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3.11. Volcanes. Erupción final

IEV: midiendo la erupción

Erupción volcán de La Palma

En el año 2021 se inició la erupción del volcán Tajogaite de la isla de La Palma.

Su actividad se mantuvo durante ochenta y cinco días, con numerosos terremotos que alcanzaron magnitud 5, y un índice de explosividad (IEV) 3 en una escala de 8.

Lava, cenizas, casas sepultadas, carreteras enterradas...

Siete mil personas fueron evacuadas, hubo un fallecido y las pérdidas fueron millonarias.

Lectura facilitada

En el año 2021 se inició la erupción del volcán Tajogaite de La Palma.

Su actividad duró ochenta y cinco días, con terremotos de magnitud 5, y un índice de explosividad (IEV) 3 en una escala de 8.

Lava, cenizas, casas sepultadas, carreteras enterradas...

Siete mil personas fueron evacuadas, hubo un fallecido y las pérdidas fueron millonarias.

Consejos

La mayoría de los consejos que puedes encontrar en páginas web españolas se refieren al volcán de La Palma.

Una de ellas es: web desarrollada por el Servicio de Innovación Proyecto la Palma Smart.

También en la Asociación Volcanes de Canarias hay información interesante.

Finalmente, hay páginas que engloban varias emergencias, como pueden ser la de AXEGA 112 en el apartado de "Autoprotección".

Recuerda que, tanto la caída de un meteorito como la erupción de un volcán, pueden provocar terremotos, por lo que también debes tener en cuenta lo aprendido en ese apartado.

Calderón Hondo

Cráter de Calderón HondoOtra isla canaria de origen volcánico es Fuerteventura, donde se puede visitar el Calderón Hondo, uno de los siete volcanes del Bayuyo, formado hace aproximadamente 50 000 años.

Su cráter está a 278 metros sobre el nivel del mar, tiene una profundidad de 70 metros y un diámetro de 100 metros.

Con la información anterior indica si las siguientes afirmaciones son verdaderas o falsas.

Pregunta 1

  • El área del cráter es 10 000 · π m2

Sugerencia

Recuerda que el área de una circunferencia es π. r2 donde r es el radio de la circunferencia.

Pregunta 2

  • Sabiendo que el área de un cono es Acono= \(π\cdot r\cdot\sqrt{r^2 + h^2}\) obtenemos que el área del cono de Calderón Hondo ocupa \(500\cdotπ\cdot \sqrt{74}\) m2

Sugerencia

Extrae factores de la raíz

Pregunta 3

  • El volcán Bayuyo tiene un diámetro de 300 metros y una profundidad de 50 metros. Por tanto podemos decir que el área de su cráter es 32 veces mayor que el área del cráter de Calderón Hondo

Sugerencia

Divide el área del cráter del volcán Bayuyo \(π\cdot150^2\) entre el área del cráter del volcán Calderón Hondo \(π\cdot50^2\) y aplica las propiedades de las potencias.

Saliendo del cráter

Potencias

Erupción de lavaEn el estudio de la fuerza de un volcán, aparecen expresiones con potencias y raíces.

Para resolverlas se aplican distintas técnicas: extraer factores, uso de propiedades...

Este es un ejemplo, calcula \(\frac{10^{10} - 10^9}{10^8}\) 

Fíjate: en el numerador de esta operación \(\frac{10^{10} - 10^9}{10^8}\) hay una resta.

Lo ideal es sacar factor común la base elevada a la menor de las potencias, es decir:

 \(\frac{\textcolor{red}{10^9}\ · (10 - 1)}{10^8}\) = \(\frac{\textcolor{red}{10^9}\ }{10^8}\) · (10 - 1)

A continuación aplica las propiedades de las potencias, \(\textcolor{red}{10^{9-8}}\cdot(10 - 1)\) y por último realiza las operaciones, obteniendo 10\(\cdot\)9 = 90

Raíces

ErupciónAnaliza la siguiente operación \(\frac{\sqrt{24}}{\sqrt{2}\cdot\sqrt{3}}\)

Céntrate ahora en el denominador.

