{"id":1279,"date":"2015-09-02T01:09:26","date_gmt":"2015-09-02T01:09:26","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=1279"},"modified":"2024-08-23T13:15:06","modified_gmt":"2024-08-23T13:15:06","slug":"associacao-de-molas","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/mecanica\/dinamica\/mhs\/associacao-de-molas\/","title":{"rendered":"Associa\u00e7\u00e3o de molas"},"content":{"rendered":"

Associa\u00e7\u00e3o de molas<\/b><\/span><\/span><\/span><\/p>\n

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

Duas molas <\/b><\/span><\/span><\/span>1 e 2<\/b><\/span><\/span><\/span> tem <\/b><\/span><\/span><\/span>constantes el\u00e1sticas k<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e k<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>,<\/b><\/span><\/span><\/span> respectivamente.<\/b><\/span><\/span><\/span> Podemos <\/b><\/span><\/span><\/span>associ\u00e1-las em s\u00e9rie<\/b><\/span><\/span><\/span> <\/b>ou em paralelo<\/b><\/span><\/span><\/span>. Em <\/b><\/span><\/span><\/span>cada uma<\/b><\/span><\/span><\/span> dessas associa\u00e7\u00f5es podemos<\/b><\/span><\/span><\/span>substituir as duas molas<\/b><\/span><\/span><\/span> por uma \u00fanica, que produza o <\/b><\/span><\/span><\/span>mesmo efeito<\/b><\/span><\/span><\/span> e que chamamos de\u00a0<\/b><\/span><\/span><\/span>mola equivalente de constante el\u00e1stica<\/b><\/span><\/span><\/span> k<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Associa\u00e7\u00e3o em paralelo<\/b><\/span><\/span><\/span><\/p>\n

Nesse caso a <\/b><\/span><\/span><\/span>deforma\u00e7\u00e3o <\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/span> sofrida por <\/b><\/span><\/span><\/span>cada uma das molas \u00e9 a mesma.<\/b><\/span><\/span><\/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\"\"<\/span><\/p>\n

Quando <\/b><\/span><\/span><\/span>deformadas de <\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/span>, a mola 1 fica sujeita a uma for\u00e7a <\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= k<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.x<\/b><\/span><\/span><\/span> e a mola 2 a uma for\u00e7a <\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= k<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.x<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>mola equivalente<\/b><\/span><\/span><\/span>, quando submetida \u00e0 <\/b><\/span><\/span><\/span>mesma for\u00e7a F,<\/b><\/span><\/span><\/span> sofre a <\/b><\/span><\/span><\/span>mesma deforma\u00e7\u00e3o x<\/b><\/span><\/span><\/span> de modo que <\/b><\/span><\/span><\/span>F = k<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>.x.<\/b><\/span><\/span><\/span><\/p>\n

Observe que <\/b><\/span><\/span><\/span>F = F<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0+ F<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\" \u00a0<\/b><\/span><\/span><\/sub><\/span>k<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>.x = k<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.x + k<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.x<\/b><\/span><\/span><\/span> \"\"<\/b><\/span><\/span><\/span> <\/b>k<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span> = k<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> + k<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se voc\u00ea tiver <\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/span>molas<\/b><\/span><\/span><\/span> \u00a0\"\" <\/b><\/span><\/span><\/span>K<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span> = K<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> + K<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> + K<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span> + …. K<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Associa\u00e7\u00e3o em s\u00e9rie<\/b><\/span><\/span><\/span><\/p>\n

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

Nesse caso as <\/b><\/span><\/span><\/span>molas 1 e 2 est\u00e3o sujeitas \u00e0 mesma for\u00e7a F<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>sofrem deforma\u00e7\u00f5es diferentes<\/b><\/span><\/span><\/span> <\/b>x<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e x<\/b><\/span><\/span><\/span>2.<\/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\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

Se voc\u00ea tiver <\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/span>molas<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/span>\/<\/b><\/span><\/span><\/span>K<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span> = 1\/K<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> + 1\/K<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> + 1\/K<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span> + …. 1\/K<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

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

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

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\"\" A <\/b><\/span><\/span>constante el\u00e1stica<\/b><\/span><\/span><\/span> \u00e9 algo que <\/b><\/span><\/span><\/span>define a mola<\/b><\/span><\/span><\/span>,<\/b><\/span><\/span><\/span> isto \u00e9, suas <\/b><\/span><\/span>caracter\u00edsticas f\u00edsicas<\/b><\/span><\/span><\/span> <\/b>(maleabilidade,<\/b><\/span><\/span><\/span> <\/b>maciez),<\/b><\/span><\/span><\/span> <\/b>constantes el\u00e1sticas maiores tendem a ter uma rigidez maior<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Associa\u00e7\u00e3o em s\u00e9rie<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" Associa\u00e7\u00e3o em paralelo<\/b><\/span><\/span><\/span><\/p>\n

