{"id":3258,"date":"2017-09-27T23:05:25","date_gmt":"2017-09-27T23:05:25","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=3258"},"modified":"2024-09-04T14:44:38","modified_gmt":"2024-09-04T14:44:38","slug":"resolucoes-gravitacao-2013-2014","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/vestibulares-recentes\/mecanica\/gravitacao-2013-2014\/resolucoes-gravitacao-2013-2014\/","title":{"rendered":"Resolu\u00e7\u00f5es – Gravita\u00e7\u00e3o – 2013-2014"},"content":{"rendered":"

RESOLU\u00c7\u00d5ES<\/b><\/span><\/span><\/span><\/p>\n

2013 – 2014<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>0<\/b><\/span><\/span><\/span>1-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>a) O\u00a0<\/b><\/span><\/span><\/span>\u201cNote e adote\u201d\u00a0<\/b><\/span><\/span><\/span>afirma que voc\u00ea pode considerar as \u00f3rbitas como sendo\u00a0<\/b><\/span><\/span><\/span>circulares<\/b><\/span><\/span><\/span>\u00a0e, assim, a\u00a0<\/b><\/span><\/span><\/span>Terra<\/b><\/span><\/span><\/span>\u00a0executa um movimento circular uniforme\u00a0<\/b><\/span><\/span><\/span>(MCU) em torno do Sol com velocidade angular W<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0constante\u00a0<\/b><\/span><\/span><\/span>— ent\u00e3o, a\u00a0<\/b><\/span><\/span><\/span>for\u00e7a gravitacional\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>G <\/b><\/span><\/span><\/sub><\/span>que o Sol de massa\u00a0<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>\u00a0aplica sobre a Terra de massa\u00a0<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0ser\u00e1 a\u00a0<\/b><\/span><\/span><\/span>for\u00e7a<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>resultante centr\u00edpeta\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>que \u00e9 respons\u00e1vel por\u00a0<\/b><\/span><\/span><\/span>manter a Terra em \u00f3rbita circular ao redor do Sol\u00a0<\/b><\/span><\/span><\/span>—\u00a0<\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0= F<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

b) A\u00a0<\/b><\/span><\/span><\/span>velocidade angular orbital W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>do sat\u00e9lite pedida \u00e9 a mesma que a da\u00a0<\/b><\/span><\/span><\/span>Terra W<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0j\u00e1 que ambos, sat\u00e9lite e Terra giram alinhados ao redor do Sol \u201cvarrendo\u201d a mesma \u00e1rea no mesmo tempo — W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=W<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=2\"\"\/T, onde\u00a0<\/b><\/span><\/span><\/span>T\u00a0<\/b><\/span><\/span><\/span>\u00e9 o per\u00edodo de rota\u00e7\u00e3o da Terra em torno do Sol e pelo \u201cNote e adote\u201d\u00a0<\/b><\/span><\/span><\/span>T=1 ano=3,14.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>s\u00a0<\/b><\/span><\/span><\/span>— W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=2×3,14\/3,14.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>\u00a0—\u00a0<\/b><\/span><\/span><\/span>W<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=2.10<\/b><\/span><\/span><\/span>-7<\/b><\/span><\/span><\/sup><\/span>\u00a0rad\/s.<\/b><\/span><\/span><\/span><\/p>\n

