Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Fluid mechanics ↓


Buoyancy and Archimedes' principle


In the study of fluid mechanics, it is important to understand how objects interact with fluids. Two fundamental concepts in this field are buoyancy and Archimedes' principle. This lesson will provide detailed information on these concepts, explaining their principles, importance, and real-world applications.

Bounce

Buoyancy is the upward force exerted by a fluid that opposes the weight of an object placed in it. This is why objects float or sink in water. Let's take a deeper look at how this force works and what factors affect it.

What is buoyancy force?

When an object is immersed in a fluid (fully or partially), it experiences an upward buoyancy force. This force is equal to the weight of the fluid displaced by the object. The principle governing buoyancy is the same for all fluids, which means it applies to both liquids and gases.

Buoyancy force (F_b) = weight of displaced fluid

Factors affecting buoyancy

  1. Volume of the object: Larger objects displace more fluid, increasing the buoyancy force.
  2. Density of the fluid: The denser the fluid, the greater the buoyancy force for a given amount of displacement.

Visual example

Water object

Archimedes principle

Archimedes' principle explains why buoyancy occurs. It states that an object immersed in a fluid is lifted up by a force equal to the weight of the fluid it displaces. This principle helps predict whether an object will float or sink.

F_b = ρ_fluid × V_displacement × g

Where:

  • F_b is the buoyancy force.
  • ρ_fluid is the density of the fluid.
  • V_displaced is the volume of the fluid displaced.
  • g is the acceleration due to gravity (about 9.81 m/s² on Earth).

Understanding through examples

Examples: floating ship

A ship floats because it displaces an amount of water equal to its own weight. When it enters the water, it sinks until the weight of the displaced water equals its own weight, after which it floats.

Why do ships float?

Even though ships are made of heavy materials, they are able to float because of their shape which displaces a large volume of water. The total density of the ship (including its hollow parts filled with air) is less than the density of water, allowing it to float.

Real life applications: submarines

Submarines can either float on the surface or sink to the bottom of the ocean by controlling their buoyancy. They adjust their buoyancy by changing the amount of water in their ballast tanks.

Visual example

Submarine

Calculation of buoyancy force

To calculate the buoyancy force acting on an object, we need to know the volume of the object immersed in the fluid and the density of the fluid. Once these values are known, the formula for buoyancy can be applied.

Example: calculating the buoyancy force

Consider a piece of wood with a volume of 0.5 m 3 immersed in water. If the density of water is 1000 kg/m 3, what will be the buoyancy force?

Using F_b = ρ_fluid × V_displaced × g:
F_b = 1000 kg/m³ × 0.5 m³ × 9.81 m/s²
F_b = 4905 N

The buoyant force acting on the block is 4905 N.

Floating and sinking: density and buoyancy

Whether an object floats or sinks is determined by comparing the density of the object to the density of the fluid in which it is located.

  • Floating: If the density of an object is less than the density of the fluid then the object will float.
  • Sinking: If the density of an object is greater than the density of the fluid then the object will sink.

Example: will it float?

A piece of plastic with a density of 600 kg/m³ is placed in an oil with a density of 800 kg/m³. Will the plastic float?

Since the density of plastic (600 kg/m³) is less than the density of oil (800 kg/m³), the plastic will float.

Density and Archimedes' principle

Archimedes' principle is not limited to the context of water but applies to any fluid. It allows one to predict an object's ability to float based on its density. This universal applicability makes it a cornerstone of fluid mechanics.

In conclusion

Buoyancy and Archimedes' principle are essential components of fluid mechanics, providing a framework for understanding why and how objects interact with fluids. By mastering these concepts, one gains insight into how objects float, sink, and move in fluid systems. This knowledge is used in a variety of fields, including engineering, biology, oceanography, and even aerospace.

Through calculations, theorems, and examples, Buoyancy and Archimedes' Principle reveals the fascinating interactions between objects and the fluids they contain, and demonstrates the fundamental laws of physics that govern everyday phenomena.


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Buoyancy and Archimedes' principle

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