{"id":3577,"date":"2018-02-12T02:05:51","date_gmt":"2018-02-12T02:05:51","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=3577"},"modified":"2024-08-21T13:19:20","modified_gmt":"2024-08-21T13:19:20","slug":"resolucao-comentada-sistema-de-unidades-analise-dimensional","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/enem\/sistema-de-unidades-analise-dimensional\/resolucao-comentada-sistema-de-unidades-analise-dimensional\/","title":{"rendered":"Sistema de Unidades \u2013 An\u00e1lise Dimensional – Resolu\u00e7\u00e3o"},"content":{"rendered":"

Resolu\u00e7\u00e3o Comentada<\/b><\/span><\/span><\/span><\/p>\n

Sistema de Unidades \u2013 An\u00e1lise Dimensional<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

01-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Utilizando um a regra de tr\u00eas\u00a0 —\u00a0 8s \u2013 10<\/b><\/span><\/span><\/span>-2 <\/b><\/span><\/span><\/sup><\/span>km<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 32.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>s \u2013 n km<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 n=32.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>.10<\/b><\/span><\/span><\/span>-2<\/b><\/span><\/span><\/sup><\/span>\/8\u00a0 —\u00a0 n = 4.10<\/b><\/span><\/span><\/span>4 <\/b><\/span><\/span><\/sup><\/span>km<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sup><\/span>= 40.000 km<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

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

02-<\/b><\/span><\/span><\/span> <\/b>O ano-luz \u00e9, uma unidade de\u00a0comprimento\u00a0 —\u00a0 ela corresponde ao espa\u00e7o percorrido por um raio de luz em 1 ano, no v\u00e1cuo, com velocidade de 3.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span>m\/s\u00a0 —\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

R- D<\/b><\/span><\/span><\/span> <\/b>—\u00a0 Observa\u00e7\u00e3o: \u00e9 uma medida grande demais para nossas aplica\u00e7\u00f5es comuns aqui na Terra.\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Essa unidade se destina a marcar dist\u00e2ncias no espa\u00e7o c\u00f3smico, entre as estrelas de uma mesma gal\u00e1xia ou entre gal\u00e1xias distintas. Ela \u00e9 \u00fatil para os astr\u00f4nomos.<\/b><\/span><\/span><\/span><\/p>\n

03<\/b><\/span><\/span><\/span>–\u00a0Trata-se da equa\u00e7\u00e3o de Torricelli, V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0+ 2.a.h\u00a0 — com V = 0\u00a0 —\u00a0 cuja dedu\u00e7\u00e3o \u00e9 feita a partir de V<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/sub><\/span> = \u0394S\/\u0394t\u00a0 —\u00a0 onde\u00a0\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/sub><\/span>= (V + V<\/b><\/span><\/span><\/span>0<\/b><\/span><\/span><\/sub><\/span>)\/2=h\/t\u00a0 —\u00a0 h=(V + V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>)t\/2\u00a0 —\u00a0 h=V<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/sub><\/span>.t\/2\u00a0 —\u00a0 observe nessa equa\u00e7\u00e3o que h \u00e9 proporcional a V<\/b><\/span><\/span><\/span>m<\/b><\/span><\/span><\/sub><\/span>\u00a0e a t\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- E<\/b><\/span><\/span><\/span><\/p>\n

04-\u00a0Calorias corresponde \u00e0 unidade de energia, que no SI \u00e9 medida em joules (J)\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- D<\/b><\/span><\/span><\/span><\/p>\n

05-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>1 nanograma=10<\/b><\/span><\/span><\/span>-9<\/b><\/span><\/span><\/sup><\/span>\u00a0g\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- B\u00a0\u00a0<\/b><\/span><\/span><\/span>—\u00a0 veja tabela abaixo<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

06-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>1kW equivale a 10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>W\u00a0 —\u00a0 1h equivale a 3,6.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>s\u00a0 —\u00a0 rela\u00e7\u00e3o entre Joule e w.s\u00a0 —\u00a0\u00a0 1J = 1w.s\u00a0 —<\/b><\/span><\/span><\/span><\/p>\n

\u00a0 1kWh = 10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>W . 3,6.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>s = 3,6.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>W.s\u00a0 —\u00a0 1kWh = 3,6.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>J\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- D<\/b><\/span><\/span><\/span><\/p>\n

07-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>De acordo com o texto o di\u00e2metro de um fio de cabelo pode medir cerca de<\/b><\/span><\/span><\/span><\/p>\n

100.000nm = 10<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/sup><\/span>nm=10<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/sup><\/span>.10<\/b><\/span><\/span><\/span>-9<\/b><\/span><\/span><\/sup><\/span> m =10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>m =10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.10<\/b><\/span><\/span><\/span>-6<\/b><\/span><\/span><\/sup><\/span> m =100.10<\/b><\/span><\/span><\/span>-6<\/b><\/span><\/span><\/sup><\/span>m=100mm\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- E<\/b><\/span><\/span><\/span><\/p>\n

08<\/b><\/span><\/span><\/span>\u00a0\u00a0–\u00a01. Correta\u00a0 —\u00a0 6 m<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= 6\u00a0(100 cm)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= 6.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>\u00a0cm<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= 60.000 cm<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

2. Correta\u00a0 —\u00a0 216 km\/h = 216\/3,6\u00a0\"\"m\/s = 60 m\/s.<\/b><\/span><\/span><\/span><\/p>\n

3. Errada\u00a0 —\u00a0 3.000 m<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0= 3.000\u00a0(1.000 L) = 3.000.000 L.<\/b><\/span><\/span><\/span><\/p>\n