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

02-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Gravidade artificial –\u00a0Na Terra estamos acostumados com a \u201csensa\u00e7\u00e3o se peso\u201d e que quando estamos apoiados ela (<\/b><\/span><\/span><\/span>sensa\u00e7\u00e3o de peso<\/b><\/span><\/span><\/span>) ocorre devido \u00e0 for\u00e7a de\u00a0<\/b><\/span><\/span><\/span>rea\u00e7\u00e3o normal\u00a0\"\"\u00a0do apoio sobre nosso corpo<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Estando em equil\u00edbrio\u00a0\"\"e\u00a0\"\"\u00a0possuem a mesma intensidade, ou seja,\u00a0<\/b><\/span><\/span><\/span>N=P\u00a0\u00a0<\/b><\/span><\/span><\/span>—\u00a0 N=m.g— como a massa\u00a0<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/span>\u00a0\u00e9 sempre constante, se variarmos a \u201cgravidade\u201d\u00a0<\/b><\/span><\/span><\/span>g<\/b><\/span><\/span><\/span>, estaremos variando essa \u201c<\/b><\/span><\/span><\/span>sensa\u00e7\u00e3o de peso<\/b><\/span><\/span><\/span>\u201d.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Essa \u201c<\/b><\/span><\/span><\/span>sensa\u00e7\u00e3o de peso\u201d<\/b><\/span><\/span><\/span>\u00a0pode ser obtida fazendo a\u00a0<\/b><\/span><\/span><\/span>esta\u00e7\u00e3o espacial<\/b><\/span><\/span><\/span>, que deve ter a forma de um\u00a0<\/b><\/span><\/span><\/span>cilindro oco<\/b><\/span><\/span><\/span>, efetuar movimento cont\u00ednuo de rota\u00e7\u00e3o com velocidade angular W.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Essa\u00a0<\/b><\/span><\/span><\/span>simula\u00e7\u00e3o da \u201cgravidade<\/b><\/span><\/span><\/span>\u201d ocorre, pois todo corpo em movimento circular tende a se afastar do centro e, no caso, \u201c<\/b><\/span><\/span><\/span>colando<\/b><\/span><\/span><\/span>\u201d nas paredes internas do cilindro— o<\/b><\/span><\/span><\/span>\u201cpeso aparente\u201d do astronauta\u00a0<\/b><\/span><\/span><\/span>\u00e9 percebido pela\u00a0<\/b><\/span><\/span><\/span>rea\u00e7\u00e3o normal\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0das paredes da nave sobre ele, que \u00e9 a pr\u00f3pria for\u00e7a resultante centr\u00edpeta F<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=m.V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R, que deve ser igual ao\u00a0<\/b><\/span><\/span><\/span>peso do astronauta na Terra\u00a0<\/b><\/span><\/span><\/span>onde g==10m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0— portanto, para que as pessoas tenham a\u00a0<\/b><\/span><\/span><\/span>sensa\u00e7\u00e3o de peso<\/b><\/span><\/span><\/span>, como se\u00a0<\/b><\/span><\/span><\/span>estivessem na Terra\u00a0<\/b><\/span><\/span><\/span>a condi\u00e7\u00e3o \u00e9 —<\/b><\/span><\/span><\/span>N=P\u00a0<\/b><\/span><\/span><\/span>com N=mW<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>R e P=mg — no caso do exerc\u00edcio s\u00e3o dados — R=100m — g=10m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0— portanto, N=P — mW<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>R=mg — W<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.100=10 — W=\u221a(10\/100) — W=\u221a(0,1)\u22480,316 rad\/s —\u00a0<\/b><\/span><\/span><\/span>R- B<\/b><\/span><\/span><\/span><\/p>\n

03-<\/b><\/span><\/span><\/span>\u00a0Tit\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, 16 dias terrestres ao redor do planeta:<\/b><\/span><\/span><\/span><\/p>\n

T<\/b><\/span><\/span><\/span>Tit\u00e3<\/b><\/span><\/span><\/sub><\/span>=16d\u00a0<\/b><\/span><\/span><\/span>e\u00a0<\/b><\/span><\/span><\/span>r<\/b><\/span><\/span><\/span>Tit\u00e3<\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span>1 200 000km=<\/b><\/span><\/span><\/span>12.10<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/sup><\/span>km.<\/b><\/span><\/span><\/span><\/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 e pede-se seu per\u00edodo de transla\u00e7\u00e3o ao redor de Saturno:<\/b><\/span><\/span><\/span><\/p>\n

T<\/b><\/span><\/span><\/span>T\u00e9tis<\/b><\/span><\/span><\/sub><\/span>=?\u00a0<\/b><\/span><\/span><\/span>—\u00a0<\/b><\/span><\/span><\/span>r<\/b><\/span><\/span><\/span>T\u00e9tis<\/b><\/span><\/span><\/sub><\/span>=300 000km<\/b><\/span><\/span><\/span>=3.10<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/sup><\/span>km.<\/b><\/span><\/span><\/span><\/p>\n

