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author | lorenzor |
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permlink | modelo-experimental-para-la-determinacion-de-la-densidad-relativa-de-un-solido-a-partir-de-la-ley-de-home-y-el-principio-de |
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title | "Modelo experimental para la determinación de la densidad relativa de un sólido a partir de la ley de Home y el principio de Arquímedes" |
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body | "<h3>¡Hola amigos de Hive Blog!</h3>
<h3>Reciban un Cordial saludo.</h3>
<div class="text-justify">La densidad de los materiales es una de las propiedades físicas de la materia con gran relevancia en el campo científico, industrial y domestico. </div><p>
<div class="text-justify">El incremento de las nuevas tecnologías y una acelerada demanda de nuevos materiales en el campo industrial, aéreo, farmacéutico, marino, alimentos, exploración petrolera, etcétera ha incrementado el interés en la caracterización de los materiales, siendo la densidad uno de los parámetros fundamentales para tal fin.</div><p>
<div class="text-justify">Si bien en la actualidad existen instrumentos de alta precisión que permiten la obtención de este `parámetro, en este trabajo presentaremos un modelo experimental fundamentado en la Ley de <b>Hooke</b> y el principio de <b>Arquímedes</b> para la determinación de la densidad relativa de un sólido, siendo este una alternativa experimental en la cuantificación de dicho parámetro que permita además, la aplicación y consolidación de los fundamentos físicos adquiridos. </div>
<h1>Fundamentos Teóricos</h1>
<h1>Densidad </h1>
<div class="text-justify">La densidad de un material es un parámetro que nos permite cuantificar la cantidad de masa por unidad de volumen y es matemáticamente expresado de la forma:</div>
<center>![image.png](https://images.hive.blog/DQmeiZ5KxGCxuPzdjuMjv8VWgFJKgyS43Jf1eYp1SzeQV9h/image.png)</center>
<h1>Densidad Relativa</h1>
<div class="text-justify">Usualmente, la densidad de un material es expresada como una función de la densidad de un líquido referencial de densidad conocida. En el caso de sólidos y líquidos, la densidad referencial utilizada es el agua, por lo que la densidad relativa es expresada de la forma:</div>
<center>![image.png](https://images.hive.blog/DQmRdq5buyeBCr2oKbH4SLxwuWnXf8iN81j5SrSRfBQ25Ah/image.png)</center>
<h1>Ley de Hooke</h1>
<div class="text-justify">Cuando los cuerpos sometidos a fuerzas o tensiones presentan una deformación y luego recuperan su estado original una vez cesa la aplicación de dichas fuerzas, son clasificados como cuerpos elásticos. Si estas fuerzas actuantes no exceden los límites elásticos del cuerpo, la ley de <b>Hooke</b> establece que existe una relación lineal y directamente proporcional entre la deformación experimentada por el cuerpo y la fuerza aplicada sobre este, matemáticamente esta Ley es expresada de la forma:</div>
<center>![image.png](https://images.hive.blog/DQmSnQ2M5wu35apcsnR3Zj6vpXXVJ2pDDZCKRKdC5NwJ6dM/image.png)</center>
<em>K → Constante Elástica [New/m]</em>
<em>x → Deformación [metro]</em>
<div class="text-justify">En la siguiente imagen se ilustra un resorte cuyo comportamiento elástico, dentro de los límites permitidos, satisface la ley de <b>Hooke</b>.</div>
<center>![image.png](https://images.hive.blog/DQmWGvh5LTAwyaTQvPfX7T3ZXS8nxdZMmBcLT1MKEz68bUS/image.png)</center>
<center><em><sup>Figura 1. Sistema masa – resorte en el aire
(Elaborada por @lorenzor)</sup></em></center>
<div class="text-justify">En este caso, la fuerza responsable de la deformación del resorte "<b>∆L</b>" esta dado por el peso del cuerpo solido de masa “<b>m<sub>s</sub></b>”.</div><p>
