13.9
Le principe d'Archimède
Le principe d'Archimède stipule qu'une force de poussée vers le haut exercée sur un corps immergé partiellement ou totalement dans un fluide est égale…
Considérons un objet au repos, complètement immergé dans un fluide. Il déplace un volume égal de fluide pour occuper cet espace.
Une force de flottaison vers le haut maintient l’objet immobile.
Si l’objet est retiré du fluide, l’espace est rempli par le même volume de fluide précédemment déplacé par celui-ci.
Ce volume de fluide est maintenant agi par la même force de flottabilité agissant précédemment sur l’objet. Comme le volume du fluide est au repos, la force de flottabilité est équilibrée par son poids.
Ainsi, l’intensité de la force de flottabilité agissant sur un objet dans un fluide est égale au poids du fluide déplacé par celui-ci. C'est ce qu'on appelle le principe d'Archimède.
Mathématiquement, la force de flottabilité est égale au produit de la masse du fluide déplacé et de l’accélération due à la gravité.
En utilisant la relation entre la masse et la densité, la force de flottabilité peut également être représentée comme le produit de la densité du fluide, du volume du fluide déplacé et de l’accélération due à la gravité.
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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.