Aplicando a\u00a0<\/b><\/span><\/span><\/span>terceira lei de Kepler:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

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

\"\"<\/p>\n

\"\"<\/p>\n

Energia adicional\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0E<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span>= – 0,96.10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>\u00a0\u2013 ( – 5,7.10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>)\u00a0\"\"\u00a0<\/b><\/span><\/span><\/span>E<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span>= 4,74.10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>\u00a0J<\/b><\/span><\/span><\/span><\/p>\n

05-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Sat\u00e9lites geoestacion\u00e1rios\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span>ou geosincr\u00f4nicos (sincronizados com o movimento de rota\u00e7\u00e3o da Terra) —\u00a0A\u00a0<\/b><\/span><\/span><\/span><\/span>maioria dos sat\u00e9lites de telecomunica\u00e7\u00f5es s\u00e3o sat\u00e9lites geoestacion\u00e1rios\u00a0<\/b><\/span><\/span><\/span><\/span>pois se\u00a0<\/b><\/span><\/span><\/span><\/span>encontram 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 \u00e9 o mesmo que o da Terra (24h),\u00a0<\/b><\/span><\/span><\/span><\/span>o raio de sua \u00f3rbita \u00e9 de, aproximadamente 36000km, tem a\u00a0<\/b><\/span><\/span><\/span><\/span>mesma velocidade angular (W) que a Terra e se encontram em \u00f3rbitas sobre a linha do equador<\/b><\/span><\/span><\/span><\/span>.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

06-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Sat\u00e9lites geoestacion\u00e1rios\u00a0 ou geosincr\u00f4nicos<\/b><\/span><\/span><\/span><\/span>(<\/b><\/span><\/span><\/span><\/span>sincronizados com o movimento de rota\u00e7\u00e3o da Terra<\/b><\/span><\/span><\/span><\/span>) — A maioria dos\u00a0<\/b><\/span><\/span><\/span><\/span>sat\u00e9lites de telecomunica\u00e7\u00f5es s\u00e3o sat\u00e9lites geoestacion\u00e1rios\u00a0<\/b><\/span><\/span><\/span><\/span>pois se encontram\u00a0<\/b><\/span><\/span><\/span><\/span>parado<\/b><\/span><\/span><\/span><\/span>s em rela\u00e7\u00e3o a um\u00a0<\/b><\/span><\/span><\/span><\/span>ponto fixo sobre a Terra.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Seu per\u00edodo \u00e9 o mesmo que o da Terra (24h),<\/b><\/span><\/span><\/span><\/span>\u00a0o raio de sua \u00f3rbita \u00e9 de, aproximadamente 36000km, tem a mesma velocidade angular (W) que a Terra e 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 aproximada de 36000km o per\u00edodo do sat\u00e9lite aumenta e abaixo desse valor, diminui.<\/b><\/span><\/span><\/span><\/p>\n

R- D\u00a0<\/b><\/span><\/span><\/span><\/p>\n

07-<\/b><\/span><\/span><\/span>\u00a0Se voc\u00ea n\u00e3o domina o conte\u00fado, leia atentamente a teoria a seguir: <\/b><\/span><\/span><\/span>Para colocar um objeto em \u00f3rbita ao redor da Terra, como fazemos com os sat\u00e9lites artificiais, a partir de sua superf\u00edcie da Terra, devemos lan\u00e7\u00e1-lo com uma velocidade m\u00ednima, que denominamos\u00a0velocidade de escape V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Essa velocidade m\u00ednima\u00a0 (V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>) deve ser a velocidade\u00a0 necess\u00e1ria para que um objeto,\u00a0sem propuls\u00e3o pr\u00f3pria, saia da superf\u00edcie da Terra e chegue no infinito com velocidade zero.<\/b><\/span><\/span><\/span><\/p>\n

