Jeg vil starte med at forklare lidt hvad et tyngdepunkt er. og derefter vil jeg bevise matematisk hvordan man finder "tyngdepunktet" Tyngdepunktet har ogs\303\245 et andet navn, som giver mere mening for det mere almindelige menneske nemmelig massemidtpunktet. 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vi ser p\303\245 dette billede, kan vi se at der h\303\246nger nogle v\303\246gte p\303\245, stangen vi ser, h\303\246nger total vandret dette kan tyde p\303\245 at v\303\246gten af de 3 "lodder" er ligefordelt p\303\245 begge sider. Men hvis vi forestillede os at "vippen" der holder p\303\245 stangen, var skubbet en smule til venstre, ville den h\303\270jrer side falde til bunden, og derved er Tyngdepunktet ikke opfyldt. Dette vil sige at tyngdepunktet, er det sted p\303\245 stangen hvor stangen vil v\303\246re total vandret, pga v\303\246gten, og man har stillet "vippen" stedet hvor tyngdepunktet findet, man kan ogs\303\245 sige at tyngdepunktet er det sted for tyngdekraften ikke spiller ind. Nu vil jeg vise hvordan man finder dette matematisk. Vi ser igen p\303\245 tegningen, vi kan se at lodderne h\303\246nger p\303\245 koordinaterne. 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KiYsKComJkkibUc2IjYjIiIiRikmSSJ4R0YnRihGKUYpKiYmRiY2IyIiI0YpJkYrRi5GKUYpKiYmRiY2IyIiJEYpJkYrRjNGKUYpRilJIk1HRichIiI=

Eller for at g\303\270re det en smule enklere. 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

LCgqKEkiTUc2IiEiIiZJIm1HRiU2IyIiIkYqJkkieEdGJUYpRipGKiooRiRGJiZGKDYjIiIjRiomRixGL0YqRioqKEYkRiYmRig2IyIiJEYqJkYsRjRGKkYq

Det skal lige siges at M = er ligmed den sammelede masse, alts\303\245 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

Vou come\303\247ar explicando um pouco o que \303\251 um centro de gravidade. e ent\303\243o provarei matematicamente como encontrar o "centro de gravidade" O centro de gravidade tamb\303\251m tem outro nome, que faz mais sentido para o ser humano mais comum, ou seja, centro de massa. 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olharmos para esta foto, podemos ver que h\303\241 alguns pesos pendurados, a haste que vemos est\303\241 totalmente suspensa na horizontal, isso pode indicar que o peso dos 3 "pesos" est\303\241 uniformemente distribu\303\255do em ambos os lados.Mas se imagin\303\241ssemos que o "balancim" que segurava a haste fosse empurrado um pouco para a esquerda, o lado direito cairia para o fundo e, assim, o centro de gravidade n\303\243o seria encontrado. Isso significa que o centro de gravidade \303\251 o local da haste onde a haste ficar\303\241 totalmente horizontal, devido ao peso, e a "inclina\303\247\303\243o" foi definida onde o centro de gravidade se encontra, tamb\303\251m se pode dizer que o centro de gravidade \303\251 o lugar onde a gravidade n\303\243o entra em a\303\247\303\243o. Agora, quero mostrar como encontrar isso matematicamente. Olhando novamente para o desenho, podemos ver que os pesos est\303\243o nas coordenadas. 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e tem as massas. 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a coordenada do centro de gravidade \303\251 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

KiYsKComJkkibUc2IjYjIiIiRikmSSJ4R0YnRihGKUYpKiYmRiY2IyIiI0YpJkYrRi5GKUYpKiYmRiY2IyIiJEYpJkYrRjNGKUYpRilJIk1HRichIiI=

Ou para torn\303\241-lo um pouco mais simples. 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

LCgqKEkiTUc2IiEiIiZJIm1HRiU2IyIiIkYqJkkieEdGJUYpRipGKiooRiRGJiZGKDYjIiIjRiomRixGL0YqRioqKEYkRiYmRig2IyIiJEYqJkYsRjRGKkYq

S\303\263 tem que ser dito que M = \303\251 igual \303\240 massa total, ou seja 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

Se olharmos para este exemplo. 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deduzir que a \303\241rea da faixa (a faixa verde escura) tomando \316\224x ou seja, o comprimento da pe\303\247a, e multiplicar f(x) e arraste a segunda fun\303\247\303\243o g(x) de. 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 e, assim, tamb\303\251m se pode derivar a \303\201rea total, usando esta f\303\263rmula. 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 encontrar o conjunto de coordenadas para o centro de gravidade usando esta f\303\263rmula.x,1/2f(x)-g(x) para ent\303\243o encontrar o centro de gravidade, dividimos a fun\303\247\303\243o em v\303\241rias faixas.a coordenada do centro de gravidade da faixa que eu chamo 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O que fazemos em rela\303\247\303\243o \303\240 f\303\263rmula \303\251 isso. que tomamos a soma de todos os nossos 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