For\303\247a, Massa e Acelera\303\247\303\243o physicsleninac@hotmail.com

Newton estabeleceu que a for\303\247a total em uma part\303\255cula \303\251 igual \303\240 taxa de varia\303\247\303\243o de seu momento linear, que \303\251 o produto de sua massa e sua velocidade: 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 Se a massa da part\303\255cula \303\251 constante, a for\303\247a total \303\251 igual ao produto de sua massa e sua acelera\303\247\303\243o: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Uma vez que uma unidade de massa foi escolhida, a unidade de for\303\247a \303\251 definida como a for\303\247a necess\303\241ria para dar \303\240 unidade de massa uma acelera\303\247\303\243o de magnitude unit\303\241ria. Por exemplo, o newton, que \303\251 a unidade SI de for\303\247a, \303\251 a for\303\247a necess\303\241ria para imprimir uma acelera\303\247\303\243o de um metro por segundo ao quadrado a uma massa de um quilograma. Se a massa de uma part\303\255cula e a for\303\247a total que atua sobre ela s\303\243o conhecidas, a segunda lei determina sua acelera\303\247\303\243o. Portanto, com a segunda lei, o movimento de uma part\303\255cula pode ser determinado se a for\303\247a total que age sobre ela \303\251 conhecida, ou a for\303\247a total pode ser encontrada quando o movimento \303\251 conhecido. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

A segunda lei de Newton \303\251 postulada para uma part\303\255cula, ou pequeno elemento da mat\303\251ria, mas uma equa\303\247\303\243o com exatamente a mesma forma descreve o movimento do centro de massa de um objeto arbitr\303\241rio. Pode-se mostrar que a for\303\247a externa total em qualquer corpo \303\251 igual ao produto de sua massa pela acelera\303\247\303\243o de seu centro de massa. Para isso, um sistema arbitr\303\241rio de N part\303\255culas \303\251 considerado. Seja mi a massa da i-\303\251sima part\303\255cula, e seja ri seu vetor posi\303\247\303\243o (veja a figura a). Seja m a massa total das part\303\255culas; quer dizer, 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= onde a soma com o \303\255ndice i significa "a soma sobre i de 1 a N". A posi\303\247\303\243o do centro de massa do sistema \303\251: 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 Derivar esta express\303\243o duas vezes d\303\241: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= onde a \303\251 a acelera\303\247\303\243o do centro de massa do objeto. A i-\303\251sima part\303\255cula pode ser submetida a for\303\247as exercidas pelas outras part\303\255culas. Seja fij a for\303\247a exercida pela i-\303\251sima part\303\255cula no j-\303\251simo. A terceira lei de Newton afirma que a j-\303\251sima part\303\255cula exerce sobre a i-\303\251sima part\303\255cula uma for\303\247a de igual magnitude e dire\303\247\303\243o oposta: fji=-fij. Se a for\303\247a externa na i-\303\251sima part\303\255cula for denotada (isto \303\251, a for\303\247a total exercida por outros objetos na i-\303\251sima part\303\255cula) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobXN1YnN1cEdGJDYoLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LUYjNiUtRi82JVEiRUYnRjJGNUYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRkQvSSttc2VtYW50aWNzR0YkUSxbbm9uZSxub25lXUYnL0Y2USdub3JtYWxGJw== con la segunda ley de Newton para la i-\303\251sima part\303\255cula es (figura b): 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 Esta equa\303\247\303\243o pode ser escrita para cada part\303\255cula do sistema. Adicionando as equa\303\247\303\265es resultantes de i = 1 a N, obtemos; 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 O primeiro termo do lado esquerdo, que \303\251 a soma das for\303\247as internas no sistema, \303\251 zero pela terceira lei de Newton: 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 O segundo termo do lado esquerdo da pen\303\272ltima equa\303\247\303\243o \303\251 a soma das for\303\247as externas no sistema. Denotando esta soma com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEmJlN1bTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTY2NjY2N2VtRictSSNtaUdGJDYlUSJGRicvJSdpdGFsaWNHRjkvRjBRJ2l0YWxpY0YnRi8= y usando a equa\303\247\303\243o 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 Conclui-se que a soma das for\303\247as externas \303\251 igual ao produto da massa total e a acelera\303\247\303\243o do centro de massa: 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 Visto que essa equa\303\247\303\243o \303\251 id\303\252ntica em forma ao postulado de Newton para uma \303\272nica part\303\255cula, tamb\303\251m \303\251 chamada de segunda lei de Newton por conveni\303\252ncia. Observe que, ao obter a equa\303\247\303\243o final, nenhuma suposi\303\247\303\243o foi feita para restringir a natureza do sistema de part\303\255culas ou seu estado de movimento. A soma das for\303\247as externas sobre um objeto ou conjunto de objetos, s\303\263lidos, l\303\255quidos ou gasosos, \303\251 igual ao produto da massa total e a acelera\303\247\303\243o do centro de massa. Por exemplo, suponha que o \303\264nibus espacial esteja em \303\263rbita e ainda tenha combust\303\255vel em seus tanques. Se seus motores forem ligados, o combust\303\255vel come\303\247a a se agitar de uma forma complicada, afetando o movimento do \303\264nibus espacial devido a for\303\247as internas entre o combust\303\255vel e o navio. No entanto, a \303\272ltima equa\303\247\303\243o pode ser usada para determinar a acelera\303\247\303\243o exata do centro de massa do \303\264nibus espacial, incluindo o combust\303\255vel que ele cont\303\251m, e assim obter a velocidade, posi\303\247\303\243o e trajet\303\263ria do centro de massa. