14.4 Archimedes’ Principle and Buoyancy
3 min read•june 24, 2024
Ever wonder why some things float while others sink? ###'_Principle_0### explains it all. This fundamental concept in fluid mechanics shows how objects interact with liquids and gases, determining whether they'll bob or plummet.
Understanding buoyancy is key to many real-world applications. From designing ships to explaining how fish control their depth, this principle helps us grasp the forces at play when objects are submerged or floating in fluids.
Archimedes' Principle and Buoyancy
Concept of buoyant force
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- is an upward force exerted by a fluid on an object immersed in it
- Opposes the weight of the object causing it to float or appear lighter in fluids (helium balloon in air, wood in water)
- Caused by pressure difference between top and bottom of submerged object
- Pressure increases with depth in fluid due to weight of fluid above
- Pressure at bottom of object is greater than pressure at top resulting in net upward force ()
- Magnitude of depends on of fluid and volume of displaced fluid
- where is buoyant force, is density of fluid, is volume of displaced fluid, and is acceleration due to gravity
- Denser fluids (mercury) exert greater buoyant force than less dense fluids (air) for same volume displaced
Applications of Archimedes' principle
- Archimedes' principle states buoyant force on an object equals weight of fluid displaced by object
- where is buoyant force and is weight of displaced fluid
- For fully submerged object, volume of displaced fluid equals volume of object ()
- For floating object, volume of displaced fluid equals volume of submerged portion of object
- Weight of displaced fluid equals weight of object ()
- To solve problems, apply appropriate equations based on whether object is fully submerged or floating
- For fully submerged objects, use
- For floating objects, use where is volume of submerged portion of object
- Applications include determining load capacity of boats, designing buoyancy compensators for divers, explaining how hot air balloons and submarines work
Density effects in fluids
- Object floats in fluid if its density is less than density of fluid
- Object displaces volume of fluid with weight equal to object's weight (ice cube in water)
- Object sinks in fluid if its density is greater than density of fluid
- Object displaces volume of fluid equal to its own volume (rock in water)
- Relative densities of object and fluid determine fraction of object's volume submerged when floating
- where is volume of submerged portion of object, is total volume of object, is density of object, and is density of fluid
- Objects with lower density than fluid have larger portion of volume above surface when floating compared to objects with higher density (styrofoam vs wood in water)
- Density differences explain why oil floats on water, how fish regulate buoyancy with swim bladders, and how hot air balloons rise
Fluid Statics and Buoyancy
- is the pressure exerted by a fluid at rest due to its weight
- Increases linearly with depth in a fluid
- Contributes to the buoyant force on submerged objects
- is the perceived weight of an object when submerged in a fluid
- Differs from true weight due to buoyant force
- Apparent weight = True weight - Buoyant force
- is the point through which the total buoyant force acts
- Located at the centroid of the displaced fluid volume
- Important for stability of floating objects
Key Terms to Review (28)
$ rac{V_{submerged}}{V_{object}} = rac{
ho_{object}}{
ho_{fluid}}$: This term represents the relationship between the volume of an object submerged in a fluid and the total volume of the object, which is equal to the ratio of the object's density to the fluid's density. It is a key expression in understanding the principles of buoyancy and Archimedes' Principle.
$F_b =
ho_{fluid} imes V_{displaced} imes g$: $F_b =
ho_{fluid} imes V_{displaced} imes g$ is the formula that represents the buoyant force acting on an object immersed in a fluid. This formula is central to understanding Archimedes' Principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.
$F_b = \rho_{fluid} \times V_{object} \times g$: $F_b = \rho_{fluid} \times V_{object} \times g$ is the formula that describes the buoyant force acting on an object immersed in a fluid. The buoyant force is the upward force exerted by the fluid on the object, which is equal to the weight of the fluid displaced by the object.
$F_b = W_{displaced}$: $F_b = W_{displaced}$ is a fundamental relationship in the context of Archimedes' Principle and buoyancy. It states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
$V_{displaced} = V_{object}$: $V_{displaced}$, or the volume of fluid displaced, is equal to the volume of the submerged object. This principle, known as Archimedes' Principle, describes the buoyant force exerted on an object immersed in a fluid, which is directly proportional to the volume of the object and the density of the fluid.
$W_{object} = \rho_{fluid} \times V_{submerged} \times g$: $W_{object}$ is the buoyant force or upward force exerted on an object submerged in a fluid, which is equal to the weight of the fluid displaced by the object. This term is central to understanding Archimedes' Principle and the concept of buoyancy.