<div class="text-justify">La aplicación de la Ley de <b>Hooke</b> en este modelo puede escribirse de la forma:</div>
<center>![image.png](https://images.hive.blog/DQmcm3tDaDZSpfj9LVGCBaw3Hq9GJDNbHTpPWqds4VTnrnB/image.png)</center>
Donde:
<center>![image.png](https://images.hive.blog/DQmeueFPiaLYs7RdsyHboHkYGT3xa8S6SinYBMbT6G6vDJr/image.png)</center>
![image.png](https://images.hive.blog/DQmWyB5aWSnZZcghMJJKGksNxSjcnLuTEPWYfZTtJqePMN2/image.png) → <em>Densidad del sólido</em>
![image.png](https://images.hive.blog/DQmVCT7p6PFH2h263jQe6XTSfMGbrm6f9JEvvFBZkp68rtS/image.png) → <em>Volumen del sólido</em>
<center>![image.png](https://images.hive.blog/DQmav2D99nQ8sEbzMbo1Jb5sHcLKpH56AgZJBzjo82c8A7k/image.png)
</center>
L<sub>0</sub> → <em>Longitud sin estirar del resorte</em>
L<sub>1</sub> → <em>Longitud del resorte estirado por el sólido en el aire</em>
<h1>Fuerza de flotación y principio de Arquímedes</h1>
<div class="text-justify">Cuando un cuerpo es sumergido en un líquido, la diferencia de presión "<b>∆P</b>" en sus extremos superior e inferior se traduce en una fuerza actuante conocida como fuerza de flotación, dada por la expresión:</div>
<center>![image.png](https://images.hive.blog/DQmSidoL8dAKbT2eqeEBTEHmFyijhMzPWkk5S1MDJzAwhoH/image.png)</center>
Donde la variación de presión es obtenida a partir de la expresión:
<center>![image.png](https://images.hive.blog/DQmTcCEJ8iBpGmtWHB9XWrt8xbVpdpsxwe7M48rqpHMAGk7/image.png)</center>
![image.png](https://images.hive.blog/DQmaeq9PCXQNCWD9RJsPmhF6LzhMkwa98vdaqNR3SoJFQP9/image.png) → <em>Densidad del Fluido</em>
Combinando ambas fórmulas tenemos:
<center>![image.png](https://images.hive.blog/DQmUy2GNUjVH9xdLEVRA6XbB6eVyieQkJJiceP27i2bKHGb/image.png)</center>
<div class="text-justify">Donde el término "<b>∆hArea</b>" representa el volumen del solido sumergido “<b>V<sub>S</sub></b>”.</div><p>
De esta forma, la fuerza de flotación se escribe como:
<center>![image.png](https://images.hive.blog/DQmYpY2ftEHembHq21H6rkWn2TXLviXvknrKymSDsS6SjQe/image.png)</center>
<div class="text-justify"><b>El principio de Arquímedes</b> establece que sin importar si el sólido es sumergido de forma parcial o total, existirá un desplazamiento de líquido cuya masa tendrá un peso de igual magnitud a la fuerza de empuje aplicada por el líquido sobre el sólido. </div><p>
<div class="text-justify">En el caso que planteamos, el sólido es totalmente sumergido de tal forma que:</div>
<center>![image.png](https://images.hive.blog/DQmXLJcZVYtqupWQMLUC9RoBd7XPmN8j7wUP7mGyYkPYkXh/image.png)</center>
<center>![image.png](https://images.hive.blog/DQmfRhY8BPBdwDPJwwzinDUdorQ4YbSeSCgUfVA9swarXSc/image.png)</center>
<center><em><sup>Figura 2. Presión hidrostática sobre un cuerpo
(Elaborada por @lorenzor)</sup></em></center>
<h1>Modelo experimental propuesto para la determinación de la densidad relativa de un sólido</h1>
<div class="text-justify">El modelo experimental propuesto consiste en una variante del modelo inicial dado en la figura 1. En el nuevo sistema masa –resorte vertical el sólido es sumergido en agua, tal y como se muestra en la figura 3.</div>
<center>
![image.png](https://images.hive.blog/DQmbTxbUnUPzLr4XvohhHCYC6fi4RAW3azEeEnq2WFQ5TxQ/image.png)</center>
<center><em><sup>Figura 3. Modelo experimental para la determinación de la densidad relativa de un sólido
(Elaborada por @lorenzor)</sup></em></center>
<div class="text-justify">Aplicando la condición de equilibrio en el sistema en conjunto con la ley de <b>Hooke</b> y el principio de <b>Arquímedes</b>, tenemos:</div>
<center>![image.png](https://images.hive.blog/DQmczep4rSfAekXbQdxZrB4DGe5bFFsxmFoQhUehAALWUm7/image.png) <b>Condición de equilibrio</b></center>