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Desenhando o diagrama de corpo livre de um objeto, voc\303\252 pode identificar as for\303\247as externas que agem sobre ele e usar a segunda lei de Newton para determinar a acelera\303\247\303\243o do objeto. Por outro lado, se o movimento de um objeto, a segunda lei de Newton pode ser usada para determinar a for\303\247a externa total. Em particular, se a acelera\303\247\303\243o de um objeto em uma determinada dire\303\247\303\243o \303\251 conhecida como zero, a soma das for\303\247as externas nessa dire\303\247\303\243o deve ser zero. Se a soma das for\303\247as que agem sobre um objeto de massa me a acelera\303\247\303\243o de seu centro de massa \303\251 expressa em termos de seus componentes em um sistema de refer\303\252ncia cartesiano (figura a), a segunda lei de Newton afirma que: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Resolvendo para os componentes x, y e z, tr\303\252s equa\303\247\303\265es escalares de movimento s\303\243o obtidas: 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 A for\303\247a total em cada dire\303\247\303\243o coordenada \303\251 igual ao produto da massa e o componente da acelera\303\247\303\243o nessa dire\303\247\303\243o. Se o movimento de um objeto \303\251 limitado ao plano x-y, az = 0, ent\303\243o a soma das for\303\247as na dire\303\247\303\243o z \303\251 zero. Assim, quando o movimento de um objeto \303\251 limitado a um plano fixo, o componente da for\303\247a total normal ao plano \303\251 igual a zero. Para um movimento em linha reta ao longo do eixo x (figura a), as equa\303\247\303\265es s\303\243o: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkrbXVuZGVyb3ZlckdGJDYnLUkjbW9HRiQ2LVEmJlN1bTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTY2NjY2N2VtRictRiM2JC1JI21pR0YkNiNRIUYnRjJGTS9GRFEmZmFsc2VGJy8lLGFjY2VudHVuZGVyR0ZSLUklbXN1YkdGJDYlLUZONiVRIkZGJy8lJ2l0YWxpY0dGPC9GM1EnaXRhbGljRictRiM2JS1GTjYlUSJ4RidGZW5GZ25GZW5GZ24vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYtUSI9RidGMi9GNkZSL0Y5RlIvRjtGUi9GPkZSL0ZARlIvRkJGUkZRL0ZGUSwwLjI3Nzc3NzhlbUYnL0ZJRltwLUZWNiUtRk42JVEjbWFGJ0ZlbkZnbkZpbkZeby1GLzYtUSIsRidGMkZkby9GOUY8RmZvRmdvRmhvRmlvRlFGRS9GSVEsMC4zMzMzMzMzZW1GJ0Yy 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Observa-se que em movimento em linha reta, as componentes da for\303\247a total perpendicular \303\240 linha s\303\243o iguais a zero, e a componente da for\303\247a total tangente \303\240 linha \303\251 igual ao produto da massa pela acelera\303\247\303\243o ao longo a linha (figura b). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Quando um objeto se move em um caminho curvo plano, \303\251 poss\303\255vel decompor a soma das for\303\247as que atuam sobre ele em seus componentes normal e tangencial (figura a). Voc\303\252 tamb\303\251m pode expressar a acelera\303\247\303\243o do objeto em termos de seus componentes normal e tangencial (figura b) e escrever a segunda lei de Newton, \342\210\221F = ma, na forma 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 onde: 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 y 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Equacionando os componentes normal e tangencial na equa\303\247\303\243o anterior, duas equa\303\247\303\265es escalares de movimento s\303\243o obtidas: 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 A soma das for\303\247as na dire\303\247\303\243o tangencial \303\251 igual ao produto da massa e a taxa de varia\303\247\303\243o da magnitude da velocidade, e a soma das for\303\247as na dire\303\247\303\243o normal \303\251 igual ao produto da massa e o componente normal de acelera\303\247\303\243o. Se a trajet\303\263ria do centro de massa pertence a um plano, a acelera\303\247\303\243o do centro de massa perpendicular ao plano \303\251 zero, ent\303\243o a soma das for\303\247as perpendiculares ao plano tamb\303\251m \303\251 igual a zero. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Insira a massa: insira o vetor de deslocamento: ent\303\243o a for\303\247a \303\251 use DocumentTools in restart:with(VectorCalculus): Do(%MathContainer2=%MathContainer0*diff(%MathContainer1,t$2)); end use; =N a=, , ent\303\243o a for\303\247a \303\251: a) Fun\303\247\303\243o de tempo use DocumentTools in Do(%MathContainer6=%MathContainer0*%MathContainer3); end use; = use DocumentTools in Do(v=%Slider0); Do(v0=%Slider1); Do(%Plot0=plot(%MathContainer6,t=%Dial0..%Dial1)); end use; 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v=use DocumentTools in Do(%MathContainer12=%Slider0); end use; v0=use DocumentTools in Do(%MathContainer13=%Slider1); end use; t0=use DocumentTools in Do(%MathContainer14=%Dial0); end use; t=use DocumentTools in Do(%MathContainer15=%Dial1); end use; b) Fun\303\247\303\243o tempo / deslocamento use DocumentTools in Do(%MathContainer8=%MathContainer0*%MathContainer4); end use; = use DocumentTools in Do(x=%Slider2); Do(%Plot1=plot(%MathContainer8,t=%Dial0..%Dial1)); end use; 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x=use DocumentTools in Do(%MathContainer16=%Slider2); end use; m c) Fun\303\247\303\243o de deslocamento use DocumentTools in restart: Do(%MathContainer10=%MathContainer0*%MathContainer5); end use; = use DocumentTools in Do(%Plot2=plot(%MathContainer10,X=%Dial2..%Dial3)); end use; 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