Aplica la propiedad de la raíz de un producto: \(\sqrt{a}\cdot\sqrt{b}=\sqrt{a\cdot b}\)

Por tanto \(\frac{\sqrt{24}}{\textcolor{red}{\sqrt{6}}}\)

Y ahora la propiedad de la raíz de un cociente: \(\sqrt{a}:\sqrt{b}=\sqrt{a:b}\)

El resultado es \(\sqrt{\frac{24}{6}}=\sqrt{4}=2\)

Practica

  • \(\frac{5^{20} - 5^{19}}{5^{19}}\) = 
  • \(\frac{7^{11} - 7^9}{7^8}\) =
  • \(\frac{\sqrt{90}}{\sqrt{2}\cdot\sqrt{5}}\) =
  • \(\frac{\sqrt{525}}{\sqrt{7}\cdot\sqrt{3}}\)=

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Parámetros combinados

VEI


El IEV combina varios parámetros medibles, por ejemplo, la altura de la nube de la erupción, el volumen total de los productos expulsados...

Tú también tendrás que combinar operaciones, recuerda lo aprendido en 3.9. Incendios, para saber qué orden seguir, empezando por los paréntesis, desde dentro hacia afuera.

Prueba con este ejemplo en tu cuaderno, ya sabes la solución:

\([-1\cdot(3-5)]^{4}:(-8)-5\cdot[(3\cdot5-\sqrt{81})^{2}-6^{2}] = -2 \)

Si no lo das hecho, consulta la ayuda.

Ayuda

Opera dentro de los paréntesis siguiendo el orden de las operaciones, desde dentro hacia afuera.

\([-1\cdot(-2)]^{4}:(-8)-5\cdot[(15-\sqrt{81})^{2}-6^{2}] = \)

= \( (2)^{4}:(-8)-5\cdot[(15-\sqrt{81})^{2}-6^{2}] = \)

= \(16:(-8)-5\cdot[(15-9)^{2}-36]=\)

= \(16:(-8)-5\cdot[(6)^{2}-36]=\)

= \(16:(-8)-5\cdot[36-36]=\)

= \(-2-5\cdot[36-36]=(-2)-5\cdot0=-2-0=-2\)

Sopa volcánica

2

Encuentra los resultados en esta sopa volcánica. Maximiza la pantalla para marcar la solución.

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0123456789
Su navegador no es compatible con esta herramienta.

Aplica tu fuerza mental

¿En qué cifra terminan las potencias sucesivas de un número?

Investiga en qué cifra terminan las sucesivas potencias de 2, 22, 23, ... ¿Cuál será la cifra de las unidades del número 22025?

Investiga en qué cifra terminan las sucesivas potencias de 3, 32, 33, ... ¿Cuál será la cifra de las unidades del número 32025 ?

Investígalo con todas las cifras hasta el 9. ¿Qué observas?

Ahora, sin hacer la operación, indica en qué cifra termina cada uno de las siguientes potencias:

          362          3183          10055                 874          56444           999 9994 

¿Potencias de base negativa?

Investiga el valor de (-1)n, según sea n un número par o impar. ¿Qué observas?

Investiga el valor de (-2)n , según sea n un número par o impar. ¿Qué observas?

Analiza y reflexiona

  • Si dos números son cuadrados prefectos, su producto también lo es.

Usa esta propiedad para calcular la raíz de 3136 = 49 · 64 y comprueba el resultado

Simulacro final

Elija la respuesta correcta.

2
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Su navegador no es compatible con esta herramienta.

Ubi dolor ibi vigiles

Imagen del diario de aprendizaje en el proxecto cREAgal. Representa un lápiz y un cuaderno con el logotipo del proyecto en la portada.

¿Sabías que ya había cuerpo de bomberos en el siglo I, en la antigua Roma?

Eran los "Vigiles", cuyo lema fue "Ubi dolor ibi vigiles", que significa, allí donde hay dolor están los vigilantes.

Tú también debes estar vigilante, aprovechando todo lo estudiado en esta fase 3 para completar el reto.

Reflexiona en tu diario de aprendizaje sobre esta y otras cuestiones planteadas.

Haz una puesta en común con tus compañeros de equipo de las respuestas anteriores.

Feito con eXeLearning (Nova xanela)