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

Vector Mechanics and Statics

Scalar product: a · b = |A| |B| · cos(θ)

Projection of vector b onto a: P_a b = (a · b) / |A| · a / |A|

Moment of force about a point: M₀ = OA × F

Reduction of Force Systems

Reduction to a new center: M_p = M₀ + PO × R (where R is the backbone/resultant force and PO is the vector from the new point to the original center).

Force-couple system: F_tot = R_system → M₀ = M_pair.

Newton's Laws of Motion

• 1st Law: A particle on which no forces act (or R = 0) will maintain a constant velocity (v = constant).
• 2nd Law: A particle subjected to an experimental force undergoes acceleration.
• 3rd Law: If body A exerts a force on body B, body B returns a force of the same magnitude and opposite direction.

Classification of Unranked Force

Kinematics Formulas

Position Vector

r = xi + yj

• x = r cos
• y = r sin
• r = √(x² + y²)
• tan θ = y / x

Displacement

Δr = r - r_initial

Speed, Average Speed, Instantaneous Speed

• Average Speed: v_av = Δr / Δt
• Instantaneous Speed: v = dr / dt

Average Acceleration, Instantaneous Acceleration

• Average Acceleration: a_av = Δv / Δt
• Instantaneous Acceleration: a = dv / dt

Uniform Rectilinear Motion (MRU)

• v = Δx / Δt
• v_mean = (v₀ + v) / 2
• v = v₀ + at
• x = x₀ + vt
• x = x₀ + v₀t + (1/2)at²
• v² - v₀² = 2aΔx
• v² = v₀² ± 2as

Free Fall

• Velocity: v = gt
• Position (height fallen): y = (1/2)gt²
• Velocity (upward): v = -gt
• Position (height): y = y₀ - (1/2)gt²

Upward Vertical Launch

• Velocity: v = v₀ - gt
• Position (height): y = y₀ + v₀t - (1/2)gt²
• Time to reach maximum height: t = v₀ / g
• Maximum

Magnetic Hysteresis in Ferromagnetic Materials

When a magnetic material is subjected to a changing magnetic field intensity (H), the magnetic induction (B) lags behind. This phenomenon is known as magnetic hysteresis. (See Figure 1). When a ferromagnetic substance is subjected to a cyclical (alternating positive and negative) magnetic field intensity, it traces a hysteresis loop.

Key points on the hysteresis curve (See Figure 1):

• O-B: Magnetization curve.
• O-R: Residual magnetization.
• O-D: Coercive force.

When applying an alternating magnetization intensity (+ and -) to a ferromagnetic substance, the resulting hysteresis loop is shown in the image. The magnetic induction (B) lags behind the magnetic field intensity (H). At point B, even when H = 0,... Continue reading "Magnetic Hysteresis & Autoinduction Explained" »

Coulomb's Law and Electric Force

Coulomb's Law: The electric force with which two resting charges, q₁ and q₂, attract or repel each other is directly proportional to the product of the charges and inversely proportional to the square of the distance d (or r) that separates them.

The force is a vector unit according to the direction of the charges. The constant k has a numerical value of 8.9874 × 10⁹. The unit of electric charge is the Coulomb (C): The Coulomb is the positive charge q which, when placed in a vacuum at a distance of 1 meter from another identical charge, repels it with a force of 8.9874 × 10⁹ N. This constant allows us to solve Coulomb's Law.

Permittivity and Mathematical Expression

The units are determined by the permittivity

Understanding Magnetic Properties

Bodies known as magnets possess magnetic properties. Magnets are classified into two main types:

• Natural Magnets: Found in nature, such as magnetite.
• Artificial Magnets: Materials that have acquired magnetization. These are further divided into:
  • Ferromagnetic Materials: Materials that can be magnetized.
  • Temporary Magnets: Lose their magnetic properties when the magnetizing force ceases.
  • Permanent Magnets: Maintain their magnetic properties even after the magnetizing force is removed.

