13.10
밀도와 아르키메데스의 원리
점토 덩어리를 물에 떨어뜨리면 가라앉습니다. 그러나 같은 점토 덩어리를 배 모양으로 빚으면 물에 뜨기 시작합니다. 점토배는 모양 때문에 질량이 같더라도 덩어리보다 더 많은 물을 밀어내고 더 큰 부력을 받습니다. 강철 선박의 경우에도 마찬가지입니다. 물체의 평균 밀도는…
유체에 잠긴 물체는 동일한 양의 유체를 대체합니다. 유체에 잠긴 물체의 비율은 물체에 작용하는 부력의 크기에 따라 다릅니다.
아르키메데스의 원리에 따르면 물체에 작용하는 부력은 유체 밀도와 직접적인 관련이 있습니다.
더 높은 밀도의 유체가 더 낮은 유체를 대체하면 변위된 유체 부피가 더 높은 무게를 측정하여 물체에 작용하는 부력을 증가시킵니다.
떠 있는 물체의 경우, 물에 잠긴 비율은 유체 내부에 잠긴 부피와 물체의 부피의 비율입니다.
침수된 부피는 변위된 유체의 부피와 같습니다.
부피와 질량 사이의 관계를 사용하고 물체의 질량을 변위된 유체의 질량과 동일시하여 물에 잠긴 부분을 유체 밀도에 대한 물체의 밀도의 비율로 얻습니다.
유체 밀도가 높을수록 물에 잠긴 부분이 낮아져 물체를 유체에서 더 높이 밀어 올립니다.
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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.