13.10
Densidade e o Princípio de Arquimedes
Quando um pedaço amorfo de argila é jogado na água, ele afunda. Mas se o mesmo pedaço de argila for moldado na forma de um barco, ele começa a flutuar…
Um objeto imerso em um fluido desloca uma quantidade igual de fluido. A fração do objeto submerso no fluido depende da magnitude da força de empuxo que atua sobre ele.
A partir do princípio de Arquimedes, a força de empuxo que atua sobre o objeto está diretamente relacionada à densidade do fluido.
Se um fluido de densidade mais alta substituir o mais baixo, o volume de fluido deslocado mede um peso maior, aumentando assim a força de empuxo que atua sobre o objeto.
Para um objeto flutuante, a fração submersa é a razão entre o volume imerso dentro do fluido e o volume do objeto.
O volume submerso é igual ao volume do fluido deslocado.
Usando a relação entre o volume e a massa e igualando a massa do objeto à massa do fluido deslocado, a fração submersa é obtida como a razão entre a densidade do objeto e a densidade do fluido.
Quanto maior a densidade do fluido, menor é a fração submersa, empurrando o objeto para cima no fluido.
View the full transcript and gain access to JoVE Core videos
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.