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

Key Kinematics Concepts

Reference System

A reference system is a coordinate system (O, X, Y) combined with a clock, used to define the position and motion of objects.

Position

Position is the location of a body in space, defined by coordinates within a chosen reference system.

Trajectory

The trajectory is the imaginary path or line described by a moving body, formed by the sequence of positions it occupies over time.

Distance Traveled (Path Length)

Distance traveled (or path length) is the total length of the path covered by a body along its trajectory.

Displacement

Displacement is the vector difference between a body's final and initial positions, indicating the change in position and direction. It is measured in meters (m).

Velocity

Velocity is a vector... Continue reading "Fundamental Concepts of Motion in Physics" »

Photomultiplier Characteristics

What is dark current?

The dark current is a small amount of current flowing in the photomultiplier even when it is not illuminated. This current should be minimized for accurate measurements. The region between 800 V and 1300 V is often ideal for operating the photomultiplier.

The primary source of dark current is the thermionic emission rate from the photocathode and dynodes. Other sources include:

• Leakage current
• Incandescent lighting phenomena
• Field emission
• Current from residual gas ionization
• Radioactive contamination within the device materials

What is the photomultiplier gain?

The gain (G) of a photomultiplier is the ratio between the number of electrons at the output and the number of photons incident on the photocathode.... Continue reading "Photomultiplier Dark Current, Gain & Lifetime Measurements" »

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

Motor Performance Problem

A motor has a resistance of 250 Ω and operates at 100 V at 25 °C. The temperature coefficient of resistance (α) at 25 °C is 0.0018 /°C. We need to determine the following:

Questions for Analysis

1. The resistance value when the temperature is 50 °C.
2. The current absorbed from the network when the temperature is 25 °C and 50 °C.
3. The cost of the energy consumed in 120 minutes at 50 °C if the cost per kWh is $1.
4. At what temperature and why does the motor consume less energy?

Principles of Electromagnetism

Induced Electromotive Force (EMF)

When a conductor of length (l) moves with a constant velocity (v) within a magnetic field of induction (B), an electromotive force (EMF) is induced across its ends.

• Perpendicular Motion:

Work-Energy Theorem

The work (Wt) done by the net force on an object is equal to the variation in its kinetic energy (ΔEc). This can be expressed as: Wt = ΔEc = Ec2 - Ec1, where Ec1 is the initial kinetic energy and Ec2 is the final kinetic energy.

Gravitational Potential Energy

Gravitational potential energy is the energy associated with a system of two masses attracted by a gravitational force. It is also defined as the work required to move a mass 'm' from infinity to a specific distance 'r' from the Earth.

Variation of Potential Energy

The variation of potential energy is the work required to move a mass 'm' from a first point to a second point within a force field.

Moment of a Force (Torque)

The moment of a force (F) represents the ability... Continue reading "Fundamental Concepts in Mechanics and Gravitation" »

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

Post-War Realism

The premiere of AB Vallejo's History of a Ladder in 1949 marked a significant shift in Spanish theater. Vallejo's plays sought to explore the modern Spanish tragedy, awakening compassion in audiences. His works synthesized realism and symbolism, contrasting contemplative and active characters. Vallejo's use of immersion techniques aimed to incorporate viewers into the protagonist's inner world.

Key Plays:

* History of a Ladder (1949) * In the Hot Darkness (1950) * The Sleep of Reason (1953) * The Foundation (1957)

Avant-Garde Theater

In the 1950s, avant-garde theater emerged, influenced by European innovations. Fernando Arrabal and Francisco Nieva incorporated elements of:

Theater of the Absurd:

* Colloquial language expressing communication... Continue reading "The Evolution of Spanish Theater: From Post-War Realism to Contemporary Issues" »

Heat Transfer

Heat is the transfer of energy from one part of a body to another, or between bodies that are at different temperatures. Heat is energy in transit and always flows from hotter bodies to those with a smaller temperature. Temperature is the quantity that tells us how hot or cold an object is in comparison with a reference.

Temperature Scales

• Celsius: The most used international unit for ordinary temperature measurements.
• Fahrenheit: The temperature unit proposed by Gabriel Fahrenheit, which is fixed at zero and one hundred for the freezing and boiling temperatures of ammonium chloride in water, respectively.
• Kelvin: The temperature unit scale established by William Thomson, based on the degree Celsius, with the absolute zero point set

Friction Force Fundamentals

Friction, as a contact force, is a force applied by a surface to an object in contact with it. The frictional force is always parallel to the surface, while the contact force (or normal force) is always perpendicular to the surface itself. Friction acts to oppose any externally applied force.

The vector sum of the contact force (Fc) and the friction force (Ff) represents the total force exerted by the surface on the object. There exists a maximum value for the magnitude of the friction force (Ff). If an applied force (Fa) exceeds this maximum value, it cannot be countered by the frictional force, and the block will begin to move. (Note: The contact force (Fc) also has a maximum value, beyond which the surface itself... Continue reading "Essential Principles of Force and Motion" »