Buoyancy is a phenomenon due to the buoyant force that causes an object to float. When you put an object in a liquid, an upward force is exerted on the object by the liquid. This force is equal to the weight of the liquid that has been displaced. The amount of liquid that has been displaced depends upon the density and the volume of the object immersed in the liquid. Have you ever wondered why an iron nail sinks in water, but a ship made up of iron floats? And why does an iron ball sink but a plastic ball of the same size floats in water? These wonders happen due to the phenomenon known as Buoyancy. Let's learn the buoyancy definition, buoyancy equation, and its examples in detail.
What is Buoyant Force?
Buoyant force can be defined as an upward force exerted on an object that is completely or partially submerged in liquid. The unit of the buoyant force is Newton. Buoyancy force depends upon two factors:
- Amount (Volume) of liquid displaced by the object
- The density of the object.
In the first example, the iron nail has less volume and displaces a very less amount of water, so there is less buoyant force (upward force), and therefore sinks. Whereas ships have more volume, displace more water, and therefore have greater buoyant force (upward force) by water, and it floats. When talking in terms of relative density, if the relative density is less than 1, the object floats in water, and if the relative density is more than 1, the object sinks.
In the second example, the iron ball has more density and, therefore, greater gravitational force (downward force) than the buoyant force applied by the liquid. Hence it sinks. Whereas plastic ball is hollow and very dense, so smaller gravitational force (downward force) than the buoyant force (upward force) applied by liquid, and it floats. Boats, submarines, lifeboats, life jackets, and swimming work on the principle of buoyancy.
What causes Buoyant Force?
An object when immersed in a liquid experiences buoyant force. This force is upward in the direction opposite to the gravitational force, this is responsible for the reduced weight of the object inside the fluid. It's known that the pressure increases with the depth of the fluid. The pressure at the bottom of the object is greater than the pressure experienced at the top, this difference creates the net force experienced by the object inside the liquid, which is called buoyant force.
Archimedes' Principle
The physical law of buoyancy was given by the Greek mathematician and inventor Archimedes. Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. In the image given below, fluid pressure opposes gravity, and actual gravitational forces decrease therefore given by:
Apparent weight = Weight of object (in the air) - Thrust force (buoyancy)
Archimedes' law is mathematically written as:
Fb = ρ × g × V
Where,
- Fb is the buoyant force.
- ρ is the density the fluid.
- V is the submerged volume.
- g is the acceleration due to gravity.
After rearranging the formula ρV is the density of the displaced fluid multiplied by the volume of the displaced fluid, and we know the mass, density, and volume relation.
m = ρV
That means the term ρV corresponds to the mass of the displaced fluid.
Fb = ρ × g × V
Fb = mg i.e., The mass of the displaced fluid times the magnitude of the acceleration due to gravity is just the weight of the displaced fluid.
Fb = W
The above equation, when stated in words called Archimedes' principle. Assuming Archimedes' principle to be reformulated
Apparent immersed weight = weight – Weight of displaced fluid
Then inserted into the quotient of weights, which has been explained by the mutual volume.
\frac{Density}{Density \ of \ fuild} = \frac{Weight}{Weight \ of \ displaced \ fluid}
The density of the immersed object relative to the density of the fluid can be calculated:
\frac{Density \ of \ object}{Density \ of \ fuild} = \frac{Weight}{Weight - Apparant \ immersed \ weight}
Fb = PA = g ρ V = ρ g h A ⇢ (i)
- P = pressure
- Fb = force of buoyancy in Newton,
- A = Area in meter square,
- g = acceleration due to gravity,
- h = Height at which force acts taken from the surface
- p = density of the fluid,
- V = volume of the object inserted into the fluid.
Fb = Wa – Wf ⇢ (ii)
- Fb = force of buoyancy
- Wa = Weight of the object in the air
- Wf = Weight of the object when it is immersed in the fluid
Using (l) and (ll),
g ρ V = Wa – Wf ⇢ (iii)
If the object is not sinking, then Fg - Fb:
Mg = ρ g V
Demonstration of Buoyant Force
An object that is partly or completely submerged experiences a higher pressure on the bottom surface than on its top surface. This force is called upthrust. When we put something on the water body's surface, it displaces some of the fluid. The upthrust force is equal to the weight of the fluid displaced by the object.
A floating object is stable if it tends to restore itself to an equilibrium position after a small displacement. For example, floating objects will generally have vertical stability. As if the object is pushed down slightly, this will create a greater buoyancy force, which, unbalanced by the weight force, will push the object back up. Given a small angular displacement, the vessel may return to its original position (stable), move away from its original position (unstable), Or remain where it is (neutral). Rotational stability depends on the relative lines of action of forces on an object. The upward buoyancy force on an object acts through the center of buoyancy (CB), being the centroid of the displaced volume of fluid. The weight force on the object acts through its center of gravity (CG).
The buoyant object will be stable if the center of gravity is beneath the center of buoyancy because any angular displacement will then produce a 'righting moment'. The stability of a buoyant object at the surface is more complex, and it may remain stable even if the center of gravity is above the center of buoyancy, provided that when disturbed from the equilibrium position, the center of buoyancy moves further to the same side that the center of gravity moves, thus providing a positive righting moment.
What is Upthrust?
Any object placed in a fluid receives an upward force called Upthrust. The object is pushed in an upward direction, therefore, named Upthrust. An upthrust is a force that is applied by the water, and one other force is also acting on the body due to the mass of the body which is known as gravitational force. Gravitational force is acting in the opposite direction of upthrust force, Upthrust force acts in the vertically upward direction, and the Gravitational force acts in the vertically downward direction. The unit of upthrust is Newton.
