La aceleración de la gravedad
La aceleración de la gravedad es la fuerza gravitatoria específica que actúa sobre un cuerpo en el campo gravitatorio de otro; esto es, como la fuerza gravitatoria por unidad de masa del cuerpo que la experimenta. Se representa como:
![](data:image/jpeg;base64,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)
La gravedad sobre la superficie de un planeta típicamente esférico viene dada por:
![](data:image/jpeg;base64,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)
donde G es la constante de gravitación universal y vale 6,67 * 10-11 N.m2/Kg2, M es la masa del planeta que vale 5,98.1024 Kg, R es el radio del planeta y vale 6370 km y es un vector unitario dirigido, en su sentido negativo, hacia el centro del planeta. Equivalentemente, puede definirse como el peso por unidad de masa de un objeto que se encuentra sobre la superficie del planeta:
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Este valor es constante para los cuerpos situados en las cercanías de la superficie terrestre, independientemente de su masa. Es decir, los cuerpos con distinta masa caen con la misma aceleración. Las diferencias que pueden observarse cotidianamente se deben a otro factor: el rozamiento con el aire.
Tabla comparativa de la aceleración de la gravedad
La lista adjunta muestra los valores relativos de la aceleración de la gravedad en el Sol, en la superficie de cada planeta del sistema solar y en la superficie de la Luna, tomando como unidad el valor de la gravedad estándar en superficie de la Tierra y en valor absoluto, expresada en metros sobre segundo al cuadrado (m/s²), con dos dígitos decimales de aproximación. Así, para la Tierra la aceleración de la gravedad es 9,81 m/s².
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La masa y el peso
Peso y masa son dos conceptos y magnitudes físicas muy diferentes, aunque aún en estos momentos, en el habla cotidiana, el término “peso” se utiliza a menudo erróneamente como sinónimo de masa.
La masa es la cantidad de materia que tiene un cuerpo y el peso es la fuerza con que la Tierra lo atrae, es decir, la intensidad de la fuerza gravitatoria que la Tierra ejerce sobre un cuerpo. La masa se mide en kilogramos (kg). y el peso, en newtons (N), siempre en el Sistema Internacional de unidades.
La expresión usada para calcular el peso (P) de un objeto de masa m situado en las inmediaciones de la superficie terrestre es:
Peso (P) = masa (m) x fuerza de gravedad (g).
La masa es una propiedad intrínseca de un cuerpo que no varía cuando lo desplazamos. El peso, sin embargo, sí que puede variar. Como el peso es una fuerza, tiene los cuatro elementos característicos de una magnitud vectorial: punto de aplicación, dirección, sentido y módulo.
- Punto de aplicación. Es un punto que se llama centro de gravedad (cdg). Sobre él se aplica la resultante de todas las pequeñas fuerzas-peso que actúan sobre las partículas de un cuerpo.
- Dirección. Es la línea que une el centro de gravedad (cdg) con el centro de la Tierra. Esta línea se llama vertical.
- Sentido. El sentido de la fuerza-peso es siempre hacia el centro de la Tierra.
- Módulo. El módulo o intensidad de la fuerza peso es: P=m.g siendo g = 9,8 N/kg en la superficie terrestre
A medida que nos alejamos de la superficie terrestre, el valor de g disminuye. Observa que para medir P en newtons (N), la masa tiene que venir medida en kilogramos (kg), y g, en N/kg.
Equilibrio estático
Si dejamos sobre la mesa un libro, un vaso, una caja de zapatos, una botella, etc., permanecen ahí, sin moverse, todo el tiempo que deseemos, a menos que se aplique una fuerza sobre ellos. Decimos que están en equilibrio estático. No sucede lo mismo con un lápiz colocado verticalmente. Al soltarlo, cae sobre la mesa. No está en equilibrio.
La condición para que un cuerpo apoyado sobre una superficie horizontal permanezca en equilibrio es que la vertical que pasa por su centro de gravedad pase también por su base de sustentación (la menor superficie que encierra todos los puntos de apoyo de un cuerpo).
Existen tres tipos de equilibrio
- Equilibrio estable. Si separamos un poco el cono de la posición en que se encuentra, al soltarlo regresaría a ella: equilibrio estable.
- Equilibrio inestable. Si separamos un poco el cono de la posición en que se encuentra, al soltarlo se separaría aún más de ella: equilibrio inestable.
- Equilibrio indiferente. Si separamos un poco el cono de la posición en que se encuentra, permanecería en equilibrio en la nueva posición: equilibrio indiferente.