{"id":350,"date":"2015-01-06T19:37:11","date_gmt":"2015-01-06T19:37:11","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=350"},"modified":"2024-09-02T16:56:13","modified_gmt":"2024-09-02T16:56:13","slug":"resolucao-comentada-da-ufjf-2015","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/universidades-2015\/exercicios-da-ufjf-2015\/resolucao-comentada-da-ufjf-2015\/","title":{"rendered":"Resolu\u00e7\u00e3o comentada da UFJF 2015"},"content":{"rendered":"

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

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

\"\"<\/p>\n

02- <\/b><\/span><\/span><\/span>A seguir, a teoria:<\/b><\/span><\/span><\/span><\/p>\n

Primeira lei de Kepler (lei das \u00f3rbitas)<\/b><\/span><\/span><\/span><\/p>\n

“As <\/b><\/span><\/span><\/span>\u00f3rbitas<\/b><\/span><\/span><\/span> que os planetas descrevem ao redor do Sol s\u00e3o <\/b><\/span><\/span><\/span>el\u00edpticas<\/b><\/span><\/span><\/span>, com o <\/b><\/span><\/span><\/span>Sol <\/b><\/span><\/span><\/span>ocupando um dos <\/b><\/span><\/span><\/span>focos <\/b><\/span><\/span><\/span>da elipse”.<\/b><\/span><\/span><\/span><\/p>\n

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

Numa <\/b><\/span><\/span><\/span>elipse<\/b><\/span><\/span><\/span> (figura acima), para qualquer posi\u00e7\u00e3o do ponto P a soma das dist\u00e2ncias FP com PF\u2019 \u00e9 sempre a mesma.<\/b><\/span><\/span><\/span><\/p>\n

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

\u201c O <\/b><\/span><\/span><\/span>segmento de reta <\/b><\/span><\/span><\/span>imagin\u00e1rio que <\/b><\/span><\/span><\/span>une o centro do Sol ao centro do planeta<\/b><\/span><\/span><\/span> descreve \u00e1reas <\/b><\/span><\/span><\/span>iguais\u00a0 em intervalos de tempo iguais<\/b><\/span><\/span><\/span>\u201d\"\"<\/b><\/span><\/span><\/span><\/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<\/b><\/span><\/span><\/span><\/p>\n

A<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>— \u00e1rea entre 3, 4 e o Sol<\/b><\/span><\/span><\/span><\/p>\n

\u2206t<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>— tempo que o planeta demora para ir de 1 a 2<\/b><\/span><\/span><\/span><\/p>\n

\u2206t<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>— tempo que o planeta demora para ir de 3 a 4<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Ent\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>~A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/\u2206t<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= <\/b><\/span><\/span><\/span>constante = K<\/b><\/span><\/span><\/span><\/p>\n

Terceira lei de Kepler (lei dos per\u00edodos)<\/b><\/span><\/span><\/span><\/p>\n

\u201c Os <\/b><\/span><\/span><\/span>quadrados dos per\u00edodos\u00a0<\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>de revolu\u00e7\u00e3o dos planetas (tempo que demora para efetuar uma volta completa em torno do Sol) s\u00e3o proporcionais aos <\/b><\/span><\/span><\/span>cubos das suas dist\u00e2ncias m\u00e9dias\u00a0<\/b><\/span><\/span><\/span>R<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>ao Sol\u201d<\/b><\/span><\/span><\/span><\/p>\n

T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R<\/b><\/span><\/span><\/span>3 <\/b><\/span><\/span><\/sup><\/span>= constante = K\u2019<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>raio m\u00e9dio R <\/b><\/span><\/span><\/span>da \u00f3rbita de um planeta corresponde \u00e0 <\/b><\/span><\/span><\/span>m\u00e9dia aritm\u00e9tica <\/b><\/span><\/span><\/span>entre a dist\u00e2ncia do Sol ao af\u00e9lio e a dist\u00e2ncia do Sol ao peri\u00e9lio. Observe que esse valor \u00e9 o mesmo que a medida do semi-eixo maior da elipse, que na figura acima seria\u00a0<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

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

03- <\/b><\/span><\/span><\/span>Todas est\u00e3o corretas — veja fisicaevestibular.com.br \u2013 mec\u00e2nica \u2013 din\u00e2mica \u2013 est\u00e1tica.<\/b><\/span><\/span><\/span><\/p>\n

