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____ [38]
3 years ago
6

(UPE) Terremotos são eventos naturais que não têm relação com eventos climáticos extremos, mas podem ter consequências ambientai

s devastadoras, especialmente quando seu epicentro ocorre no mar, provocando tsunamis. Uma das expressões para se calcular a violência de um terremoto na escala Richter é onde M é a magnitude do terremoto, E é a energia liberada (em joules) e E0 = 104,5 joules é a energia liberada por um pequeno terremoto usado como referência. Qual foi a ordem de grandeza da energia liberada pelo terremoto do Japão de 11 de março de 2011, que atingiu magnitude 9 na escala Richter?
Mathematics
1 answer:
Alex3 years ago
6 0

Answer:

E=10^{18} Joules

Step-by-step explanation:

1) Olá! Adicionando dados faltantes ao enunciado, como a fórmula dada: M=\frac{2}{3}log(\frac{E}{E_{0}})\\ e corrigindo a quantidade de Energia inicial: 10^{4,5} Vamos seguir aplicando a fórmula, lembrando das propriedades de logaritmo.

M=\frac{2}{3}log(\frac{E}{E_{0}})\\9=\frac{2}{3}log(\frac{E}{10^{4,5}})*3\\27=2log(\frac{E}{10^{4.5}})\\log(\frac{E}{10^{4.5}})^{2}=27\\(\frac{E^{2}}{10^{9}})=10^{27}\\E^{2}=10^{27}*10^{9}\Rightarrow E=\sqrt{10^{36}}\rightarrow E=10^{18} Joules

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