13.9
阿基米德原理
阿基米德原理指出，施加在部分或全部浸没在流体中的物体上的向上浮力等于其排开的流体的重量。 为了了解使物体漂浮需要多大的浮力，让我们考虑一下将浸没的物体从流体中移出时会发生什么。 如果物体不在流体中，物体占据的空间将被重量为wfl的流体填充。 该重量由周围流体支撑，因此浮力必须等于wfl，即物体排开的…
考虑一个静止的物体完全浸没在流体中。它会排开与其自身体积相等的流体以占据该空间。
向上的浮力使物体保持静止。
如果将物体从流体中移除，该空间将被此前物体排开的同体积流体所填充。
此时，该流体体积受到与之前作用在物体上的相同的浮力。由于该流体体积处于静止状态，浮力与其自身重力相平衡。
因此，流体中物体所受浮力的大小等于该物体排开流体的重量。这就是著名的阿基米德原理。
从数学上讲，浮力等于被排开流体的质量与重力加速度的乘积。
根据质量与密度之间的关系，浮力也可以表示为流体密度、排开流体体积以及重力加速度的乘积。
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Q1: What is Archimedes' Principle and how does it relate to buoyant force?
Archimedes' Principle states that the upward buoyant force exerted on an object immersed in a fluid equals the weight of the fluid displaced by that object. When an object occupies space in a fluid, it displaces a volume of fluid. The buoyant force supporting the object can be calculated using the product of fluid density, displaced volume, and gravitational acceleration, connecting this principle directly to density and archimedes principle.
Q2: Why does an object experience an upward force when submerged in a fluid?
Pressure in a fluid increases with depth. The pressure at the bottom of a submerged object is greater than the pressure at the top. Fluid pressure acts perpendicular to surfaces: downward at the top and upward at the bottom. Since the bottom experiences higher pressure, the net upward force exceeds the downward force, creating buoyancy that supports the object.
Q3: How can you mathematically express the buoyant force on an immersed object?
The buoyant force equals the mass of displaced fluid multiplied by gravitational acceleration. Using the relationship between mass and density, buoyant force can also be expressed as the product of fluid density, volume of displaced fluid, and acceleration due to gravity. This mathematical relationship allows precise calculation of buoyancy in any fluid system.
Q4: What happens to the space occupied by an object when it is removed from a fluid?
When a submerged object is removed from a fluid, the space it occupied is immediately filled by the surrounding fluid. This fluid volume experiences the same buoyant force that previously acted on the object. Since this fluid is at rest in equilibrium, the buoyant force is balanced by the weight of the fluid, confirming that buoyancy equals the weight of displaced fluid.
Q5: Does Archimedes' Principle apply to partially submerged objects?
Yes, Archimedes' Principle applies to objects that are partially or entirely immersed in a fluid. The buoyant force equals the weight of the fluid displaced by the submerged portion of the object. For partially submerged objects, only the volume below the fluid surface contributes to the displaced fluid volume and resulting buoyant force.
Q6: Who was Archimedes and when was this principle established?
Archimedes was a Greek mathematician who lived approximately 287–212 BCE. He stated this principle long before the modern concepts of force were well established, demonstrating remarkable insight into fluid mechanics. His work laid the foundation for understanding buoyancy and remains fundamental to fluid mechanics today.
Q7: How does fluid pressure distribution create a net upward buoyant force?
Fluid pressure acts perpendicular to an object's surface at every point. Pressure increases with depth, so the upward force from pressure at the bottom exceeds the downward force from pressure at the top. Side pressures cancel each other. This pressure distribution results in a net upward force, which is the buoyant force that supports submerged objects.