Assim, considerando:<\/b><\/span><\/span><\/span><\/p>\n

G — \u00a0constante gravitacional<\/b><\/span><\/span><\/span><\/p>\n

M\u00a0— \u00a0massa da Terra<\/b><\/span><\/span><\/span><\/p>\n

M\u00a0— \u00a0massa do objeto a ser lan\u00e7ado com velocidade V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>\u00a0e que vai escapar do campo gravitacional<\/b><\/span><\/span><\/span><\/p>\n

r=R — \u00a0Dist\u00e2ncia entre o centro do planeta (Terra) e o ponto no qual a velocidade de escape est\u00e1 sendo calculada (superf\u00edcie da Terra)<\/b><\/span><\/span><\/span><\/p>\n

Energia mec\u00e2nica na superf\u00edcie da Terra de raio R<\/b><\/span><\/span><\/span><\/p>\n

Energia potencial gravitacional \u00a0— E<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>=-GMm\/r — E<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>=-GMm\/R — Energia cin\u00e9tica — E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=mV<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2<\/b><\/span><\/span><\/span><\/p>\n

E<\/b><\/span><\/span><\/span>MT<\/b><\/span><\/span><\/sub><\/span>=E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>+E<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>\u00a0 — E<\/b><\/span><\/span><\/span>MT<\/b><\/span><\/span><\/sub><\/span>=mV<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2 \u2013 GMm\/R<\/b><\/span><\/span><\/span><\/p>\n

Energia mec\u00e2nica no infinito<\/b><\/span><\/span><\/span><\/p>\n

Energia potencial gravitacional — E<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>=-GMm\/\"\"\u00a0— \u00a0E<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>=0 — Energia cin\u00e9tica\u00a0 — E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=m0<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2 — E<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=0 —<\/b><\/span><\/span><\/span><\/p>\n

Energia mec\u00e2nica — E<\/b><\/span><\/span><\/span>M\u00a5<\/b><\/span><\/span><\/sub><\/span>=0 — pelo princ\u00edpio da conserva\u00e7\u00e3o da energia mec\u00e2nica — E<\/b><\/span><\/span><\/span>MT<\/b><\/span><\/span><\/sub><\/span>=E<\/b><\/span><\/span><\/span>M\u00a5<\/b><\/span><\/span><\/sub><\/span><\/p>\n

mV<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/2 \u2013 GMm\/R=0\u00a0 — V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>=\u221a(2GM\/R)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

Substituindo os valores de G, M, e R que conhecemos, obtemos:<\/b><\/span><\/span><\/span><\/p>\n

V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>=11,3km\/s que \u00e9 a velocidade com que um corpo,\u00a0sem propuls\u00e3o pr\u00f3pria\u00a0deve sair da superf\u00edcie da Terra para \u201clibertar-se\u201d de seu campo gravitacional.<\/b><\/span><\/span><\/span><\/p>\n

Como a velocidade de um corpo em \u00f3rbita \u00e9 dada por V=\u221a(GM\/R) e a velocidade de escape por V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>=\u221a(2GM\/R),\u00a0a velocidade de escape na altura R \u00e9\u00a0\u221a2 vezes maior que a velocidade em \u00f3rbita circular na mesma altura.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Assim, velocidade escalar adicional que o sat\u00e9lite precisa adquirir para escapar completamente do planeta.<\/b><\/span><\/span><\/span><\/p>\n

deve valer — V<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>=\u221a2. \u221a(2GM\/(R + H) – \u221a(2GM\/(R + H) <\/b><\/span><\/span><\/span>—\u00a0R- D<\/b><\/span><\/span><\/span><\/p>\n

08-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span>R<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>=4R<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>\u00a0— T<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/4\u00a0<\/b><\/span><\/span><\/span>— Terceira lei de Kepler — T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0= T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0— T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/(4R<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0=<\/b><\/span><\/span><\/span><\/p>\n

(T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/4)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0— T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/64R<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0= T<\/b><\/span><\/span><\/span>T\u00a0<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\/16R<\/b><\/span><\/span><\/span>Me<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0— T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/64 = T<\/b><\/span><\/span><\/span>T\u00a0<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\/16 — 4T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= 64T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0— T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>= 4T<\/b><\/span><\/span><\/span>t<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0—<\/b><\/span><\/span><\/span><\/p>\n

