13.9
Archimedes' Principle
Archimedes'principle states that an upward buoyant force exerted on a body that is immersed partially or entirely in a fluid is equal to the weight of…
Consider an object at rest, completely immersed in a fluid. It displaces an equal volume of fluid to occupy that space.
An upward buoyant force keeps the object stationary.
If the object is removed from the fluid, the space gets filled by the same volume of fluid earlier displaced by it.
This fluid volume is now acted upon by the same buoyant force earlier acting on the object. Since the fluid volume is at rest, the buoyant force is balanced by its weight.
Thus, the magnitude of the buoyant force acting on an object in a fluid equals the weight of the fluid displaced by it. This is known as Archimedes' Principle.
Mathematically, the buoyant force is equal to the product of mass of the fluid displaced and the acceleration due to gravity.
Using the relationship between mass and density, the buoyant force can also be represented as the product of density of fluid, volume of displaced fluid, and the acceleration due to gravity.
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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.