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

04- <\/b><\/span><\/span><\/span>a)<\/b><\/span><\/span><\/span> <\/b>Falsa <\/b><\/span><\/span><\/span>— se ele est\u00e1 em <\/b><\/span><\/span><\/span>movimento circular <\/b><\/span><\/span><\/span>ent\u00e3o sobre ele atua uma <\/b><\/span><\/span><\/span>for\u00e7a resultante centr\u00edpeta<\/b><\/span><\/span><\/span>, n\u00e3o importando se o movimento \u00e9 circular uniforme ou n\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

b) Falsa <\/b><\/span><\/span><\/span>— <\/b><\/span><\/span><\/span>pode existir for\u00e7as sim<\/b><\/span><\/span><\/span>, apenas que a <\/b><\/span><\/span><\/span>soma vetorial dessas for\u00e7as deve ser nula.<\/b><\/span><\/span><\/span><\/p>\n

c) Correta — desde que essa for\u00e7a seja a for\u00e7a resultante<\/b><\/span><\/span><\/span>, pois, pela segunda lei de Newton F = m.a.<\/b><\/span><\/span><\/span><\/p>\n

d) Falsa <\/b><\/span><\/span><\/span>— as <\/b><\/span><\/span><\/span>for\u00e7as de a\u00e7\u00e3o e rea\u00e7\u00e3o jamais se anulam<\/b><\/span><\/span><\/span>, pois s\u00e3o aplicadas em <\/b><\/span><\/span><\/span>corpos diferentes.<\/b><\/span><\/span><\/span><\/p>\n

e) Falsa <\/b><\/span><\/span><\/span>— ela \u00e9 uma <\/b><\/span><\/span><\/span>for\u00e7a resultante<\/b><\/span><\/span><\/span>, que obriga o corpo a <\/b><\/span><\/span><\/span>efetuar movimento circular.<\/b><\/span><\/span><\/span><\/p>\n

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

05- <\/b><\/span><\/span><\/span>Dist\u00e2ncia percorrida<\/b><\/span><\/span><\/span> pela Lua ao efetuar uma <\/b><\/span><\/span><\/span>volta completa <\/b><\/span><\/span><\/span>ao redor da Terra — <\/b><\/span><\/span><\/span>\u2206S = 2.\u043f.R <\/b><\/span><\/span><\/span>= 2x3x<\/b><\/span><\/span><\/span><\/p>\n

3,8.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span> — <\/b><\/span><\/span><\/span>\u2206S = 22,8.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span> m.<\/b><\/span><\/span><\/span><\/p>\n

T<\/b><\/span><\/span><\/span>empo<\/b><\/span><\/span><\/span> que demora para efetuar uma <\/b><\/span><\/span><\/span>volta completa <\/b><\/span><\/span><\/span>— <\/b><\/span><\/span><\/span>\u2206t = <\/b><\/span><\/span><\/span>27,3 diasx24=655,2hx3600=2358720<\/b><\/span><\/span><\/span><\/p>\n

\u2206t \u2248 2,36.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span> s.<\/b><\/span><\/span><\/span><\/p>\n

V = \u2206S\/\u2206t <\/b><\/span><\/span><\/span>= 22,8.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>\/2,36.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span> — <\/b><\/span><\/span><\/span>V = 9,7.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> m\/s.<\/b><\/span><\/span><\/span><\/p>\n

a<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/R <\/b><\/span><\/span><\/span>= (9,7.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\/3,8.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span> = 94,1.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>\/3,8.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span> — <\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span> <\/b>=24,8.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span> <\/b>= 2,48.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span> m\/s<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

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

06- <\/b><\/span><\/span><\/span><\/span>P = 23cm<\/b><\/span><\/span><\/span><\/span><\/p>\n

F = 10cm<\/b><\/span><\/span><\/span><\/span><\/p>\n

P\u2019 = ?<\/b><\/span><\/span><\/span><\/span><\/p>\n

1<\/b><\/span><\/span><\/span><\/span>\/f = 1\/P + 1\/P\u2019<\/b><\/span><\/span><\/span><\/span> — 1\/10 = 1\/23 + 1\/P\u2019 — 1\/10 \u2013 1\/23 = 1\/P\u2019 — (23 \u2013 10)\/230 = 1\/P\u2019 — P\u2019 = 230\/13<\/b><\/span><\/span><\/span><\/span><\/p>\n

