{"id":1252,"date":"2015-08-26T00:57:51","date_gmt":"2015-08-26T00:57:51","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1252"},"modified":"2024-08-23T13:19:50","modified_gmt":"2024-08-23T13:19:50","slug":"resolucao-comentada-dos-exercicios-de-vestibulares-sobre-funcao-horaria-da-velocidade-e-da-aceleracao-do-mhs","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/mecanica\/dinamica\/mhs\/funcao-horaria-da-velocidade-e-da-aceleracao-do-mhs\/resolucao-comentada-dos-exercicios-de-vestibulares-sobre-funcao-horaria-da-velocidade-e-da-aceleracao-do-mhs\/","title":{"rendered":"Fun\u00e7\u00e3o hor\u00e1ria da velocidade e da acelera\u00e7\u00e3o do MHS – Resolu\u00e7\u00e3o"},"content":{"rendered":"

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre<\/b><\/span><\/span><\/span><\/p>\n

Fun\u00e7\u00e3o hor\u00e1ria da velocidade e da acelera\u00e7\u00e3o do MHS<\/b><\/span><\/span><\/span><\/p>\n

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

a) A=4m\u00a0\u00a0 \u00a0\u00a0\u00a0w=prad\/s\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0j<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>=prad<\/b><\/span><\/span><\/p>\n

v= -wAsen(<\/b><\/span><\/span><\/span>j<\/b><\/span><\/span>o<\/b><\/span><\/span><\/span><\/sub>\u00a0+ wt)\u00a0 —\u00a0 v= -p.4.sen(p\u00a0+\u00a0pt)\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>v= – 4p.sen(p\u00a0+\u00a0pt)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) v maxima\u00a0 —\u00a0 v<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>= w.A\u00a0 —\u00a0 v<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=\u00a0p.4\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>v<\/b><\/span><\/span>m\u00e1ximo<\/b><\/span><\/span><\/sub>= +4pm\/s<\/b><\/span><\/span><\/p>\n

v m\u00ednima\u00a0 —\u00a0 v<\/b><\/span><\/span>m\u00ednima<\/b><\/span><\/span><\/sub>= -w.A\u00a0 —\u00a0 v<\/b><\/span><\/span>m\u00ednima<\/b><\/span><\/span><\/sub>= -p.4\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>v<\/b><\/span><\/span>m\u00ednima<\/b><\/span><\/span><\/sub>= – 4pm\/s<\/b><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

d) a= -w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.A.cos(j<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>\u00a0+ wt) \u00a0\u00a0—\u00a0 a= -p<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.4.cos(<\/b><\/span><\/span>p<\/b><\/span><\/span><\/span>\u00a0+\u00a0<\/b><\/span><\/span>p<\/b><\/span><\/span><\/span>t)\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>a= -4p<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.cos(<\/b><\/span><\/span>p<\/b><\/span><\/span><\/span>\u00a0+\u00a0<\/b><\/span><\/span>p<\/b><\/span><\/span><\/span>t)<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/p>\n

e) acelera\u00e7\u00e3o m\u00e1xima\u00a0 —\u00a0 a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>= w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>A\u00a0 —\u00a0\u00a0\u00a0<\/b><\/span><\/span>a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>= +4p<\/b><\/span><\/span>2\u00a0<\/b><\/span><\/span><\/sup>m\/s<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/p>\n

acelera\u00e7\u00e3o m\u00ednima\u00a0 —\u00a0 a<\/b><\/span><\/span>m\u00ednima<\/b><\/span><\/span><\/sub>= – w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>A —\u00a0\u00a0\u00a0<\/b><\/span><\/span>a<\/b><\/span><\/span>m\u00ednima<\/b><\/span><\/span><\/sub>= – 4p<\/b><\/span><\/span>2\u00a0<\/b><\/span><\/span><\/sup>m\/s<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/p>\n

e)<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/sup><\/p>\n

\u00a0<\/sup><\/p>\n

f)<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

 <\/p>\n

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

 <\/p>\n

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

a= -w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>Acos<\/b><\/span><\/span>j<\/b><\/span><\/span><\/span>\u00a0 —\u00a0 qdo x=A= 1\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>j<\/b><\/span><\/span><\/span>=<\/b><\/span><\/span>p<\/b><\/span><\/span><\/span>\u00a0 —\u00a0\u00a0 a= 4\u00a0 — \u00a04 = -w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.(1).cosp\u00a0 —\u00a0 4 = -w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.(1).(-1)\u00a0 —\u00a0 w =\u00a0\u00d64\u00a0 —\u00a0 w = 2 rad\/s\u00a0\u00a0 \u00a0\u00a0<\/b><\/span><\/span><\/p>\n