<center>![image.png](https://images.hive.blog/DQmVbFw1dRUfeALqvBQ71KiusTFYs8ryKEmrJoco6Ta1Yra/image.png)</center>
<em>L<sub>2</sub> → Longitud del resorte estirado por el sólido en el agua</em>
<center>![image.png](https://images.hive.blog/DQmbCB8XZuKbDmfZNd8uBU3Arq8pkkoLD5DbRtAkbimjbF8/image.png)</center>
Del primer sistema desprovisto del recipiente de agua se obtuvo que:
<center>![image.png](https://images.hive.blog/DQmZkV4VM8n5iZA8B6meMKJ3iwFvuZZFqTtzRQm3hLmtpTF/image.png)
</center>
<div class="text-justify">Sustituyendo <b>K</b> en la ecuación del nuevo sistema y simplificando se tiene:</div>
<center>![image.png](https://images.hive.blog/DQmbho9UwbpCruwJUEFsZvMBUcM5NMvSLuffAWDX1nFyFXz/image.png)</center>
<div class="text-justify">Finalmente, se puede apreciar que la ecuación obtenida con el modelo experimental planteado, nos permite obtener la densidad relativa de un sólido a partir de los parámetros medibles L<sub>0</sub> L<sub>1</sub> y L<sub>2</sub>.</div><p>
<div class="text-justify">Este modelo experimental puede utilizarse para la obtención de la densidad relativa de un líquido, conocida previamente la densidad del sólido a partir del método desarrollado en este trabajo.</div>
<h1>Referencias</h1>
* Física para Ciencias e Ingeniería. Fishbane, Gasiorowicz, Thornton. Volumen I. Prentice Hall.
* Física para la Ciencia y la Tecnología. Tipler Mosca. Volumen 1: Mecánica. Oscilaciones y ondas. Termodinámica. 5a edición. Editorial Reverté.
* Física para Ciencias e Ingeniería. Raymond A. Serway, Robert J. Beichner. 5a edición. Tomo I. McGraw-Hill.
* Física Universitaria. Sears Zemansky, Young Freedman. 9na edición. Volumen 1. Addison Wesley Longman." |
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permlink | ingsparemodeling-and-rebuilding-from-a-blouse-to-a-little-dress-remodelacion-y-reconstruccion-desde-una-blusa-hasta-un-vestidito |
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required_posting_auths | |
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id | sm_submit_team |
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required_posting_auths | |
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json | {"match_type":"Ranked","app":"steemmonsters/0.7.89"} |
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json | "{"contractName":"tokens","contractAction":"issue","contractPayload":{"symbol":"COM","to":"yolmare","quantity":"0.000065","memo":"you have mined new COM tokens for staking LIST token"}}" |
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json | "{"name":"craft","action":"claim","payload":{"identifier":{"building_name":"Hops Field","input_cards":[]},"user":"@degiro","building_condition":{"quantity":90.97,"unit":"percent"},"result":[{"type":"CARD","value":{"name":"Local Aroma Hops","quality":"OUTSTANDING"}}],"timestamp":1618373955486}}" |
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1. | required_auths | |
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json | {"contractName":"nftmarket","contractAction":"sell","contractPayload":{"symbol":"NFTSR","nfts":["3507"],"price":"99","priceSymbol":"SWAP.HIVE","fee":1000}} |
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required_posting_auths | |
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json | {"trx_id":"6152824d726ae7d67978e593bfec2a553e4b8e39","team_hash":"24843ce3282cccf30e98ea8a9e074353","summoner":"C4-167-7NJ8W2U3YO","monsters":["C4-162-BXF1DG32WG","starter-2-nj9LE","C4-161-90A2HZTA8G","starter-63-RP9iX","starter-3-G0mnV","starter-8-9mR1B"],"secret":"Gs4b9TlqSS","app":"splinterlands/0.7.99"} |
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