The relationship between the buoyancy of a floating body and its own weight is the core to understanding phenomena such as floating and suspension of objects in fluids (such as liquids or gases). The intrinsic connection between the two can be clearly described through the following principles and laws:

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1. Buoyancy Principle (Archimedes’ Principle)

The buoyant force experienced by an object in a fluid is equal to the weight of the fluid displaced by the object.

Formula:

Fbuoyance=ρfluid⋅g⋅Vdisplaced

Explanation of physical quantities:

-( Fbuoyant: The buoyant force acting on the object
– pfluid: The density of the fluid (here, \”fluid\” is a general term applicable to both liquids and gases)
-g : Acceleration due to gravity (typically taken as 9.8N/kg)
– Vdisplaced: The volume of the object immersed in the fluid, i.e., the volume of the displaced fluid

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2. Equilibrium Condition for Floating Bodies

When an object is stationary and floating or suspended in a fluid, the buoyant force and the object’s gravitational force (i.e., weight) are in a state of equilibrium, with the specific relationship being:

Fbuoyant = Gobject = mobject* g

Where:

–  Gobject: The gravitational force of the object (commonly known as \”weight\”)
– mobject: The mass of the object

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3. Core Relationship Derived from Equilibrium Conditions

By combining the formula of Archimedes’ Principle with the equilibrium condition for floating bodies \( Fbuoyant = Gobject, we can derive:

ρfluid * g *Vdisplaced = ρobject* g *Vobject

Since the acceleration due to gravity \( g \) is not zero, we can eliminate \( g \) from both sides, simplifying to:

pfluid* Vdisplaced =pobject* Vobject

Based on this simplified formula, two typical scenarios can be analyzed:

– Suspended fully immersed bodies (e.g., a submarine suspended in water): In this case, the object is completely immersed in the fluid, so Vdisplaced = Vobject. Substituting into the simplified formula gives \ρobject = ρfluid, meaning that the object’s density being equal to the fluid’s density is the key condition for suspension.

– Floating partially immersed bodies (e.g., a ship floating on water): Here, the object is only partially immersed in the fluid, so \( Vdisplaced < Vobject. Corresponding derivation leads to ρobject < ρfluid, indicating that the object’s density being less than the fluid’s density is the core prerequisite for floating.

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4. Criteria for Judging Floating Body States

– Floating:Fbuoyant = Gobject, the object partially Expose the fluid surface and is in a stationary equilibrium state.
– Suspension:Fbuoyant = Gobject, the object is completely immersed in the fluid and can remain stationary at any depth.
– Sinking to the bottom:  Fbuoyant < Gobject, the object cannot balance its weight due to insufficient buoyant force and eventually contacts the container (or the bottom of the fluid); at this point, it may receive a supporting force from the bottom to achieve balance.
– Rising: Fbuoyant > Gobject, the imbalance of the two forces causes the object to accelerate upward; as the object rises and the volume immersed in the fluid decreases, Vdisplaced becomes smaller, reducing the buoyant force gradually. This continues until  Fbuoyant= Gobject at which point the object stops rising and transitions to a floating state.

5. Practical Application Examples
– Ship Design: By optimizing the hull shape (e.g., using a hollow structure), the volume of water displaced by the hull is increased, so that the buoyant force acting on the ship exactly equals the total weight of the hull and its cargo, thereby achieving stable floating.

– Submarines: By adjusting the amount of water in the ballast tanks to change their total mass, submarines adjust their average density: when the average density equals the density of water, the submarine hovers; when it is greater than the density of water, the submarine submerges; and when it is less than the density of water, the submarine surfaces.

– Hot Air Balloons: Utilizing the property of gases expanding when heated and contracting when cooled, the gas inside the balloon is heated to reduce its density. When the total weight of the gas inside the balloon and the hot air balloon itself is less than the buoyant force exerted by the air, the hot air balloon rises.

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6. Summary of Key Points

– The magnitude of buoyancy is determined by the weight of the fluid displaced by the object and is not directly related to the object’s own density.

– The core balance condition for floating bodies (objects in a floating or suspended state) is: Buoyant Force = Object’s Weight (Gravity).

– The tendency of an object to sink or float in a fluid essentially depends on the comparison between its average density and the fluid’s density:

ρ_object < ρ_liquid → Float

◦ ρ_object = ρ_liquid → Hover

◦ ρ_object > ρ_liquid → Sink

In conclusion, the fundamental reason floating bodies can achieve floating or suspension is that the buoyant force they experience exactly balances their own weight, and this balanced state is achieved by the object displacing an appropriate volume of fluid.