Notes, abstracts, papers, exams and problems of Physics

Discobolus

Historical Context

This sculpture exemplifies the free style characteristic of the Classical Greek period. During this era, artists were greatly concerned with portraying balanced proportions of human anatomy, striving to achieve the ideal model of human beauty. To accomplish this, muscles are depicted in a more rounded and naturalistic manner, contrasting with the Praxitelean curve. Stiffness and frontality, typical of earlier periods, were abandoned in favor of a canon of mathematical proportion between the head and body. One piece, the Riace Warriors, could be the work of Alcamenes, a disciple of Polyclitus and Phidias. An old saying claims that this sculptor was the inventor of the "X" composition and the first to accurately represent... Continue reading "Discobolus: Greek Sculpture of an Athlete in Motion" »

**Coulomb's Law: Quantifying Force Between Electric Charges**

The quantification of force between electric charges is attributed to Coulomb, who used a torsion balance. Coulomb's law states that the force of attraction or repulsion between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. This can be expressed as:

F = K • (Q₁Q₂ / r²)

Where:

• F is the force
• K is Coulomb's constant
• Q₁ and Q₂ are the charges
• r is the distance between the charges

The electrical constant, K, is defined in terms of another constant called the permittivity of the medium. Coulomb's law is analogous to Newton's law of universal gravitation. Both forces are proportional to the product of the property... Continue reading "Understanding Electric and Magnetic Fields: Forces and Charges" »

Vibration: Periodic Motion

Periodic motion occurs when the magnitude that characterizes it repeats at regular intervals of time. Examples include the Moon orbiting the Earth and a piston in an internal combustion engine. In periodic motion, the period is defined as the time that passes until the motion repeats.

Oscillatory Movements

An oscillatory movement is a motion in which the path is covered in two directions. An example is a pendulum. Many oscillatory movements in nature eventually stop due to friction. These oscillations are called damped oscillations, in contrast to those that do not involve friction, which are called free oscillations.

Dynamics of Simple Harmonic Motion

Work Done by a Constant Force

The work done by a constant force is the... Continue reading "Understanding Vibrations and Harmonic Motion in Physics" »

Understanding Vehicle Dynamics: FMR, RR, RP, FMD, and FMU

FMR (Force Moving Resistance): Power required to move machines on a surface, such as through a cut or haul road. The factors determining FMR are:

FMR = RR + RP

Rolling Resistance (RR)

RR (Rolling Resistance): The force opposing the ground at the turn of a vehicle's wheels. To move, the vehicle must counteract this force.

RR = rr x factor pbv

Several factors contribute to RR, the most important being:

A. Internal Friction

Internal friction produced in the powertrain, from the engine to the tires or tracks. Mechanical components like bearings create resistance to movement.

B. Tire Flexion

Flexion of tires increases resistance due to sidewall and tread deformation during spinning. The extent of this... Continue reading "Understanding FMR, RR, RP, FMD, and FMU in Vehicle Dynamics" »

John Dalton: The First Theory of Matter

John Dalton proposed the first theory of matter.

William Crookes: Perfecting Vacuum Tubes

William Crookes (1832-1919) perfected devices using a glass tube that had undergone a partial vacuum and contained two electrodes, one positive and one negative, connected to a source of high-voltage continuous current.

J.J. Thomson: Discovering the Electron

In 1897, J.J. Thomson proved that the cathode ray consisted of minute particles of negative electric charge that are attracted by the positive electrode. He achieved determining the relationship between charge and mass for these particles. He carefully measured how magnetic and electric fields deviated the electrons' trajectory. Independently of their origin, they... Continue reading "Key Discoveries in Atomic Theory and Radioactivity" »

Wave Motion

Wave motion refers to the transmission of a disturbance from one point to another without the net transport of matter.

Wave Classification

Based on Direction of Propagation

• One-dimensional waves: Propagate in a single direction.
• Two-dimensional waves: Propagate in two directions.
• Three-dimensional waves: Propagate in three directions.

Based on Medium of Propagation

• Mechanical waves: Require a material medium for propagation. Their speed depends on the characteristics of the medium.
• Electromagnetic waves: Do not require a material medium and can propagate in a vacuum (e.g., visible light).

Based on Direction of Disturbance

• Transverse waves: The direction of propagation is perpendicular to the direction of the disturbance.
• Longitudinal waves:

Geocentric Theory

Aristotle proposed the following:

• The Earth is round and immobile at the center of a celestial sphere, which houses the stars.
• The planets and stars rotate in a celestial sphere with uniform circular motion around the Earth.

Ptolemy improved Aristotle's theory. The Ptolemaic theory was based on circular orbits but later included eccentric orbits and epicycles to describe the movement of the planets. He maintained that the Earth was the center of the universe.

Heliocentric Theory

Copernicus and Galileo, who demonstrated this theory with a microscope he had built, proposed the heliocentric theory. However, Copernicus did not reveal his theory until the 16th century. It affirmed the following points:

• The Sun is at the center of the

Concept of Slope and Gradient

The closeness of curves indicates a steep slope, while a large separation indicates a slight incline. This equidistance, whenever we have to compare the two cases, is the same. The equidistance of curves in a plane is unique.

• A series of concentric curves, where the heights rise to the center, indicates a rise or hill.
• A series of concentric curves, in which the dimensions decrease toward the center, indicates a depression or hollow.

We define slope as the ratio between the horizontal and vertical displacement, always looking from the top down. The gradient is defined as the ratio between the vertical and horizontal displacement.

Alignment

• Natural Distance (Dn): Dn is the distance traveled on the ground, following the

**Fe, Co, Ni: Ferromagnetic Materials**

_Iron (Fe), Cobalt (Co), and Nickel (Ni)_ are ferromagnetic materials. They strongly attract metals and exert attractive or repulsive forces on other materials.

**Early Discoveries in Magnetism**

• **William Gilbert:** Identified North and South Poles as magnetic.
• **First Discovered Natural Magnet:** Magnetite (iron oxide (Fe₃O₄)) and Magnesia (Chinese).

**Electric and Magnetic Fields**

• **Charge (Q) at rest:** Creates an electric field.
• **Moving charge:** Creates an electromagnetic field.

Analogy:

• Computer storage ↔ Electric field
• Mass ↔ Gravitational field
• Magnet ↔ Magnetic field

**Key Figures in Electromagnetism**

• **1831 Michael Faraday:**

  Introduced the concept of lines of force to explain the behavior of forces

Ancient Worldviews

Worldview: The Greek "cosmos" implied a beautiful order and harmony, as opposed to chaos and disorder. It represents a coherent and systematic view of the world, a total interpretation of reality.

Scientific Worldviews

Theories of science:

• Astronomy: Studies the stars.
• Cosmology: A part of astronomy that explains the origin and evolution of the universe.
• Physics: A fundamental science for understanding the world, contributing laws that explain the movements and forces affecting bodies.

Former Worldviews: 6th Century BC

• Principles of Reality

  The ancients believed that all substances came from the transformation of one or several elements that could be considered the origin of reality.

  • Basic Principle or Arche

    The Milesian school of philosophy