{"id":4879,"date":"2020-01-10T03:11:57","date_gmt":"2020-01-10T03:11:57","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=4879"},"modified":"2024-09-04T14:57:09","modified_gmt":"2024-09-04T14:57:09","slug":"resolucao-comentada-trabalho-e-energia-2018-2019","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/vestibulares-recentes\/mecanica\/trabalho-e-energia-2018-2019\/resolucao-comentada-trabalho-e-energia-2018-2019\/","title":{"rendered":"Resolu\u00e7\u00e3o Comentada \u2013 Trabalho e Energia 2018\/2019"},"content":{"rendered":"

Resolu\u00e7\u00e3o Comentada \u2013 Trabalho e Energia<\/span><\/span><\/span><\/p>\n

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

Express\u00f5es matem\u00e1ticas<\/b><\/span><\/span><\/span>\u00a0dos\u00a0<\/b><\/span><\/span><\/span>dois tipos de energias envolvidos no fen\u00f4meno<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

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

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

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

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

<\/p>\n

Bola 2<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

O mesmo \u00e9 v\u00e1lido para a bola 2 s\u00f3 que agora Epa\u00a0= 0,95%Epd<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>m2gH = 0,95m2.gh2\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span>h2\u00a0= 0,95H.<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

Como \u00e9\u00a0<\/b><\/span><\/span><\/span>pedida a diferen\u00e7a h2\u00a0\u2013 h1\u00a0voc\u00ea ter\u00e1\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span>h2\u00a0\u2013 h1<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span>= 0,95H \u2013 0,75H\u00a0<\/b><\/span><\/span><\/span>= 0,20H<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

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

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

J\u00e1 que\u00a0<\/b><\/span><\/span><\/span>podemos desprezar o atrito\u00a0<\/b><\/span><\/span><\/span>com o ar podemos\u00a0<\/b><\/span><\/span><\/span>considerar o sistema como conservativo\u00a0<\/b><\/span><\/span><\/span>e aplicar o\u00a0<\/b><\/span><\/span><\/span>princ\u00edpio da conserva\u00e7\u00e3o da energia mec\u00e2nica\u00a0<\/b><\/span><\/span><\/span>aplicando-o o\u00a0<\/b><\/span><\/span><\/span>durante qualquer ponto trajeto\u00a0<\/b><\/span><\/span><\/span>e considerando a\u00a0<\/b><\/span><\/span><\/span>energia mec\u00e2nica como constante durante todo o trajeto.<\/b><\/span><\/span><\/span><\/p>\n

O referencial adotado \u00e9 a posi\u00e7\u00e3o de equil\u00edbrio da lona onde h = 0.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

<\/p>\n

Essa\u00a0<\/b><\/span><\/span><\/span>fun\u00e7\u00e3o da energia cin\u00e9tica em fun\u00e7\u00e3o de h \u00e9 do segundo grau e o gr\u00e1fico \u00e9 uma par\u00e1bola com concavidade\u00a0<\/b><\/span><\/span><\/span>para baixo, pois o\u00a0<\/b><\/span><\/span><\/span>termo que antecede h2\u00a0\u00e9 negativo.<\/b><\/span><\/span><\/span><\/p>\n

Observe ainda que,\u00a0<\/b><\/span><\/span><\/span>quando h<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>= hm\u00edn\u00a0a energia cin\u00e9tica \u00e9 nula Ec\u00a0= 0\u00a0<\/b><\/span><\/span><\/span>(ele para, V = 0).<\/b><\/span><\/span><\/span><\/p>\n

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

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

Como\u00a0<\/b><\/span><\/span><\/span>qualquer tipo de atrito\u00a0<\/b><\/span><\/span><\/span>ou\u00a0<\/b><\/span><\/span><\/span>resist\u00eancia ao movimento \u00e9 desprezada\u00a0<\/b><\/span><\/span><\/span>o\u00a0<\/b><\/span><\/span><\/span>sistema<\/b><\/span><\/span><\/span>\u00a0pode ser considerado c<\/b><\/span><\/span><\/span>onservativo<\/b><\/span><\/span><\/span>\u00a0e voc\u00ea pode aplicar o\u00a0<\/b><\/span><\/span><\/span>princ\u00edpio da conserva\u00e7\u00e3o da energia mec\u00e2nica\u00a0<\/b><\/span><\/span><\/span>entre os pontos\u00a0<\/b><\/span><\/span><\/span>P e Q.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