T<\/b><\/span><\/span><\/span>Ma<\/b><\/span><\/span><\/sub><\/span>=2T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

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

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

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

28-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Segunda lei de Kepler (lei das \u00e1reas)\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\u201c O segmento de reta imagin\u00e1rio que une o centro do Sol ao centro do planeta descreve \u00e1reas proporcionais\u00a0 aos tempos<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0gastos para percorre-las\u201d<\/b><\/span><\/span><\/span><\/p>\n

Sendo as \u00e1reas proporcionais\u00a0 —\u00a0 regra de tr\u00eas\u00a0 —\u00a0 A \u2013 2 meses\u00a0 —\u00a0 \u03b1A \u2013 32 meses\u00a0 —\u00a0 2.\u03b1A=32.A\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0\u03b1=16;<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>29<\/b><\/span><\/span><\/span>–<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>I. Falsa\u00a0 —\u00a0 a primeira lei de Kepler afirma que as \u00f3rbitas s\u00e3o el\u00edpticas com o Sol ocupando um dos focos da elipse.<\/b><\/span><\/span><\/span><\/p>\n

II. Verdadeira \u00a0—\u00a0 Segunda lei de Kepler (lei das \u00e1reas)\u00a0 —\u00a0 \u201c O segmento de reta imagin\u00e1rio que une o centro do Sol ao centro do planeta descreve \u00e1reas proporcionais\u00a0 aos tempos gastos para percorr\u00ea-las\u201d<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>— \u00e1rea entre 1,2 e o Sol\u00a0 —\u00a0 A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>— \u00e1rea entre 3, 4 e o Sol\u00a0 —\u00a0 \u2206t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>— tempo que o planeta demora para ir de 1 a 2\u00a0 —\u2206t<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>— tempo que o planeta demora para ir de 3 a 4\u00a0 —\u00a0 ent\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u2206t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0~A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/\u2206t<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=constante=K\u00a0 —\u00a0 essa constante K depende do planeta e recebe o nome de velocidade areolar<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Observe na express\u00e3o acima que quando A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=A<\/b><\/span><\/span><\/span>2,<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2206t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=\u00a0\u2206t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>,\u00a0ou seja, para o arco maior 34, ser percorrido no mesmo<\/b><\/span><\/span><\/span><\/p>\n

intervalo de tempo que o arco menor12, a velocidade em 3,4 (mais perto do Sol –\u00a0peri\u00e9lio) deve ser maior que a velocidade em 1,2 (mais afastado do Sol \u2013\u00a0af\u00e9lio).<\/b><\/span><\/span><\/span><\/p>\n

Portanto\u00a0os planetas aceleram do af\u00e9lio para o peri\u00e9lio e retardam do peri\u00e9lio para o af\u00e9lio.<\/b><\/span><\/span><\/span><\/p>\n

III. Falsa\u00a0 —\u00a0 veja (II).<\/b><\/span><\/span><\/span><\/p>\n

IV. Falsa\u00a0 —\u00a0 a \u00f3rbita de Merc\u00fario n\u00e3o \u00e9 circular, \u00e9 el\u00edptica.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0R- C.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>30-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Leia atentamente a teoria a seguir:<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\u201c O segmento de reta imagin\u00e1rio que une o centro do Sol ao centro do planeta descreve \u00e1reas proporcionais\u00a0 aos tempos gastos para percorr\u00ea-las\u201d<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

A<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>— \u00e1rea entre 1,2 e o Sol\u00a0 —\u00a0 A<\/b><\/span><\/span><\/span>y<\/b><\/span><\/span><\/sub><\/span>\u00a0 — \u00e1rea entre 3, 4 e o Sol\u00a0 —\u00a0 \u2206t<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>— tempo que o planeta demora para ir de 1 a 2\u00a0 —<\/b><\/span><\/span><\/span><\/p>\n