P\u2019 = 17,69 cm (P\u2019 > imagem real).<\/b><\/span><\/span><\/span><\/p>\n

i\/o = -P\u2019\/P <\/b><\/span><\/span><\/span>— <\/b><\/span><\/span><\/span><\/b>i\/o = – 17,69\/23 = – 0,8 — <\/b><\/span><\/span><\/span>i = – 0,8 o — ( a imagem \u00e9 invertida e 80% do tamanho do <\/b><\/span><\/span><\/span>objeto)<\/b><\/span><\/span><\/span><\/p>\n

Voc\u00ea pode tamb\u00e9m tra\u00e7ar os raios de luz e determinar as caracter\u00edsticas da imagem — veja que o <\/b><\/span><\/span><\/span>objeto est\u00e1 a 23cm da lente, ou seja, antes do dobro da dist\u00e2ncia focal (ponto antiprincipal A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>) que \u00e9 de 20cm:<\/b><\/span><\/span><\/span><\/p>\n

Objeto P antes de A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/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\"\"<\/span><\/p>\n

Caracter\u00edsticas da imagem P\u2019:<\/b><\/span><\/span><\/span><\/p>\n

Natureza\u00a0<\/b><\/span><\/span><\/span>\u2013 Real (obtida no cruzamento do pr\u00f3prio raio luminoso (linha cheia)<\/b><\/span><\/span><\/span><\/p>\n

Localiza\u00e7\u00e3o\u00a0<\/b><\/span><\/span><\/span>\u2013 entre F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0e A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Tamanho e orienta\u00e7\u00e3o\u00a0<\/b><\/span><\/span><\/span>\u2013 menor que o objeto e invertida em rela\u00e7\u00e3o ao mesmo<\/b><\/span><\/span><\/span><\/p>\n

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

07- <\/b><\/span><\/span><\/span>Para a \u00e1gua, por exemplo, e o <\/b><\/span><\/span><\/span>volume diminui na fus\u00e3o e, portanto, aumenta na solidifica\u00e7\u00e3o<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Para elas,\u00a0um <\/b><\/span><\/span><\/span>aumento de press\u00e3o acarreta uma diminui\u00e7\u00e3o na temperatura de fus\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

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

08- <\/span><\/span><\/span>Na <\/b><\/span><\/span><\/span>Celsius <\/b><\/span><\/span><\/span>voc\u00ea tem <\/b><\/span><\/span><\/span>4 intervalos de 5cm <\/b><\/span><\/span><\/span>que equivalem a <\/b><\/span><\/span><\/span>100<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C\/4 = 25<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C <\/b><\/span><\/span><\/span>que, somados a 0<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C fornecem <\/b><\/span><\/span><\/span>25<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C.<\/b><\/span><\/span><\/span><\/p>\n

Na <\/b><\/span><\/span><\/span>Fahrenheit <\/b><\/span><\/span><\/span>voc\u00ea tem <\/b><\/span><\/span><\/span>4 intervalos de 5cm <\/b><\/span><\/span><\/span>que equivalem a <\/b><\/span><\/span><\/span>180<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C\/4 = 45<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C <\/b><\/span><\/span><\/span>que, somados a 32<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>F fornecem <\/b><\/span><\/span><\/span>77<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>F.<\/b><\/span><\/span><\/span><\/p>\n

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

 <\/p>\n

Voltar para os Exerc\u00edcios<\/a><\/span><\/h3>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

RESOLU\u00c7\u00d5ES 01- 02- A seguir, a teoria: Primeira lei de Kepler (lei das \u00f3rbitas) “As \u00f3rbitas que os planetas descrevem ao redor do Sol s\u00e3o el\u00edpticas, com o Sol ocupando um dos focos da elipse”. Numa elipse (figura acima), para qualquer posi\u00e7\u00e3o do ponto P a soma das dist\u00e2ncias FP com PF\u2019 \u00e9 sempre a mesma. Segunda lei de Kepler<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":348,"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-350","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/350","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=350"}],"version-history":[{"count":1,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/350\/revisions"}],"predecessor-version":[{"id":351,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/350\/revisions\/351"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/348"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}