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

Properties of Matter

Matter occupies space that can be measured. Two pieces of matter cannot occupy the same space.

The objects that surround us and which have defined limits are known as material bodies. If the limits are not precise, then we speak of material systems.

Properties of Matter

All the qualities of a material body are properties of matter.

• Extensive properties of matter: Extensive properties depend on the size of the material body we are observing, such as mass and volume.
• Intensive properties of matter: Intensive properties are not dependent on body size observed. They serve to differentiate material bodies. We say that two material bodies are composed of the same substance when they have the same intensive properties.

Measurement

What

The Modern Scientific Worldview

Until the 19th Century, the scientific process was dominated by the conceptual schemes of Isaac Newton and Galileo Galilei. Many scientists felt they were nearing a point where no significant new laws remained to be discovered. However, two new branches of physics would completely transform our worldview, affecting both the macrocosm and the microcosm: the theory of relativity and quantum physics.

The Theory of Relativity: Revolution in the Macrocosm

Albert Einstein published the theory of special relativity in 1905. It posits that there is no absolute space or time independent of the subject who experiences them. Instead, space and time are relative to speed. Time elapses differently for two observers traveling... Continue reading "Modern Physics and the Evolution of the Universe" »

Analytic Geometry: Distances and Angles

Distance Between a Point and a Line

The distance of a point, P, to a line, r, is the smallest distance from the point to the infinite points on the line.

This distance corresponds to the perpendicular from the point to the line.

Distance Between Parallel Lines

The distance of a line, r, to another parallel line, s, is the distance from any point on r to s.

Distance Between Intersecting Lines

The distance between two intersecting lines is measured along the common perpendicular.

Let and be the direction vectors of the lines r and s.

Vectors determine a parallelepiped whose height is the distance between the two lines.

The volume of a parallelepiped is .

Given that the volume is the absolute value of the scalar... Continue reading "Analytic Geometry: Distances and Angles in Space" »

Measuring the Photoelectric Effect

The electrons emitted by illuminating the cathode originate an electric current of intensity I upon collision with the anode. This intensity is proportional to the number of electrons ejected. The number of electrons reaching the anode is measured by the current flowing through the ammeter. The work W necessary to eject an electron from the metal depends on its binding energy. The minimum energy required is called the work function of the metal (W₀), defined as: W₀ = h f₀.

If the anode is positive, it will attract electrons; if the anode is negative, electrons will be repelled. In the latter case, the current will only reach the anode if the electrons possess an initial kinetic energy (E_c) sufficient to overcome... Continue reading "Quantum Physics: Photoelectric Effect and Atomic Spectra" »

Fluid Pressure and its Effects

A fluid exerts pressure in all directions on a body immersed in it (P = d * h * g). The magnitude increases with depth. The pressure does not depend on the area. If h is the same, the pressure will be the same. But the force depends on the area. The force of the water at the bottom of a lake is greater than that exerted in a pool (F = P * A). The pressure exerted by a liquid also depends on its density. If the liquid in Torricelli's experiment had been any other than mercury and of lower density, the column would have increased.

Bathysphere: A spherical steel tank used for underwater observations, supported by a cable from a ship.

States of Matter

• Solid: Molecules are linked by very strong cohesion and have a definite

A Personal Update

Dear Uncle Joaquin,

Thank you very much for sending me the FIFA 20 for my birthday. It’s amazing; you remembered it's my favorite game!

I had an extraordinary day. My family has been congratulating me all day. Then I went with my cousins to play football. In the evening, I opened my parents' present – it was a ball from the Champions League! And in the afternoon, I went to the shopping center to buy a lot of clothes.

I’m looking forward to seeing you at the weekend.

Love,

Carlos

Football Team Analysis

In my review, I compared three prominent football teams: Real Madrid, Liverpool, and Bayern Munich. All three play very well in both attacking and defending.

Real Madrid: Young Talent and Dominance

Real Madrid is a dominant team... Continue reading "Football Team Performance & Sustainable Living Practices" »

Foundational Concepts in Physics

Early Ideas on Falling Bodies

Historically, Aristotle believed that objects with higher mass fall faster. However, Galileo Galilei famously disagreed, demonstrating that all objects fall at the same rate in a vacuum, regardless of their mass (neglecting air resistance).

Understanding Force

Force is defined as the measure of interaction between bodies. Forces can be categorized as:

• Contact forces: Require direct contact between objects.
• Distance forces: Act without direct contact (e.g., gravity, magnetism).

Forces are typically measured using a dynamometer.

Newton's Laws of Motion

Newton's First Law: Inertia

Newton's First Law states: "If a body is not acted upon by any force, or if the total force acting on it is zero,

Unit III: Material Properties

1. Determination of the Characteristic Curve

It represents the functional relationships between the parameters characterizing a bomb. These curves show how and when a particular trip unit will act for a given time and current. A curve is represented by a band created by a minimum and a maximum value of time or current.

2. Lateral Deformation or Narrowing

It is a scale that measures how the width or space of a material is reduced due to an applied force.

3. Effort

Effort is the internal relationship of the materials when subjected to loads. It is usually expressed in intensity of force, i.e., force per unit area. The concept of effort is artificial; therefore, efforts cannot be measured experimentally. However, there... Continue reading "Understanding Material Properties: Stress, Strain, and Elasticity" »

Kinematics and Motion

• Path: The line that describes the motion of an object.
• Displacement: The straight-line distance between the object's initial and final positions.
• Scalars: Quantities that only require a number and a unit, such as temperature, distance, time, and mass.
• Vectorial Magnitudes: Quantities that require a number, unit, direction, and sense, such as velocity and force.

Vector Components

• Origin: The end of the vector not bearing the arrow.
• Line of Action: The line on which the vector is located.
• Direction: Indicated by the arrow.

Types of Motion

• MRU (Uniform Rectilinear Motion): Movement where the trajectory is a straight line and speed is constant.
• Accelerated Movement: Movement where speed varies over time.
  • Case 1: If speed increases, acceleration