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

Physics Formulas

Speed

V: Average velocity

• V = s / t
• s: Distance traveled
• s = v · t
• t: Time spent
• t = s / v
• Minutes to hours = min / 60

SI units:

• Speed is the distance traveled by a mobile unit per unit of time.
• m / s
• km / h
• cm / s

Acceleration

a: Acceleration

• a = V_f - V₀ / t
• V_f: Final velocity
• V_f = V₀ + a · t
• V₀: Initial velocity
• V₀ = V_f - a · t
• t: Time

SI units:

• Acceleration is the change in speed per unit of time.
• m / s²

Forces

F: Force in newtons

• F = m · a
• m: Mass in kg
• a: Acceleration in m / s²

SI units:

• Force is a physical quantity associated with movement.
• Newton (N)
• Kilogram-force (kgf)
• Pound (lb)
• Dyne (dyn)

Forces in the same direction:

• F_R = F₁ + F₂

Forces in opposite directions:

• F_R = F₁ - F₂

Mass

m: Mass in kg

• m = F / a
• F: Force in newtons
• a: Acceleration in m / s²

SI units:

Understanding Physical Forces

Forces can act on objects even when they are not physically in contact. For example, a magnet attracts another through its magnetic field.

What Effects Do Forces Produce?

Depending on the applied force and the body receiving it, different outcomes can occur:

1. Shape Shifting (Deformation)

When a force is applied to a body, it may deform. There are two primary types of deformation:

• Plastic Deformation (Permanent): This deformation is maintained over time, permanently changing the object's shape. Such bodies are called inelastic. For example, if you press hard on a ping-pong ball, it deforms and does not return to its original shape naturally.
• Elastic Deformation (Temporary): This deformation is only maintained while the

Basic Laws of Cartesian Physics

Descartes invokes God to explain extension and motion: God is the creator of matter and of a certain amount of motion that remains constant, because God is unchangeable both in being and in operation. He therefore regards the universe as a closed system. He formulates three fundamental laws:

Three Fundamental Laws of Motion

1. Law of inertia: Every body tends to remain in its state of rest or of uniform motion in a straight line unless acted on by an external force.
2. Law of straight-line motion: Any body in motion tends to continue moving in a straight line unless an external force intervenes; otherwise there would be no reason to explain a deviation.
3. Law of conservation of motion: Motion is not lost in collisions between

Understanding Hooke's Law

Hooke's Law states that the deformation of an object is proportional to the force applied. When one magnitude or signal is proportional to another, a relationship can be established between both magnitudes by multiplying one of them by a coefficient of proportionality.

In this case, the force applied (F) is proportional to the elongation (x) of a spring. This relationship is expressed as:

F = kx

Where k is the coefficient of proportionality, known as the spring constant. Its value is defined as:

k = F / x

Units and Elastic Characteristics

In the International System of Units (SI), the spring constant is measured in N/m. This constant is a characteristic of the spring's stiffness:

• Hard springs: Have a high k value.
• Lazy (soft)

San Pietro in Montorio, Bramante, 1502

Religious Architecture, Cinquecento, Rome

Introduction: This is an early work of Bramante in Rome. It is a chapel, built between 1502-1503, located in a small courtyard. According to tradition, Saint Peter was crucified on this site. It is a model of a religious building with a central plan, inspired by the Hellenistic *monopteros* temples, and its elevation recalls the Temple of the Sibyl at Tivoli.

Analysis and Features: It is considered the aesthetic ideal of the Renaissance in the 16th century. This architectural ideal is achieved by using:

• A monumental and grandiose architectural language, achieved through a rigorous study of the proportions of each part of the building.
• The creation of a complete architectural

Huygens' Principle: Understanding Wave Propagation

Huygens' Principle is a wave propagation model that helps explain various wave phenomena. It states that a wave propagates as a wave front or surface connecting all points reached by the wave motion at the same instant. Every point of an isotropic medium which experiences a disturbance behaves as a source emitting secondary waves (or wavelets) that propagate in the direction of the disturbance. The surface tangent to all these wavelets at a given instant forms the next wave front. The radius of the wavelets at any instant is vt (velocity × time).

Wave Reflection

When a wave propagating through one medium reaches the boundary with a different medium, part of the wave is reflected and continues... Continue reading "Huygens' Principle: Wave Propagation & Phenomena" »

Modern Physics

This branch of physics considers the theory of relativity and quantum theory in describing microscopic systems like atoms.

Model of Modern Physics

In the late nineteenth century, it was a common belief that all phenomena of nature could be described by Newton's laws, principles of thermodynamics, and the laws of electromagnetism, which were based on a mechanical conception of the universe.

Reaffirmation of Modern Physics

In 1905, Albert Einstein produced a series of works that revolutionized physics, mainly due to the wave-particle duality of light and the theory of relativity, among others.

Classification of Modern Physics

It is generally known to study phenomena that occur at the speed of light or values close to it, or whose spatial... Continue reading "Modern Physics: Relativity, Quantum Mechanics, and Nuclear Processes" »

Understanding Geospatial Concepts

Geographical Coordinates

The geographic coordinate system determines all positions on the Earth's surface using two angular coordinates of a spherical coordinate system, which is aligned with the Earth's axis of rotation. It defines two angles measured from the center of the Earth:

• Latitude: Measures the angle between any point and the Equator. Lines of latitude are called parallels and are circles parallel to the Earth's surface.
• Longitude: Measures the angle along the Equator from anywhere on Earth. In most modern societies, Greenwich, London, is accepted as the 0° longitude. Lines of longitude are great circles passing through the poles and are called meridians.

Aerial Photography (Photogrammetry)

Photogrammetry... Continue reading "Essential Geospatial and Mapping Concepts" »

Work and Power in Physics

Work acts on a body when a force moves it through a distance; we say that force has done a job. Therefore, the work will be calculated as: W = F · s. The work unit in the SI is the Joule (J), which is defined as the work performed by applying a force of 1 Newton over 1 meter (1J = 1N · 1m).

Conditions for No Work

No work is done when:

• 1. There is no displacement (space is 0); the work is zero.
• 2. The force and displacement are perpendicular (90°).

Power and Efficiency

Power: The quantity that relates work over time; therefore, P = W / t. The SI unit is the Watt (W), defined as work performed at 1 Joule per second (1W = 1J / 1s). It can also be expressed as: P = F · v.

Efficiency: The performance of a machine is never 100%... Continue reading "Fundamental Principles of Work, Power, and Energy" »