4. Correta\u00a0 —\u00a0 7.200 s =7.200\/3.600h = 2 h.<\/b><\/span><\/span><\/span><\/p>\n

5. Correta\u00a0 —\u00a0\u00a02,5\u00a010<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/sup><\/span>\u00a0g =\u00a0\"\"2,5.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0kg = 250 g\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

09-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Energia de um caminh\u00e3o\u00a0 —\u00a0 E<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=10kWh=10.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>Wh=10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>Wh\u00a0 —\u00a0 Energia total\u00a0 — E<\/b><\/span><\/span><\/span>t <\/b><\/span><\/span><\/sub><\/span>= 200.mil.MWh=200.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>Wh=2.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>Wh\u00a0 —\u00a0 regra de tr\u00eas\u00a0 —\u00a0 1 kg de carv\u00e3o \u2013 10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>Wh\u00a0 —\u00a0 M de carv\u00e3o \u2013 2.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>Wh\u00a0 —\u00a0 M=2.10<\/b><\/span><\/span><\/span>11<\/b><\/span><\/span><\/sup><\/span>\/10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 M=2.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>\u00a0kg de carv\u00e3o\u00a0 —\u00a0 outra regra de tr\u00eas\u00a0 —\u00a0 1 caminh\u00e3o \u2013 1ton=10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>kg\u00a0 —\u00a0 n caminh\u00f5es \u2013 2.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>kg\u00a0 —\u00a0 n=2.10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>\/10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 n=2.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0caminh\u00f5es\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- D<\/b><\/span><\/span><\/span><\/p>\n

10-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Carlos tem 10 minutos em cada 30 para viajar na BOMPASSEIO e 20 minutos a cada 30 para viajar na ANDABEM. <\/b><\/span><\/span><\/span><\/p>\n

Assim, considerando que a express\u00e3o \u201cduas vezes maior\u201d significa o dobro, a probabilidade de Carlos viajar num \u00f4nibus da empresa ANDABEM \u00e9 duas vezes maior do que a probabilidade de ele viajar num \u00f4nibus da empresa BOMPASSEIO.<\/b><\/span><\/span><\/span><\/p>\n

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

11-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe que a medida de Pedro possui 4 algarismos significativos enquanto que a de Gabriel 3\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- B<\/b><\/span><\/span><\/span><\/p>\n

12-<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>tota<\/b><\/span><\/span><\/sub><\/span>l = 1.000.000.000km<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>.10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>m<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>tota<\/b><\/span><\/span><\/sub><\/span>l=10<\/b><\/span><\/span><\/span>18<\/b><\/span><\/span><\/sup><\/span>m<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 — \u00a0V<\/b><\/span><\/span><\/span>peixe<\/b><\/span><\/span><\/sub><\/span>=100×100.100\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>peixe<\/b><\/span><\/span><\/sub><\/span>=10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>m<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>total<\/b><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span>peixe<\/b><\/span><\/span><\/sub><\/span>=10<\/b><\/span><\/span><\/span>18<\/b><\/span><\/span><\/sup><\/span>m<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\/10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>m<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>total<\/b><\/span><\/span><\/sub><\/span>\/V<\/b><\/span><\/span><\/span>peixe<\/b><\/span><\/span><\/sub><\/span>=10<\/b><\/span><\/span><\/span>12<\/b><\/span><\/span><\/sup><\/span>\u00a0beijos\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- B<\/b><\/span><\/span><\/span><\/p>\n

13-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>E=1354kWh=1,354.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>W.3,6.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>s\u00a0 —\u00a0 E=4,9.10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>Ws\u00a0 —\u00a0 OG=10.10<\/b><\/span><\/span><\/span>9<\/b><\/span><\/span><\/sup><\/span>=10<\/b><\/span><\/span><\/span>10<\/b><\/span><\/span><\/sup><\/span>\u00a0J\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- A<\/b><\/span><\/span><\/span><\/p>\n

14-<\/b><\/span><\/span><\/span>\u00a0\u00c1rea da superf\u00edcie da Terra\u00a0 —\u00a0 STerra=\u03c0.r<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=3,14.(6,4.10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 S<\/b><\/span><\/span><\/span>Terra<\/b><\/span><\/span><\/sub><\/span>=129.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0km<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 ano 2000\u00a0 —\u00a0 S\u00b4=5%\u00a0 de 129.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 S\u2019=0,05×129.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 S\u2019=6,45.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 6,45>3,16\u00a0 —\u00a0 OG=10.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 OG=10<\/b><\/span><\/span><\/span>7<\/b><\/span><\/span><\/sup><\/span>\u00a0km<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>R- C<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

 <\/p>\n

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

Resolu\u00e7\u00e3o Comentada Sistema de Unidades \u2013 An\u00e1lise Dimensional   01-\u00a0Utilizando um a regra de tr\u00eas\u00a0 —\u00a0 8s \u2013 10-2 km2\u00a0 —\u00a0 32.106s \u2013 n km2\u00a0 —\u00a0 n=32.106.10-2\/8\u00a0 —\u00a0 n = 4.104 km2 = 40.000 km2. R- E 02- O ano-luz \u00e9, uma unidade de\u00a0comprimento\u00a0 —\u00a0 ela corresponde ao espa\u00e7o percorrido por um raio de luz em 1 ano, no v\u00e1cuo,<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3573,"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-3577","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3577","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=3577"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3577\/revisions"}],"predecessor-version":[{"id":10706,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3577\/revisions\/10706"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/3573"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=3577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}