13.9
アルキメデスの原理
アルキメデスの原理では、流体に部分的または全体的に浸された物体にかかる上向きの浮力は、物体によって押しのけられる流体の重量に等しいと述べています。 物体を浮かせるにはどのくらいの浮力が必要かを理解するために、水中に沈んだ物体を流体から取り出すときに何が起こるかを考えてみましょう。 物体が流体内にない…
完全に流体に浸された静止している物体を考えてみましょう。それはそのスペースを占めるために等量の流体を変位させます。
上向きの浮力により、物体は静止したままになります。
オブジェクトが流体から除去されると、スペースは以前にそれによって置換されたのと同じ量の流体で満たされます。
この流体ボリュームは、以前にオブジェクトに作用したのと同じ浮力によって作用されます。流体の体積が静止しているため、浮力はその重量によってバランスが取れています。
したがって、流体中の物体に作用する浮力の大きさは、それによって変位する流体の重量に等しくなります。これはアルキメデスの原理として知られています。
数学的には、浮力は、変位した流体の質量と重力による加速度の積に等しくなります。
質量と密度の関係を利用して、浮力は流体の密度、変位した流体の体積、重力による加速度の積としても表すことができます。
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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.