Notes, summaries, assignments, exams, and problems for Physics

Gases

1.The volume
In the International System is measured in m ³
2.La temperature
In the International System is measured in Kelvin (K)
3.La pressure
Def.: Force exerted on the walls of a material that contains delrecipiente.
In the International System is measured in pascals (Pa).

Kinetic corpuscular

It is based on the kinetic model-corpuscular
Applied to gases says:
The gases are composed of particles separated from each other in continuous motion.
They have a disordered motion Brownian motion
They occupy the entire container volume
The faster you move higher temperature.

Gas Laws
Oley Boyle

üCuando constant temperature, increasing the pressure decreases the volume and vice versa.
üFórmula: P · V = constant. P ₁ V ₁ =... Continue reading "Air law" »

Electric Field of a Uniformly Charged Sphere

Suppose a sphere has a uniformly distributed charge. We want to calculate the electric field at a point r from the center of the sphere. By constructing a concentric Gaussian sphere that passes through the point, we apply Gauss's Law, where the flux is equal to Q / ε₀. Matching the flux, we conclude that E = kQ / r², which is identical to the field of a point charge located at the center of the sphere.

Field of a Uniformly Charged Indefinite Plane

To calculate this, we consider a parallelepiped centered on the plane. The flux is equal on both sides, resulting in E = Q / (2Sε₀). Since Q / S represents the surface charge density (σ), the field can be expressed in terms of that density.

Electric

The Compound Microscope: Function and Structure

The microscope is fundamentally a system designed to enhance the image of objects. The compound microscope, also known as the optical microscope, is an instrument featuring several lenses. It allows the observation of objects smaller than 0.1 mm, magnifying them up to 1500 times.

Key Systems of the Compound Microscope

The compound microscope is structurally divided into three primary systems:

• The Mechanical System (Support and Movement)
• The Optical System (Magnification)
• The Lighting System (Illumination)

The Mechanical System: Support and Movement

This system includes all parts that provide support and allow for movement and precise adjustment of the microscope components.

• Base or Foot: Provides stability

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" »

Kepler's Laws of Planetary Motion

• First Law (Orbit): Planets describe elliptical orbits around the Sun, with the Sun occupying one focus of the ellipse. The perihelion is the shortest distance of the planet to the Sun, while the aphelion is the longest.
• Second Law (Areas): The planet's radius vector sweeps out equal areas in equal times. The sector velocity remains constant; therefore, planets move faster at perihelion than at aphelion.
• Third Law (Period): The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Universal Gravitation

All bodies in the universe attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance... Continue reading "Kepler's Laws and Planetary Motion: Orbital Mechanics Explained" »

**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" »

Uniform Circular Motion

Uniform circular motion (UCM) describes the movement of a body along a circular trajectory, covering equal arc lengths in equal time intervals.

Key Concepts in Circular Motion

• Radian: An angle whose arc length is equal to the radius of the circle.
• Linear Path (s): The distance traveled along the circumference.
• Angular Path: The angle swept by the radius vector.
• Revolution: A complete circle or 360 degrees.
• Conversions: 1 revolution = 360 degrees = 2π radians.

Angular Velocity (ω)

In UCM, the angular velocity is constant and measured in radians per second (rad/s).

Linear Speed (v)

Linear speed is the product of angular velocity and the radius vector: v = ω · r.

Centripetal Acceleration (a_c)

This acceleration is always perpendicular... Continue reading "Uniform Circular Motion: Principles and Celestial Models" »

Kinematics: Types of Motion and Key Formulas

Uniform Motion (MU)

Uniform Motion is characterized by constant velocity, meaning zero acceleration.

Fundamental Equations

• Displacement (D): D = |e_final - e_initial|
• Average Velocity (V_m): V_m = D / t
• Position (e): e = e₀ + v · t

Graphical Representation

• In the Position vs. Time (e/t) graph, the line is straight and inclined.
• In the Velocity vs. Time (V/t) graph, the line is straight and horizontal (zero inclination).

Uniformly Accelerated Motion (MUA)

Uniformly Accelerated Motion is characterized by constant acceleration.

Fundamental Equations

• Acceleration (a): a = (v_final - v_initial) / t
• Velocity (v): v = v₀ + a · t
• Position (e): e = e₀ + v₀t + ¹/₂ · a · t²
• Time-Independent Equation: v² - v₀² = 2 · a · Δe.

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" »