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

Wave Properties and Characteristics

1. Mechanical waves can travel in any type of medium.

2. Refraction occurs when the amplitude of a wave changes as it goes from one medium to another.

Wave Classification and Behavior

• Transverse waves move particles back and forth along the same direction in which the waves travel.
• Mechanical waves can travel either through matter or through empty space.
• The amount of diffraction depends on the size of the obstacle and the wavelength of the wave.

Multiple Choice Questions

Which of the following is NOT a medium through which a mechanical wave can travel?

Answer: b. vacuum

Sound waves do not travel through a(n) _____.

Answer: d. empty space

Sound waves are _____.

Answer: a. longitudinal

Which of the following is transferred

Ideal vs. Practical Voltage Sources

1. Arc Welding (AW)

• General: Uses an electric arc to melt base metals and electrode to form a weld pool that solidifies.

Shielded Metal Arc Welding (SMAW) / Stick Welding

• Uses a consumable electrode coated with flux.

• Filler metal matches base metal.

• Common for steels; not ideal for aluminum, copper, titanium.

• Disadvantages: Frequent rod replacement, flux may melt prematurely at high currents.

Gas Metal Arc Welding (GMAW) / MIG

• Uses bare wire electrode with shielding gas.

• Advantages: Continuous wire = higher deposition rate, no slag, automatable.

Flux-Cored Arc Welding (FCAW)

• Like SMAW but electrode is a tubular wire filled with flux.

• Offers higher efficiency and is better suited for automation.

Electrogas Welding

• Vertical position welding with flux-cored

DC Motor Speed-Torque Characteristics

• Graph Interpretation

  • Y-axis: Speed (N).
  • X-axis: Torque (T).
  • Shape: Linear downward slope (speed decreases as torque increases).

• Speed-Torque Formula

  N=V−IaRaϕN=ϕV−Ia​Ra​​,
  where I_a = armature current, R_a = armature resistance, ϕ = flux.

• Key Performance Points

  • At No Load: High speed, low torque.
  • At Full Load: Low speed, high torque (due to armature reaction).

• Applications

  Used in electric vehicles and cranes for variable speed control.

Working Principle of 3-Phase Induction Motor

• Stator Function

  • A 3-phase AC supply produces a Rotating Magnetic Field (RMF).
  • RMF Speed (Synchronous Speed, N_s): Ns=120fPNs​=P120f​.

• Rotor Operation

  • Conductors (aluminum bars) are cut by the RMF, inducing current (Faraday’s

1. Vector Calculus

Gradient

The gradient of a scalar field represents the rate of maximum increase of the function and its direction.

Formula: ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Procedure

• Step 1: Differentiate w.r.t x
• Step 2: Differentiate w.r.t y
• Step 3: Differentiate w.r.t z
• Step 4: Substitute the coordinates

Divergence

Divergence measures the outward flow of a vector field.

Formula: ∇·A = ∂Ax/∂x + ∂Ay/∂y + ∂Az/∂z

Curl

Curl measures the rotational nature of a vector field.

Formula: ∇×A (determinant method)

2. Electrostatics

Coulomb's Law

The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance. The direction is along the line joining... Continue reading "Electromagnetism and Vector Calculus Essential Concepts" »

Capillary Action and Surface Tension

Capillary action describes the phenomenon where the level of a liquid inside a narrow tube (relative to its container) is either raised or lowered. This height difference is maintained by surface tension forces. The direction and magnitude of this change depend on the liquid's surface tension and its interaction with the tube material (wettability).

The vertical component of the surface tension force acting on the tube walls must balance the weight of the liquid column of height h. Horizontal forces typically cancel out.

The capillary height h can be determined by balancing these forces:

• Surface tension force (vertical component): Fv = γ · 2πR · cosθ
• Weight of liquid column: P = ρ · g · πR2h

Equating... Continue reading "Fundamental Fluid Properties and Transport Phenomena" »

Santa Maria degli Angeli (Florence)

(Demolished after 3 years)

• Blended integration and relation of elements.
• Centralized floorplan: Representing an aesthetic ideal and an expression of the order of the universe – absolute symmetry.
• Surrounded by a world of well-proportioned beauty.
• Relation with Villa Rotonda; centralized building as a key urban form.

Michelozzo: Palazzo Medici (Florence)

• An urban palace where the facade is an important aspect.
• The wall treatment softens and smooths in the upper levels, representing the wealth of the Medici family.
• Exterior conveys solemnity, giving higher status to the city as well.
• Features a very heavy cornice at the top.

Leon Battista Alberti: Theory and Practice

• Had extensive contact with Florentine Humanists; friend

Thermal Expansion and Heat Energy Calculations

Section 4.1-2: Thermal Properties

The change in length due to thermal expansion is calculated using the following formula:

L₂ - L₁ = αL₁(T₂ - T₁)

• α (Alpha): Coefficient of thermal expansion, measured in °C^-1 or °F^-1.
• L₁ & L₂: Initial and final lengths, measured in mm (in), corresponding to temperatures T₁ & T₂.

Heat Energy Required for Temperature Change

The amount of heat energy ($H$) required to change the temperature of a material is given by:

H = C W (T₂ - T₁)

• H: Amount of heat energy, measured in J (Btu).
• C: Specific heat of the material, measured in J/Kg°C (Btu/lb°F).
• W: Weight of the material, measured in kg (lb).
• (T₂ - T₁): Change in temperature, measured in °C (°F).

Volumetric Specific

Numerical Methods for Solving Equations

1.1 Solving an Algebraic System

This code defines a function f(V) and then solves the system f([x,y,z]) = [x,y,z] to find its fixed points using the algsys command.

faux(x,y,z) := [(x^2)/2 + 1/3, x+y+z/4, x^2-y^2+(z^2)/4];
f(V) := faux(V[1], V[2], V[3]);

ecus : f([x,y,z]) - [x,y,z];
algsys(ecus, [x,y,z]), numer;

1.2 Fixed-Point Iteration Method

This block implements the fixed-point iteration method. It starts with an initial guess (seed) and iteratively applies the function f until the norm of the difference between successive iterations is smaller than a given tolerance (10^-14).

nor(V) := sqrt(V.V);
fpprec:100;

block(
  semilla:[0,0,0],
  while nor(f(semilla)-semilla) > 10^(-14) do 
    semilla:bfloat(

Motion in a Plane

Magnitude of vector: |A| = √(a_x² + a_y² + a_z²)

Unit vector: â = vector a / |a|

Resultant: R = √(A² + B² + 2AB cos θ)

Time period of projectile motion (T): 2u sin θ / g

Maximum height (H): u² sin² θ / 2g

Range (R): u² sin 2θ / g

Uniform Circular Motion (UCM)

• Centripetal acceleration (a_c): v² / r
• Angular velocity (ω): θ / t

Relation between linear velocity and angular velocity: v = rω

Gravitation

The Universal Law of Gravitation: Masses attract each other with a force proportional to their masses and inversely proportional to the square of the distance between them.

Force (F): G m₁m₂ / r²

Gravity at height (g_h): g_h = g_s / (1 + h/r)² or g_h = g_s(1 - 2h/r) if h < 300 km

Gravity at depth (g_d): g_d = g_s(1 - d/R)

Escape