Why does an Object float or sink in the water?
Any liquid can be considered a concoction of many overlying layers. These layers are lying one over another and have fluctuating pressure. Since the pressure increases with depth, thus the pressure at the bottom will be more than the pressure at the top which will cause the buoyant force. The difference in pressure at these layers gives rise to the buoyant force. The magnitude of the force is given by the weight of the liquid displaced by the object submerged in the liquid. Due to this phenomenon, objects float in the water.
Types of Buoyancy
There are three types of buoyancy:
- Positive buoyancy: When the weight of an object is lighter than the fluid it displaces is called positive buoyancy. For example, a boat that weighs (3000 kg) but displaces (4500 kg) of water will easily float
- Negative buoyancy: When the weight of an object is greater than the fluid it displaces is called negative buoyancy. For example, an iron nail may weigh 27 grams, but if it only displaces 17 grams of water, it will sink.
- Natural buoyancy: When the weight of an object is equal to the fluid it displaces. For example, a submarine can adjust its weight by adding or expelling water in special tanks called ballast tanks is an example of natural buoyancy.
Applications of Buoyancy
The buoyancy force is a phenomenon that can be observed in a lot of places in real life and in nature. The force makes it possible for us to swim, and build machines like ships and planes. Let's learn about some examples in more detail,
Hot Air Balloon
The atmosphere is filled with air, which is also a certain type of fluid. Hot air balloons uses the buoyancy effect. Air inside exerts a force on the balloon. The balloon rises up when the force exerted is more than the weight of the balloon and conversely, it descends when the force exerted is less than the weight of the balloon. Sometimes hot air balloons become stationary in mid-air, in that particular case, the weight of the balloon becomes equal to the force applied by the displaced liquid (air).
Ship
- The boat is designed in a way so that the shape of the boat is hollow. Due to the hollow shape, the density becomes less than the density of the sea. The volume of water displaced by the boat is equal to the weight of the boat and this helps the ship to float.
- Fishes stay buoyant underwater. Fishes have a special organ called a swim bladder that is usually filled with gases thus making the body lighter. This enables the fish to go up.
- Floatation of submarines in the water.
- To find the volume of the body.
- To keep swimmers on top of the water body.
Read More,
Solved Examples on Buoyancy
Example 1: Find the volume of the immersed object if M is 10000 kg.
Solution:
ρ = 997 kg/m3
10000 kg × g = g × 997 kg/m3 V
1000 kg = 997 kg/ m3 V
V = \frac{10000 kg }{997 kg/m^3}=10.03 m^3
Example 2: A block of wood with length = 3.2 m, width = 0.8 m, and height = 0.6 m. The density of water is 1000 kg/m3. If the block is placed in the water, what is the buoyant force? Acceleration due to gravity is 10 N/kg.
Solution:
Volume of the block (V) = length × width × height = 3.2 × 0.8 × 0.6 = 1.53 m3
Density = 1000 kg/m3
Gravity = 10 N/Kg
F = density × gravity × volume
F = 1000 × 10 × 1.53 = 15300N
F = 15300N
Example 3: The weight of an object in the air is 108 N. The object is placed in a liquid. The increase in the volume of liquid is 1.8 m3. If the specific weight of the liquid is 10 N/m3, what is the weight of the object in the liquid?
Solution:
Object’s weight in liquid = object’s weight in air – buoyant force
Object’s weight in liquid = 108 N – buoyant force
F = ρ g V
The density of liquid is 1 kg/m3
F = ρgV = 1 × 10 × 1.8 = 18 kg m/s2 = 18N.
Object’s weight in fluid = 108N - 18 N = 90N
Example 4: An object weighs 12N in air. When immersed fully in water, it weighs only 9N. What would be the weight of the liquid displaced by the object?
Solution:
According to Archimedes’s law:
Apparent weight = Weight of object (in the air) – Thrust force (buoyant force)
Apparent weight = 9N
Weight of object (in the air) = 12N
Thrust force (buoyant force) = ?
Apparent weight = 12N - Fb
Fb = 12N - 9N = 3N
Example 5: The weight of an object in the air is 108 N. The object is placed in a liquid. The increase in the volume of liquid is 1.8 m3. If the specific weight of the liquid is 10 N/m3, what is the weight of the object in liquid?
Solution:
Object’s weight in liquid = object’s weight in air – buoyant force
Object’s weight in liquid = 108 N – buoyant force
FA = ρ g V
The density of liquid is 1 kg/m3
FA = ρgV = (1kg/m3)(10m/s2)(1.8m3) = 18kgm/s3 = 18N
Object’s weight in fluid = 100 N – 18 N = 82N
Example 6: A piece of marble tile weighs 285 g in air. If its density is 3.5 g/cc, what will be its weight in water?
Solution:
Weight in air = 285 g
Volume = 285g /(3.5 g/cc) = 81.4 cc
Weight in water = 285 g - 81.4g = 203.6 g
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Introduction to Waves - Definition, Types, PropertiesA wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables o
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Wave MotionWave Motion refers to the transfer of energy and momentum from one point to another in a medium without actually transporting matter between the two points. Wave motion is a kind of disturbance from place to place. Wave can travel in solid medium, liquid medium, gas medium, and in a vacuum. Sound wa
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OscillationOscillations are defined as the process of repeating vibrations of any quantity about its equilibrium position. The word “oscillation†originates from the Latin verb, which means to swing. An object oscillates whenever a force pushes or pulls it back toward its central point after displacement. This
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Oscillatory Motion FormulaOscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
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Amplitude FormulaThe largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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