\u2206t<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>\u00a0— tempo que o planeta demora para ir de 3 a 4\u00a0 —\u00a0 pela lei das \u00e1reas de Kepler\u00a0 —\u00a0 A<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>\/\u2206t<\/b><\/span><\/span><\/span>x\u00a0<\/b><\/span><\/span><\/sub><\/span>~ A<\/b><\/span><\/span><\/span>y<\/b><\/span><\/span><\/sub><\/span>\/\u2206t<\/b><\/span><\/span><\/span>y<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 essa constante K depende do planeta e recebe o nome de velocidade areolar.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Observe na express\u00e3o acima que, quando A<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>=A<\/b><\/span><\/span><\/span>y<\/b><\/span><\/span><\/sub><\/span>,\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>\u2206t<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>=\u2206t<\/b><\/span><\/span><\/span>y<\/b><\/span><\/span><\/sub><\/span>,\u00a0ou seja, para o arco maior 34, ser percorrido no mesmo intervalo de tempo que o arco menor12, a velocidade em 3,4 (mais perto do Sol –\u00a0peri\u00e9lio) deve ser maior que a velocidade em 1,2 (mais afastado do Sol \u2013\u00a0af\u00e9lio).<\/b><\/span><\/span><\/span><\/p>\n

Portanto\u00a0os planetas aceleram do af\u00e9lio para o peri\u00e9lio e retardam do peri\u00e9lio para o af\u00e9lio. Ainda, de acordo com essa lei, se as \u00f3rbitas forem circulares a velocidade de transla\u00e7\u00e3o ser\u00e1 constante e se a \u00f3rbita do planeta tiver raio R e seu\u00a0 per\u00edodo de transla\u00e7\u00e3o for T, sua velocidade areolar (constante K) ser\u00e1 dada por: K=A\/\u2206t =\u03c0R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/T.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>R- B.<\/b><\/span><\/span><\/span><\/p>\n

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

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

16<\/b><\/span><\/span><\/span>–<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Considere um planeta de massa m em \u00f3rbita aproximadamente circular ao redor do Sol de massa M\u00a0 —\u00a0 a for\u00e7a gravitacional entre o planeta e Sol tem intensidade F<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>=GMm\/r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>, sendo G a constante de gravita\u00e7\u00e3o universal\u00a0 e R a dist\u00e2ncia entre os centros do Sol e do planeta\u00a0 —\u00a0 a intensidade da for\u00e7a resultante centr\u00edpeta sobre o planeta vale F<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>=mV<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R, sendo V a velocidade escalar (de transla\u00e7\u00e3o) do planeta em torno do Sol\u00a0 —\u00a0 sobre o planeta essas duas for\u00e7as s\u00e3o iguais\u00a0 —\u00a0 F<\/b><\/span><\/span><\/span>G<\/b><\/span><\/span><\/sub><\/span>\u00a0= F<\/b><\/span><\/span><\/span>C<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 GMm\/R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0mV<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R\u00a0 —\u00a0 V=\u221a(G.M\/R)\u00a0 —\u00a0 observe por essa express\u00e3o que, quanto mais afastado o planeta estiver do Sol, menor ser\u00e1 sua velocidade orbital e que essa velocidade n\u00e3o depende da massa m do planeta\u00a0 —\u00a0 assim, a velocidade orbital de transla\u00e7\u00e3o da Terra \u00e9 maior que a de Marte\u00a0 —\u00a0 esse \u00e9 o motivo da trajet\u00f3ria em forma de la\u00e7o, que voc\u00ea pode entender observando atentamente a figura abaixo<\/b><\/span><\/span><\/span>.\"\"<\/b><\/span><\/span><\/span><\/p>\n

R- A.<\/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-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>A velocidade orbital de um sat\u00e9lite ao redor de um planeta (no caso, a Terra) \u00e9 fornecida por\u00a0 —\u00a0 V=\u221a(GM\/r)\u00a0 —\u00a0 G-constante gravitacional, M – massa da Terra e r – raio da \u00f3rbita\u00a0 —\u00a0 s\u00e3o dados\u00a0 —\u00a0 \"\"<\/b><\/span><\/span><\/span><\/p>\n