Na\u00a0<\/b><\/span><\/span><\/span>posi\u00e7\u00e3o mais baixa Q\u00a0<\/b><\/span><\/span><\/span>as\u00a0<\/b><\/span><\/span><\/span>for\u00e7as<\/b><\/span><\/span><\/span>\u00a0que agem\u00a0<\/b><\/span><\/span><\/span>sobre<\/b><\/span><\/span><\/span>\u00a0a\u00a0<\/b><\/span><\/span><\/span>pessoa<\/b><\/span><\/span><\/span>\u00a0s\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

Seu\u00a0<\/b><\/span><\/span><\/span>peso P, vertical<\/b><\/span><\/span><\/span>\u00a0e para\u00a0<\/b><\/span><\/span><\/span>baixo<\/b><\/span><\/span><\/span>\u00a0de\u00a0<\/b><\/span><\/span><\/span>intensidade P =m.g<\/b><\/span><\/span><\/span>\u00a0= 60.10\u00a0\u00a0<\/b><\/span><\/span><\/span>P = 600 N.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

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

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

<\/p>\n

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

Defini\u00e7\u00e3o do Teorema da Energia Cin\u00e9tica<\/b><\/span><\/span><\/span>: \u201cO\u00a0<\/b><\/span><\/span><\/span>trabalho da resultante\u00a0<\/b><\/span><\/span><\/span>de\u00a0<\/b><\/span><\/span><\/span>todas<\/b><\/span><\/span><\/span>\u00a0as for\u00e7as que agem sobre um corpo\u00a0<\/b><\/span><\/span><\/span>\u00e9 igual \u00e0 varia\u00e7\u00e3o da energia cin\u00e9tica sofrida pelo corpo\u201d<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

As express\u00f5es acima\u00a0<\/b><\/span><\/span><\/span>s\u00e3o v\u00e1lidas seja a for\u00e7a resultante conservativa ou n\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

S\u00e3o dados:<\/b><\/span><\/span><\/span>\u00a0massa do sat\u00e9lite\u00a0<\/b><\/span><\/span><\/span>m = 6,0.103\u00a0kg\u00a0<\/b><\/span><\/span><\/span>\u00a0velocidade inicial do sat\u00e9lite\u00a0<\/b><\/span><\/span><\/span>Vi\u00a0= 0\u00a0<\/b><\/span><\/span><\/span>\u00a0velocidade final do sat\u00e9lite\u00a0<\/b><\/span><\/span><\/span>Vf\u00a0= 3,0.103\u00a0m\/s.<\/b><\/span><\/span><\/span><\/p>\n

<\/p>\n

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

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

<\/p>\n

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

Breve teoria<\/b><\/span><\/span><\/span><\/p>\n

Rela\u00e7\u00e3o entre pot\u00eancia m\u00e9dia (Pm) e velocidade m\u00e9dia (Vm)<\/b><\/span><\/span><\/span><\/p>\n

Considere uma\u00a0<\/b><\/span><\/span><\/span>for\u00e7a constante de intensidade F<\/b><\/span><\/span><\/span>\u00a0realizando um\u00a0<\/b><\/span><\/span><\/span>trabalho W<\/b><\/span><\/span><\/span>\u00a0num\u00a0<\/b><\/span><\/span><\/span>deslocamento d,<\/b><\/span><\/span><\/span>\u00a0de modo que a\u00a0<\/b><\/span><\/span><\/span>dire\u00e7\u00e3o de\u00a0F\u00a0forme um \u00e2ngulo\u00a0\u03b1<\/b><\/span><\/span><\/span>\u00a0com a\u00a0<\/b><\/span><\/span><\/span>dire\u00e7\u00e3o do deslocamento.<\/b><\/span><\/span><\/span><\/p>\n

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

<\/p>\n

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

<\/p>\n

2. Verdadeira<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0pelo\u00a0<\/b><\/span><\/span><\/span>gr\u00e1fico,<\/b><\/span><\/span><\/span>\u00a0quando\u00a0<\/b><\/span><\/span><\/span>t = 15 s<\/b><\/span><\/span><\/span>\u00a0e em\u00a0<\/b><\/span><\/span><\/span>qualquer instante entre 10 s e 20 s<\/b><\/span><\/span><\/span>\u00a0o\u00a0<\/b><\/span><\/span><\/span>objeto<\/b><\/span><\/span><\/span>\u00a0est\u00e1\u00a0<\/b><\/span><\/span><\/span>parado na posi\u00e7\u00e3o x = \u2013 20 m,\u00a0<\/b><\/span><\/span><\/span>sua\u00a0<\/b><\/span><\/span><\/span>velocidade \u00e9 nula\u00a0<\/b><\/span><\/span><\/span>e, consequentemente a\u00a0<\/b><\/span><\/span><\/span>acelera\u00e7\u00e3o a tamb\u00e9m ser\u00e1 nula (a = 0).<\/b><\/span><\/span><\/span><\/p>\n

