Understanding Key Concepts in Fluid Mechanics and Elasticity
Hooke’s Law: Elasticity
When an object is subjected to external forces, it undergoes changes in size or shape, or both. These changes depend on the arrangement of atoms and their bonds in the material. When a weight pulls and stretches another, and when released, this weight returns to its normal size, we say it is an elastic body.
- Elasticity: The property to change shape when a force acts on an object, causing deformation, and the object returns to its original shape when the deformation ceases.
- Inelastic
Cosmic Composition: From Elements to Solar Systems
The Universe: Composition and Organization
The universe is composed of approximately 75% hydrogen, 20% helium, and 5% other elements. Dark matter, which we cannot see, makes up 90% of the universe, while visible matter (galaxies, stars, and planets) accounts for only 10%.
Organization of the Universe
- Universe: A vast collection of billions of galaxies.
- Super-Virgo Cluster: A group of millions of galaxies.
- Local Group of Galaxies: A group of about 30 galaxies.
- Milky Way: Our galaxy, containing approximately
Vector Calculus: Velocity, Acceleration, and Fields
Example 1: Ferris Wheel Motion
A child is sitting on a Ferris wheel with a diameter of 10 meters, making one revolution every 2 minutes. Find the speed of the child and draw velocity vectors at two different times.
Solution: The child moves at a constant speed around a circle of radius 5 meters, completing one revolution every 2 minutes. One revolution around a circle of radius 5 is a distance of 10π, so the child’s speed is 10π/2 = 5π ≈ 15.7 m/min. Hence, the magnitude of the velocity vector
Read MoreUnderstanding Motion, Force, and Energy in Physics
Item 5
Force is an interaction between two objects. There are four types of forces:
- The gravitational force
- The electromagnetic force, which causes chemical reactions
- Strong nuclear forces, which are responsible for the stability of atomic nuclei
- Weak nuclear forces, which are responsible for the instability of atomic nuclei
Weight (P) = Mass (M) * Gravity (G)
Item 6
Movement is a physical phenomenon defined as any change of position in space experienced by bodies in a system with respect to themselves
Read MoreAncient Cosmology: From Rationalism to Heliocentric Models
Rationalism and Empiricism
Rationalism and Empiricism: Empiricism and Rationalism made people rethink monism. If reality is one thing, then how can there be nothing, or motion, or how can anything be destroyed or created? If the real world is as Parmenides says, is this world not real? What is real?
Pythagoras
Pythagoras: Born c. 585 to 565 BCE on the island of Samos. He studied under Anaximander and founded a quasi-religious “brotherhood” influencing the Croton area of Southern Italy. This was
Read MoreElectrostatics and Magnetism: Key Principles and Laws
Electrostatics and Magnetism: Key Principles
Coulomb’s Law
The force of attraction or repulsion between two point electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance separating them. The force is directed along the straight line joining the charges. It is repulsive if the charges have the same sign and attractive if they have opposite signs. These are distance forces, and no material medium is needed between the charges.
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