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\u00a0 —\u00a0 R<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 — sat\u00e9lite A\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=\u221a(GM\/r<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>)\u00a0 —\u00a0 2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=\u221a(GM\/r<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>) (I)\u00a0 —\u00a0 sat\u00e9lite B\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=\u221a(GM\/r<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>)\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=\u221a(GM\/10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>r<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>) (II).<\/b><\/span><\/span><\/span><\/p>\n

(I)\/(II)\u00a0 —\u00a0 2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\/V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=\u221a(GM\/r<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>)\/\u221a(GM\/10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>r<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>)\u00a0 —\u00a0 2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\/V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>={\u221a(GM)\/\u221ar<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>}x{\u221a(10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>r<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>)\/\u221a(GM)\u00a0 —\u00a0 2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\/V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=10\u221ar<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\/\u221ar<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 10V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=2.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>m\/s\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- D.<\/b><\/span><\/span><\/span><\/p>\n

19-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Dados\u00a0 —\u00a0 R=380 000km\u00a0 —\u00a0 T=28diasx24hx3600s=2 419 200s\u00a0 —\u00a0 \u03c0=3\u00a0 —\u00a0 V=2\u03c0R\/T=2X3X380 000km\/2 419 200s\u00a0 —\u00a0 V=0,94km\/s\u00a0 —\u00a0<\/b><\/span><\/span><\/span>R- E.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>20-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>1. Falsa\u00a0 —\u00a0 A intensidade da for\u00e7a gravitacional entre cada sat\u00e9lite e o planeta P \u00e9 dada por\u00a0 —\u00a0 F<\/b><\/span><\/span><\/span>g<\/b><\/span><\/span><\/sub><\/span>=GM<\/b><\/span><\/span><\/span>S<\/b><\/span><\/span><\/sub><\/span>.M<\/b><\/span><\/span><\/span>P<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 observe nessa express\u00e3o que para o sat\u00e9lite S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0o raio da \u00f3rbita \u00e9 vari\u00e1vel, assim a intensidade da for\u00e7a gravitacional entre o sat\u00e9lite S<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>\u00a0e o planeta P tamb\u00e9m \u00e9 vari\u00e1vel.<\/b><\/span><\/span><\/span><\/p>\n

2. Verdadeira\u00a0 —\u00a0 Por meio de c\u00e1lculos que fogem ao n\u00edvel do ensino m\u00e9dio podemos demonstrar que a energia potencial gravitacional de um sat\u00e9lite em rela\u00e7\u00e3o ao outro, adotando-se o referencial no infinito, \u00e9 dada por:<\/b><\/span><\/span><\/span><\/p>\n

Ep=-GMm\/r\u00a0 —\u00a0 observe que essa energia potencial gravitacional \u00e9 fun\u00e7\u00e3o da dist\u00e2ncia r entre os dois sat\u00e9lites, que \u00e9 vari\u00e1vel.<\/b><\/span><\/span><\/span><\/p>\n

3. Falsa\u00a0 —\u00a0 essa afirmativa \u00e9 v\u00e1lida para o sat\u00e9lite B \u00a0mas para o sat\u00e9lite B \u00e9 falsa, pois em \u00f3rbitas el\u00edpticas ele acelera do af\u00e9lio para o peri\u00e9lio variando sua velocidade o que implica numa varia\u00e7\u00e3o da energia cin\u00e9tica e da velocidade angular.<\/b><\/span><\/span><\/span><\/p>\n

R- B.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

21-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Sat\u00e9lites geoestacion\u00e1rios\u00a0 ou geosincr\u00f4nicos (sincronizados com o movimento de rota\u00e7\u00e3o da Terra)\u00a0 —\u00a0 a maioria dos sat\u00e9lites de telecomunica\u00e7\u00f5es s\u00e3o sat\u00e9lites geoestacion\u00e1rios pois se encontram parados em rela\u00e7\u00e3o a um ponto fixo<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

sobre a Terra\u00a0 —\u00a0 seu per\u00edodo \u00e9 o mesmo que o da Terra (24h),\u00a0o raio de sua \u00f3rbita \u00e9 de, aproximadamente 36000km, tem a mesma velocidade angular (W) que a Terra e 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><\/p>\n