Methods of Obtaining Magnets

• Rubbing: Rubbing a steel bar with a magnet allows the bar to acquire magnetic properties, which can be observed by its ability to attract iron filings.
• Contact: Bringing an iron needle into physical contact

Gas Metal Arc Welding (GMAW): MIG and MAG Processes

MIG/MAG welding (Gas Metal Arc Welding) is a heat fusion process that joins pieces of metal using an electric arc generated between a consumable electrode wire and the workpiece. The weld pool is protected by a shielding gas, which prevents contamination of the liquid metal.

• MIG (Metal Inert Gas): Utilizes an inert gas (e.g., Argon or Helium) for protection.
• MAG (Metal Active Gas): Utilizes an active gas (e.g., Carbon Dioxide or mixtures) for protection.

MIG/MAG Welding Equipment Components

1. Power Source

   Plugs into the electrical network (220 V or 380 V). It consists of a transformer and rectifier, providing adjustable, continuous DC voltage, which may fluctuate slightly during operation.

2. Electrode

Fundamental Heat Exchanger Concepts

Key Formulas in Heat Transfer

• Heat Exchanged (q): q = m · Cp · ΔT (Heat absorbed or released by a fluid)
• Heat Transfer Rate (Q): Q = U · A · ΔT (Overall heat transfer rate through an exchanger)
• Energy Balance for Heat Exchangers: M_c · Cp_c · (ΔT_c) = M_f · Cp_f · (ΔT_f) (Heat gained by cold fluid equals heat lost by hot fluid)
• Other Formulas (Context Dependent): ct = w1 + w2 · PC1 · CP2

Definition of a Heat Exchanger

A heat exchanger is a device designed to efficiently transfer heat from one fluid to another. Common examples include:

• Condenser: Transfers heat from a hot fluid to a colder one, causing the hot fluid to condense (e.g., steam to water).
• Evaporator: Transfers heat to a cold fluid, causing it to

Energy

Energy is the capacity of bodies to produce transformations in themselves or other bodies.

Energy Sources

Energy sources are natural resources from which humans can obtain usable energy.

Types of Energy Sources

• Non-renewable: Found in limited quantities and are depleted with use.
• Renewable: Considered inexhaustible as they are continuously renewed.

Energy Principles

• Conservation of Energy: The total energy in the universe remains constant in any process.
• Degradation Principle: With each transformation, energy loses quality and produces new transformations.

Work and Power

Work (W) is done when a constant force (F) is applied to a body, causing a displacement (d) in the same direction as the force: W = F * d.

Power is the rate at which work is done.... Continue reading "Energy, Waves, Sound, Light, and Electricity: Physics Fundamentals" »

Fundamental Concepts of Fluid Statics

Definition of Pressure

The Pressure (P) is defined as the ratio of the exerted Force (F) to the surface Area (S) over which it acts:

$$P = \frac{F}{S}$$

Hydrostatic Pressure

Hydrostatic Pressure is the pressure exerted by a liquid at all points within it.

Fundamental Equation of Fluid Statics

The pressure at a depth $h$ in a fluid of density $\rho$ under gravity $g$ is given by:

$$P = \rho g h$$

Communicating Vessels Principle

When several containers of different shapes containing the same liquid are connected at the bottom, the height of the liquid surface is identical in all vessels.

Application of Communicating Vessels

This principle is fundamental to water distribution systems for communities.

Determining Relative

Massage Session Protocol

1 - Abdomen (10 min)

• Making contact.
• Passes soft (Frictions).
• Venous Vaciaje.
• Friction palms circular (clockwise).
• Digital kneading.
• Frictions the entire colon (triangle).
• Venous Vaciaje.
• Palmar kneading (grasping).
• Pinching (roller technique).
• Click.
• Vibration on the solar plexus (hands alternating).
• Final Venous Vaciaje passes.

2 - Arms (3 min each)

• Rubbing in glove.
• Frictions.
• Simple knuckle kneading.
• Digital Roces (scratch with yolks).

Breast (1 min)

• Digital kneading the top.
• Circles around the breasts.

3 - Facial (5 min)

(Specific facial techniques would be listed here, content was empty.)

4 - Legs Supine (5 min per leg)

Ankle to Groin

• Palmar stroking (ankle to groin).

Thighs

• Palmar stroking (middle internal and external).
• Digital kneading