes raz\u00f5es: massa da Terra\/massa de Marte ~ 10 e raio m\u00e9dio da Terra\/raio m\u00e9dio de Marte ~ 2, a compara\u00e7\u00e3o com descida similar, realizada na superf\u00edcie terrestre, resulta que a raz\u00e3o correta entre a tens\u00e3o em cada cabo de suspens\u00e3o do jipe em Marte e na Terra T<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00e9, aproximadamente, de<\/b><\/span><\/span><\/span><\/p>\n

(A) 0,1. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(B) 0,2. \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(C) 0,4. \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(D) 2,5. \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(E) 5,0.<\/b><\/span><\/span><\/span><\/p>\n

Confira as resolu\u00e7\u00f5es comentadas<\/span><\/a><\/h3>\n

 <\/p>\n

Clique aqui para ver sobre o tema!<\/a><\/p>\n

Confira as v\u00eddeo aulas!<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

GRAVITA\u00c7\u00c3O 2014 e 2013 Gravita\u00e7\u00e3o 01-(FUVEST-SP-014) H\u00e1\u00a0um\u00a0ponto\u00a0no\u00a0segmento\u00a0de\u00a0reta\u00a0unindo\u00a0o\u00a0Sol\u00a0\u00e0\u00a0Terra,\u00a0denominado\u00a0\u201cPonto\u00a0de\u00a0Lagrange\u00a0L1\u201d.\u00a0Um\u00a0 sat\u00e9lite\u00a0artificial\u00a0colocado\u00a0nesse\u00a0ponto,\u00a0em\u00a0\u00f3rbita\u00a0ao\u00a0redor\u00a0do\u00a0Sol,\u00a0permanecer\u00e1\u00a0sempre\u00a0na\u00a0mesma\u00a0posi\u00e7\u00e3o\u00a0relativa\u00a0entre\u00a0o\u00a0Sol\u00a0e\u00a0a\u00a0Terra.\u00a0Nessa situa\u00e7\u00e3o, ilustrada na figura abaixo, a velocidade angular orbital WA\u00a0do orbital WA\u00a0do sat\u00e9lite em torno do Sol ser\u00e1 igual \u00e0 da Terra, WT. Para essa condi\u00e7\u00e3o, determine a) WT\u00a0em fun\u00e7\u00e3o da constante gravitacional G, da massa MS\u00a0do Sol e da dist\u00e2ncia R entre a Terra e o Sol; b) o\u00a0valor\u00a0de\uf020 WA\u00a0em\u00a0rad\/s; c)a\u00a0express\u00e3o\u00a0do\u00a0m\u00f3dulo\u00a0Fr\u00a0da\u00a0for\u00e7a\u00a0gravitacional\u00a0resultante\u00a0que\u00a0age\u00a0sobre\u00a0o\u00a0sat\u00e9lite,\u00a0em\u00a0fun\u00e7\u00e3o\u00a0de\u00a0G,\u00a0MS,\u00a0MT,\u00a0m,\u00a0R\u00a0e\u00a0d,\u00a0sendo\u00a0MT\u00a0e\u00a0m,\u00a0respectivamente,\u00a0as\u00a0massas\u00a0da\u00a0Terra\u00a0e\u00a0do\u00a0sat\u00e9lite\u00a0e\u00a0d\u00a0a\u00a0dist\u00e2ncia\u00a0entre\u00a0a\u00a0Terra\u00a0e\u00a0o\u00a0sat\u00e9lite.\u00a0<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3123,"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-3256","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3256","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=3256"}],"version-history":[{"count":4,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3256\/revisions"}],"predecessor-version":[{"id":9886,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3256\/revisions\/9886"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3123"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=3256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}