$W_{object} = W_{displaced}$: $W_{object} = W_{displaced}$ is a key relationship that describes the buoyant force acting on an object submerged in a fluid. It states that the weight of the object is equal to the weight of the fluid displaced by the object, which is a fundamental principle in understanding Archimedes' Principle and buoyancy.
Apparent Weight: Apparent weight is the force exerted by an object on a surface or support, which may differ from its true weight due to the effects of buoyancy or other external forces. It is a crucial concept in understanding Archimedes' Principle and the behavior of objects in fluids.
Archimedes: Archimedes was a renowned ancient Greek mathematician, physicist, engineer, and inventor. He is best known for his principles related to buoyancy and the concept of the center of mass, which have important applications in physics and engineering.
Archimedes’ principle: Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This principle explains why objects float or sink depending on their density relative to the fluid.
Archimedes' Principle: Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This principle explains why some objects float while others sink, and it has important applications in understanding the behavior of objects in fluids.
Buoyant force: Buoyant force is the upward force exerted by a fluid on an object submerged in it. This force opposes the weight of the object and is responsible for making objects float.
Buoyant Force: Buoyant force is the upward force exerted by a fluid on an object immersed in it. This force acts to counteract the weight of the object and is a key principle in understanding the behavior of objects in fluids.
Center of Buoyancy: The center of buoyancy is the point at which the buoyant force, or upward force exerted by a fluid on an object, is considered to act. It is the geometric center of the volume of the displaced fluid, and its location is crucial in understanding the stability and equilibrium of objects immersed in or floating on a fluid.
Density: Density is a fundamental physical property that describes the mass per unit volume of a substance. It is a measure of how much matter is packed into a given space and is a crucial concept in understanding the behavior of fluids, solids, and gases across various physics topics.
Flotation: Flotation is the ability of an object to float or remain buoyant on the surface of a liquid, such as water. It is a fundamental concept in the study of Archimedes' Principle and the behavior of objects submerged in fluids.
Fluid Displacement: Fluid displacement is the physical principle that describes the buoyant force exerted on an object immersed in a fluid, such as water or air. It is the amount of fluid that is displaced, or pushed aside, when an object is placed in the fluid, and it is directly related to the weight of the fluid displaced.
Fluid Statics: Fluid statics is the study of fluids at rest and the pressures they exert. It encompasses the principles and concepts that govern the behavior of fluids, such as liquids and gases, when they are not in motion, focusing on the properties and effects of pressure within these stationary systems.
Hydrostatic Pressure: Hydrostatic pressure is the pressure exerted by a fluid, such as water or air, due to the force of gravity acting on the weight of the fluid. It is a fundamental concept in the study of fluids, density, and buoyancy.
Kg/m^3: kg/m^3 is a unit of measurement that represents the density of a substance, specifically the mass per unit volume. It is commonly used to express the density of materials, liquids, and gases in the context of physics and engineering applications.
Linear mass density: Linear mass density is the measure of mass per unit length of a one-dimensional object, such as a string or rod. It is typically denoted by the symbol $\lambda$ and expressed in units of kg/m.
Neutral Buoyancy: Neutral buoyancy refers to the state in which an object is suspended in a fluid, such as water or air, without sinking or floating. This occurs when the weight of the object is exactly equal to the buoyant force acting upon it, resulting in a net zero force and the object remaining stationary within the fluid.
Newtons: Newtons are the standard unit of force in the International System of Units (SI). They are named after Sir Isaac Newton, the renowned physicist who formulated the laws of motion and the theory of universal gravitation. Newtons are a fundamental concept in physics, as they quantify the amount of force acting on an object, which is crucial in understanding various physical phenomena.
Pascals: Pascals are the units used to measure pressure, specifically the force exerted per unit area. They are named after the French mathematician and physicist Blaise Pascal, who made significant contributions to the understanding of fluid mechanics and hydrostatics.
Relative Density: Relative density, also known as specific gravity, is a dimensionless quantity that compares the density of a substance to the density of a reference substance, typically water at a standard temperature and pressure. It is used to determine the buoyancy of objects and the behavior of fluids in the context of Archimedes' Principle.
Specific Gravity: Specific gravity is the ratio of the density of a substance to the density of a reference substance, typically water at 4°C. It is a dimensionless quantity that compares the mass of a given volume of a material to the mass of an equal volume of water, providing information about the relative density of the substance.
Submerged Volume: Submerged volume refers to the volume of an object that is completely immersed or submerged in a fluid, such as water. This concept is particularly important in the context of Archimedes' Principle and understanding buoyancy forces acting on objects.
Upthrust: Upthrust is the upward force exerted by a fluid, such as water or air, on an object immersed in or floating on the fluid. This force is a crucial concept in understanding Archimedes' Principle and the phenomenon of buoyancy.