13.10
Densidad y el Principio de Arquímedes
Cuando un trozo de arcilla se deja caer en el agua, se hunde. Pero si el mismo trozo de arcilla se moldea en forma de barco, comienza a flotar. Debido…
Un objeto sumergido en un fluido desplaza una cantidad igual de fluido. La fracción del objeto sumergido en el fluido depende de la magnitud de la fuerza de flotación que actúa sobre él.
Según el principio de Arquímedes, la fuerza de flotación que actúa sobre el objeto está directamente relacionada con la densidad del fluido.
Si un fluido de mayor densidad sustituye al inferior, el volumen de fluido desplazado mide un mayor peso, aumentando así la fuerza de flotación que actúa sobre el objeto.
Para un objeto flotante, la fracción sumergida es la relación entre el volumen sumergido dentro del fluido y el volumen del objeto.
El volumen sumergido es igual al volumen del fluido desplazado.
Utilizando la relación entre el volumen y la masa e igualando la masa del objeto con la masa del fluido desplazado, la fracción sumergida se obtiene como la relación entre la densidad del objeto y la densidad del fluido.
Cuanto mayor es la densidad del fluido, menor es la fracción sumergida, empujando el objeto más arriba en el fluido.
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Q1: Why does an object's shape affect whether it floats or sinks?
An object's shape determines how much fluid it displaces. A clay lump sinks, but the same clay molded into a boat floats because the boat shape displaces more water, creating a greater buoyant force. Even though mass remains constant, increased displacement generates sufficient upward force to overcome the object's weight, allowing it to float.
Q2: How does fluid density affect the buoyant force on a submerged object?
Buoyant force is directly related to fluid density. When a higher-density fluid replaces a lower-density one, the displaced fluid volume weighs more, increasing the buoyant force. This relationship means denser fluids exert stronger upward forces on submerged objects, allowing heavier objects to float in them.
Q3: What determines whether an object will float or sink in a fluid?
An object's average density compared to the surrounding fluid determines floating or sinking. If the object's density is less than the fluid's density, it floats because the fluid contains more mass and weight in the same volume. If the object is denser than the fluid, it sinks.
Q4: How is the submerged fraction of a floating object calculated?
The submerged fraction equals the ratio of the object's density to the fluid's density. Mathematically, it represents the volume submerged divided by the object's total volume. This relationship reveals that higher fluid density results in a lower submerged fraction, pushing the object higher in the fluid.
Q5: Why do loaded and unloaded ships have different submerged depths?
An unloaded ship has lower average density and floats higher with minimal submersion. When loaded, the ship's average density increases, causing it to sink deeper into the water. The submerged fraction changes because the object's density relative to water density increases, requiring more displacement to support the added weight.
Q6: What real-world examples demonstrate objects floating in higher-density fluids?
Lower-density objects float in higher-density fluids: oil floats on water, hot-air balloons rise in the atmosphere, cork floats in wine, icebergs float in saltwater, and hot wax rises in a lava lamp. Even mountain ranges float on the higher-density crust and mantle beneath them, showing that Earth exhibits fluid characteristics.
Q7: How does an immersed object's volume relate to the fluid it displaces?
An object immersed in a fluid displaces an equal amount of fluid by volume. The submerged volume equals the volume of displaced fluid, which is fundamental to calculating buoyant force through energy conservation and bernoulli equation principles that govern fluid behavior and pressure distribution.