 <\/p>\n

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

 <\/p>\n

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

R=A=20\/2\u00a0 —\u00a0 R=10cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 f=60rpm=60\/60\u00a0 —\u00a0\u00a0 f=1Hz\u00a0 —\u00a0 T=1s<\/b><\/span><\/span><\/p>\n

W=2p\/T\u00a0 —\u00a0 w=2p\/1\u00a0 —\u00a0 w=2p\u00a0rad\/s<\/b><\/span><\/span><\/p>\n

V \u00e9 m\u00e1xima quando\u00a0j=3p\/2, sendo sen3p\/2= – 1\u00a0 —\u00a0 v= -w.A.senj\u00a0 —\u00a0 v= -w.10.sen3p\/2\u00a0 —\u00a0 v= -2p.10.(-1)<\/b><\/span><\/span><\/p>\n

V<\/b><\/span><\/span>max<\/b><\/span><\/span><\/sub>\u00a0= 20p\u00a0cm\/s<\/b><\/span><\/span><\/p>\n

 <\/p>\n

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

V<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=2pm\/s\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 —-\u00a0\u00a0\u00a0\u00a0 A=20cm=0,2m<\/b><\/span><\/span><\/p>\n

V<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>= w.A\u00a0 —\u00a0 2p=w.0,2\u00a0 —\u00a0 w=10prad\/s\u00a0 —\u00a0 w=2p\/T\u00a0 —\u00a0 10p=2p\/T\u00a0 —\u00a0 T=0,2s<\/b><\/span><\/span><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

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

a) v<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>=0 (vide gr\u00e1fico)<\/b><\/span><\/span><\/p>\n

Como v=0 nos extremos, sua fase inicial ou \u00e9 zero ou\u00a0prad e observando o\u00a0 gr\u00e1fico verificamos que\u00a0j<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>=prad<\/b><\/span><\/span><\/p>\n

b) T=ps (veja gr\u00e1fico)\u00a0 —\u00a0 w=2p\/T\u00a0 —\u00a0 w=2p\/p\u00a0 —\u00a0 w=2rad\/s<\/b><\/span><\/span><\/p>\n

v<\/b><\/span><\/span>m\u00e1ximo<\/b><\/span><\/span><\/sub>=10m\/s (veja gr\u00e1fico)\u00a0 —\u00a0 v<\/b><\/span><\/span>m\u00e1ximo<\/b><\/span><\/span><\/sub>=wA\u00a0 —\u00a0 10=2A\u00a0 —\u00a0 A=5m\u00a0<\/b><\/span><\/span><\/p>\n

c) \u00e9 a amplitude, ou seja, 5m<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

d) a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.A\u00a0 —\u00a0 a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=2<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.5\u00a0 —\u00a0 a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=20m\/s<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/p>\n

 <\/p>\n

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

Quando o carrinho se choca com a mola, o m\u00f3dulo de V<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>\u00a0\u00e9 m\u00e1ximo e vale v<\/b><\/span><\/span>m\u00e1ximo<\/b><\/span><\/span><\/sub>=w.A\u00a0 —\u00a0\u00a0 V<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>=w.A\u00a0 —\u00a0 V<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>=2p\/T.A\u00a0 —<\/b><\/span><\/span><\/p>\n

T=2pA\/V<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/p>\n

\u00a0<\/sub><\/p>\n

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

a) Observe pelo gr\u00e1fico que o per\u00edodo do movimento vale T=0,2s. Como a freq\u00fc\u00eancia f \u00e9 o inverso do per\u00edodo T, temos\u00a0 f=1\/T<\/b><\/span><\/span><\/p>\n

—\u00a0 f=1\/0,2\u00a0 —\u00a0 f=5Hz.<\/b><\/span><\/span><\/p>\n

A amplitude \u00e1 a dist\u00e2ncia da origem ao ponto m\u00e1ximo. Logo, A=0,1m<\/b><\/span><\/span><\/p>\n

Pulsa\u00e7\u00e3o – ou velocidade angular\u00a0 —\u00a0 w=2p\/T\u00a0 —\u00a0 w=2p\/0,2\u00a0 —\u00a0 w=10prad\/s.\u00a0<\/b><\/span><\/span><\/p>\n

b) Equa\u00e7\u00e3o da elonga\u00e7\u00e3o ou da posi\u00e7\u00e3o, na vertical \u00e9 y=-Acos(j<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>\u00a0+ wt)\u00a0 —\u00a0 y= .0,1.cos(0 + 10pt)\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>y= 0,1cos10p<\/b><\/span><\/span><\/p>\n

j<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sub>=0, pois, quando t=o, A=+0,1m (elonga\u00e7\u00e3o m\u00e1xima).\u00a0\u00a0<\/b><\/span><\/span><\/p>\n