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

R- A.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

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

18-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Pelo enunciado eles possuem a mesma densidade\u00a0 —\u00a0 d<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=d<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 d<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/(4\/3)\u03c0R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 d<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=m<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=m<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\/(4\/3)\u03c0R<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span> —\u00a0 d<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>= m<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\/(4\/3)\u03c0(3R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 d<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=m<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\/36<\/b><\/span><\/span><\/span>\u03c0<\/b><\/span><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 d<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=d<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/(4\/3)\u03c0R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>= m<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\/(4\/3)36\u03c0R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 m<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=27m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 acelera\u00e7\u00e3o da gravidade na superf\u00edcie da Terra\u00a0 —\u00a0 g=Gm<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 acelera\u00e7\u00e3o da gravidade na superf\u00edcie de<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>Y\u00a0 —\u00a0 g<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=Gm<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>=G.27m<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/(3R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 g<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=27Gm<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/9R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 g<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=3.Gm<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 g<\/b><\/span><\/span><\/span>Y<\/b><\/span><\/span><\/sub><\/span>=3g\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- E.<\/b><\/span><\/span><\/span><\/p>\n

19-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>O peso do jipe na Terra\u00a0 —\u00a0 P<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=m.g<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 a massa do jipe \u00e9 a mesma na Terra e em Marte\u00a0 —\u00a0 peso do jipe em Marte\u00a0 —\u00a0 P<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>=m.g<\/b><\/span><\/span><\/span>M\u00ad<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 como, pelo enunciado, o ve\u00edculo foi suave e lentamente baixado at\u00e9 o solo, ele se encontra em equil\u00edbrio din\u00e2mico e a for\u00e7a resultante sobre ele \u00e9 nula\u00a0 —\u00a0 assim, a tra\u00e7\u00e3o T nos cabos \u00e9 igual ao peso, tanto na Terra como em Marte\u00a0 —\u00a0 P<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=m.g<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\u00a0e P<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>=T<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>=m.g<\/b><\/span><\/span><\/span>M\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0—\u00a0 a acelera\u00e7\u00e3o da gravidade na superf\u00edcie\u00a0 de um planeta \u00e9 fornecida por\u00a0 —\u00a0 g=G.M\/R<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 G \u00e9 uma constante, M a massa do planeta e R o raio m\u00e9dio do planeta\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=m.g<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span><\/p>\n

m.GM<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>=mG.10M<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/(2R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=2,5mGM<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\u00a0(I)\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>=m.g<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>=m GM<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\u00a0(II)\u00a0 —\u00a0 (II)\/(I)\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=<\/b><\/span><\/span><\/span><\/p>\n

(mGM<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>)x (R<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/2,5GM<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>)\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>M<\/b><\/span><\/span><\/sub><\/span>\/T<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/sub><\/span>=1\/2,5=0,4\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>R- C.<\/b><\/span><\/span><\/span><\/p>\n

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

Voltar para os exerc\u00edcios<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

RESOLU\u00c7\u00d5ES 2013 – 2014 \u00a001-\u00a0a) O\u00a0\u201cNote e adote\u201d\u00a0afirma que voc\u00ea pode considerar as \u00f3rbitas como sendo\u00a0circulares\u00a0e, assim, a\u00a0Terra\u00a0executa um movimento circular uniforme\u00a0(MCU) em torno do Sol com velocidade angular WT\u00a0constante\u00a0— ent\u00e3o, a\u00a0for\u00e7a gravitacional\u00a0FG que o Sol de massa\u00a0MS\u00a0aplica sobre a Terra de massa\u00a0MT\u00a0ser\u00e1 a\u00a0for\u00e7a\u00a0resultante centr\u00edpeta\u00a0Fc\u00a0que \u00e9 respons\u00e1vel por\u00a0manter a Terra em \u00f3rbita circular ao redor do Sol\u00a0—\u00a0FG\u00a0= Fc b) A\u00a0velocidade<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3256,"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-3258","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3258","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=3258"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3258\/revisions"}],"predecessor-version":[{"id":3261,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3258\/revisions\/3261"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3256"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=3258"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}