13.10
密度とアルキメデスの原理
粘土の塊を水に落とすと沈みます。 しかし、同じ粘土の塊を船の形に成形すると、船は浮き始めます。 その形状により、たとえその質量が同じであっても、粘土ボートは塊よりも多くの水を押しのけ、より大きな浮力を受けます。 鋼船についても同様です。 物体が浮くかどうかは、物体の平均密度によって主に決まります。…
流体に浸された物体は、同量の流体を変位させます。流体に沈む物体の割合は、物体に作用する浮力の大きさによって異なります。
アルキメデスの原理から、物体に作用する浮力は流体密度に直接関係しています。
密度の高い流体が低い流体に置き換わると、変位した流体の体積はより大きな重量を測定するため、物体に作用する浮力が増加します。
浮遊オブジェクトの場合、水中分率は、流体の内部に沈んでいる体積とオブジェクトの体積の比率です。
水没した体積は、変位した流体の体積と等しくなります。
体積と質量の関係を使用し、オブジェクトの質量を変位した流体の質量と等しくすると、水中分率は、オブジェクトの密度と流体の密度の比率として得られます。
流体密度が高いほど、水中分画が低くなり、物体が流体の上位に押し上げられます。
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.