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

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

\"\" Na associa\u00e7\u00e3o <\/b><\/span><\/span><\/span>de molas em s\u00e9rie onde 1\/k<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>\u00a0= 1\/k<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0+ 1\/k<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>, o valor de <\/b><\/span><\/span><\/span>k<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>\u00a0fica bastante reduzido,<\/b><\/span><\/span><\/span> sendo que a <\/b><\/span><\/span><\/span>mola equivalente \u00e9 menos r\u00edgida,<\/b><\/span><\/span><\/span> <\/b>mais deform\u00e1vel.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se <\/b><\/span><\/span><\/span>quisermos aumentar a rigidez da mola equivalente<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>torna-a menos deform\u00e1vel<\/b><\/span><\/span><\/span>, devemos <\/b><\/span><\/span><\/span>associar as molas em paralelo, onde k<\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/sub><\/span>= k<\/b><\/span><\/span><\/span>1\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0+ k<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span> <\/b>\u00c9 mais eficaz e ocupa menos espa\u00e7o.<\/b><\/span><\/span><\/span><\/p>\n

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

\u00a0<\/span>Voc\u00ea <\/b><\/span><\/span>parte uma mola de <\/b><\/span><\/span><\/span>constante el\u00e1stica <\/b><\/span><\/span><\/span>K<\/b><\/span><\/span><\/span> em <\/b><\/span><\/span>duas partes iguais<\/b><\/span><\/span><\/span>, de modo a obter <\/b><\/span><\/span>duas molas id\u00eanticas.<\/b><\/span><\/span><\/span><\/p>\n

\"\" C\u00e1lculo da <\/b><\/span><\/span><\/span>constante el\u00e1stica K\u2019 de cada peda\u00e7o<\/b><\/span><\/span><\/span> que \u00e9 <\/b><\/span><\/span><\/span>diferente de K,<\/b><\/span><\/span><\/span> pois apesar do material ser o mesmo, o <\/b><\/span><\/span><\/span>n\u00famero de espiras diminui:<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>mola original<\/b><\/span><\/span><\/span> de <\/b><\/span><\/span><\/span>constante el\u00e1stica K<\/b><\/span><\/span><\/span> \u00e9 composta das <\/b><\/span><\/span><\/span>duas metades de constantes el\u00e1sticas K\u2019<\/b><\/span><\/span><\/span>,<\/b><\/span><\/span><\/span> <\/b>associadas em s\u00e9rie.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\" Na <\/b><\/span><\/span><\/span>associa\u00e7\u00e3o em s\u00e9rie 1\/K = 1\/K\u2019 + 1\/K\u2019<\/b><\/span><\/span><\/span> \"\" 1\/K = 2\/K\u2019 \"\" <\/b><\/span><\/span><\/span>K\u2019 = 2K<\/b><\/span><\/span><\/span> <\/b>(a rigidez de cada metade fica o dobro da constante da mola original, tornando-as menos deform\u00e1veis).<\/b><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span>voc\u00ea associar cada uma dessas metades de (K\u2019 = 2K) em paralelo<\/b><\/span><\/span><\/span> <\/b>voc\u00ea obter\u00e1 uma mola de<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

constante el\u00e1stica equivalente <\/b><\/span><\/span><\/span>K<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span>,<\/b><\/span><\/span><\/span> tal que <\/b><\/span><\/span>K<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span> = K\u2019 + K\u2019<\/b><\/span><\/span><\/span> = 2K + 2K \"\" <\/b><\/span><\/span>K<\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/sub><\/span> = 4K<\/b><\/span><\/span><\/span> <\/b>(a rigidez da mola equivalente da associa\u00e7\u00e3o paralelo dessas duas metades fica quatro vezes maior que o da constante da mola original, tornando a mola equivalente menos deform\u00e1vel).<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00e3o comentada<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Associa\u00e7\u00e3o de molas \u00a0 Duas molas 1 e 2 tem constantes el\u00e1sticas k1\u00a0e k2, respectivamente. Podemos associ\u00e1-las em s\u00e9rie ou em paralelo. Em cada uma dessas associa\u00e7\u00f5es podemossubstituir as duas molas por uma \u00fanica, que produza o mesmo efeito e que chamamos de\u00a0mola equivalente de constante el\u00e1stica ke. Associa\u00e7\u00e3o em paralelo Nesse caso a deforma\u00e7\u00e3o x sofrida por cada uma<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1236,"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-1279","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1279","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=1279"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1279\/revisions"}],"predecessor-version":[{"id":1286,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1279\/revisions\/1286"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/1236"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=1279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}