 <\/p>\n

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

a) A=7cm\u00a0 —\u00a0 w=<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span>\/2rad\/s\u00a0 —\u00a0 w=2<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span>\/T\u00a0 —\u00a0\u00a0p\/2=2p\/T\u00a0 —\u00a0 T=4s<\/b><\/span><\/span><\/span><\/p>\n

Para que o m\u00f3vel v\u00e1 da posi\u00e7\u00e3o de equil\u00edbrio at\u00e9 o ponto de elonga\u00e7\u00e3o m\u00e1xima, ele se move durante 1\/4\u00a0 de seu per\u00edodo, que \u00e9 de 4s (tempo que demora para efetuar uma volta completa) \u00a0\u00a0— \u00a0t=T\/4\u00a0 —\u00a0 t=4\/4\u00a0 —\u00a0<\/b><\/span><\/span>\u00a0t=1s<\/b><\/span><\/span><\/p>\n

b) v<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=w.A=p\/2.7\u00a0 —\u00a0 v<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=3,5pcm\/s<\/b><\/span><\/span><\/p>\n

a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=w<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.A\u00a0 —\u00a0 a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=(p\/2)<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>.7\u00a0 —\u00a0 a<\/b><\/span><\/span>m\u00e1xima<\/b><\/span><\/span><\/sub>=1,75p<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup>cm\/s<\/b><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/p>\n

 <\/p>\n

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

12-\u00a0<\/b><\/span><\/span>a) O gr\u00e1fico fornece a posi\u00e7\u00e3o da pe\u00e7a em fun\u00e7\u00e3o do tempo\u00a0 —\u00a0 o per\u00edodo \u00e9 o intervalo de tempo para que a situa\u00e7\u00e3o cinem\u00e1tica se repete\u00a0 —\u00a0 observe que isso ocorre a cada 4s\u00a0 —\u00a0 portanto T=4s\u00a0 —\u00a0 a frequ\u00eancia \u00e9 o inverso do per\u00edodo\u00a0 —\u00a0 f=1\/T=1\/4\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>f=0,25 Hz<\/b><\/span><\/span><\/p>\n

b) A velocidade da pe\u00e7a \u00e9 nula nos instantes em que a elonga\u00e7\u00e3o \u00e9 m\u00e1xima ou m\u00ednima, quando ocorre invers\u00e3o no sentido do movimento, ou seja:<\/b><\/span><\/span>\u00a0t = 1 s; t = 3 s e t = 5 s.<\/b><\/span><\/span><\/p>\n

c) Os instantes em que a acelera\u00e7\u00e3o da pe\u00e7a \u00e9 m\u00e1xima (em m\u00f3dulo) s\u00e3o os instantes em a for\u00e7a el\u00e1stica tem intensidade m\u00e1xima. Como F = k |x|, a for\u00e7a \u00e9 m\u00e1xima onde a elonga\u00e7\u00e3o \u00e9 m\u00e1xima ou m\u00ednima, ou seja:<\/b><\/span><\/span>\u00a0t = 1 s; t = 3 s e t = 5 s. \u00a0<\/b><\/span><\/span><\/p>\n

 <\/p>\n

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

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre Fun\u00e7\u00e3o hor\u00e1ria da velocidade e da acelera\u00e7\u00e3o do MHS 1- a) A=4m\u00a0\u00a0 \u00a0\u00a0\u00a0w=prad\/s\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0jo=prad v= -wAsen(jo\u00a0+ wt)\u00a0 —\u00a0 v= -p.4.sen(p\u00a0+\u00a0pt)\u00a0 —\u00a0\u00a0v= – 4p.sen(p\u00a0+\u00a0pt)\u00a0 b) v maxima\u00a0 —\u00a0 vm\u00e1xima= w.A\u00a0 —\u00a0 vm\u00e1xima=\u00a0p.4\u00a0 —\u00a0\u00a0vm\u00e1ximo= +4pm\/s v m\u00ednima\u00a0 —\u00a0 vm\u00ednima= -w.A\u00a0 —\u00a0 vm\u00ednima= -p.4\u00a0 —\u00a0\u00a0vm\u00ednima= – 4pm\/s c) d) a= -w2.A.cos(jo\u00a0+ wt) \u00a0\u00a0—\u00a0 a= -p2.4.cos(p\u00a0+\u00a0pt)\u00a0 —\u00a0\u00a0a= -4p2.cos(p\u00a0+\u00a0pt)\u00a0<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1248,"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-1252","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1252","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=1252"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1252\/revisions"}],"predecessor-version":[{"id":10838,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1252\/revisions\/10838"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1248"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}