13.10
密度和阿基米德原理
当一块粘土掉入水中时，它会下沉。 但如果将同一块粘土塑造成船的形状，它就会开始漂浮。 由于其形状，即使质量相同，粘土船也能比团块排出更多的水，并承受更大的浮力。 对于钢质船舶来说也是如此。 物体的平均密度主要决定该物体是否会漂浮。 如果物体的平均密度小于周围流体的平均密度，它就会漂浮。 原因是，具有…
浸入流体中的物体会排开等量的流体。物体浸入流体中的比例取决于作用在其上的浮力大小。
根据阿基米德原理，作用在物体上的浮力与流体密度直接相关。
如果密度较高的流体取代了密度较低的流体，被排开的流体体积将具有更大的重量，从而增加作用在物体上的浮力。
对于漂浮物体，浸没分数是物体浸入流体中的体积与其总体积的比值。
浸没体积等于排开液体的体积。
利用 体积与质量之间的关系，并将物体的质量等同于所排开流体的质量，可得到浸没部分的比例为物体密度与流体密度之比。
流体密度越高，物体浸入流体中的比例越低，从而使物体在流体中浮得更高。
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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.