Pela lei fundamental da din\u00e2mica\u00a0<\/b><\/span><\/span><\/span>FR\u00a0= m.a\u00a0<\/b><\/span><\/span><\/span>\u00a0FR\u00a0= m.0\u00a0\u00a0<\/b><\/span><\/span><\/span>FR\u00a0= 0.<\/b><\/span><\/span><\/span><\/p>\n

3. Falsa<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>entre 0 s e 10 s\u00a0\u00a0\u2206x =\u00a0<\/b><\/span><\/span><\/span>x \u2013 xo<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>= -20 \u2013 0 = \u2013 20m (retr\u00f3grado).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>entre 10 s e 20 s\u00a0\u00a0\u2206x = 0\u00a0\u00a0parado na posi\u00e7\u00e3o x = \u2013 20m.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>entre 20 s e 30 s\u00a0\u00a0\u2206x =\u00a0<\/b><\/span><\/span><\/span>x \u2013 xo<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>= 20 \u2013 (-20) = 40m (progressivo).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>entre 30 s e 40 s\u00a0\u00a0\u2206x = 0\u00a0\u00a0parado na posi\u00e7\u00e3o x = 20m.<\/b><\/span><\/span><\/span><\/p>\n

\u2206<\/span>xtotal\u00a0=\u00a0<\/b><\/span><\/span><\/span>-20 + 40\u00a0<\/b><\/span><\/span><\/span>= + 20 m (progressivo)\u00a0<\/b><\/span><\/span><\/span>ou\u00a0<\/b><\/span><\/span><\/span>\u2206xtotal\u00a0= x \u2013 xo<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>= 20 \u2013 0\u00a0<\/b><\/span><\/span><\/span>= + 20m (progressivo).<\/b><\/span><\/span><\/span><\/p>\n

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

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

Rela\u00e7\u00e3o entre pot\u00eancia m\u00e9dia (Pm) e velocidade m\u00e9dia (Vm<\/b><\/span><\/span><\/span>)<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

Considere uma\u00a0<\/b><\/span><\/span><\/span>for\u00e7a constante de intensidade F<\/b><\/span><\/span><\/span>\u00a0realizando um\u00a0<\/b><\/span><\/span><\/span>trabalho W<\/b><\/span><\/span><\/span>\u00a0num\u00a0<\/b><\/span><\/span><\/span>deslocamento d,<\/b><\/span><\/span><\/span>\u00a0de modo que a\u00a0<\/b><\/span><\/span><\/span>dire\u00e7\u00e3o de\u00a0F\u00a0forme um \u00e2ngulo\u00a0\u03b1<\/b><\/span><\/span><\/span>\u00a0com a\u00a0<\/b><\/span><\/span><\/span>dire\u00e7\u00e3o do deslocamento.<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

<\/p>\n

A\u00a0<\/b><\/span><\/span><\/span>pot\u00eancia instant\u00e2nea Po<\/b><\/span><\/span><\/span>\u00a0\u00e9 obtida substituindo-se a\u00a0<\/b><\/span><\/span><\/span>velocidade m\u00e9dia Vm\u00a0pela instant\u00e2nea V<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>Po\u00a0= F.V.<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

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

Resolu\u00e7\u00e3o Comentada \u2013 Trabalho e Energia 01- Express\u00f5es matem\u00e1ticas\u00a0dos\u00a0dois tipos de energias envolvidos no fen\u00f4meno R- B 02- R-C 03- Bola 2 O mesmo \u00e9 v\u00e1lido para a bola 2 s\u00f3 que agora Epa\u00a0= 0,95%Epd\u00a0\u00a0m2gH = 0,95m2.gh2\u00a0\u00a0h2\u00a0= 0,95H. Como \u00e9\u00a0pedida a diferen\u00e7a h2\u00a0\u2013 h1\u00a0voc\u00ea ter\u00e1\u00a0\u00a0h2\u00a0\u2013 h1\u00a0= 0,95H \u2013 0,75H\u00a0= 0,20H R- A 04- J\u00e1 que\u00a0podemos desprezar o atrito\u00a0com o ar<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":4877,"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-4879","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4879","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=4879"}],"version-history":[{"count":1,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4879\/revisions"}],"predecessor-version":[{"id":4880,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4879\/revisions\/4880"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/4877"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=4879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}