Engineering Trigonometry, Materials Science, and Stoichiometry

Comprehensive vocabulary flashcards covering right triangle trigonometry, material and mechanical properties, stress-strain behavior, units of stress, and stoichiometry with Avogadro's number calculations.

Right Triangle Trigonometry

A branch of mathematics that studies the geometric relationships between the angles and sides of right triangles, in which one interior angle measures $90^{\circ}$.

Hypotenuse

The longest side in a right triangle, situated directly opposite the $90^{\circ}$ right angle.

Opposite Side

The side of a right triangle located directly across from the specific angle of interest ($\theta$).

Adjacent Side

The side of a right triangle located next to the specific angle of interest ($\theta$) that is not the hypotenuse.

Sine Function

A primary trigonometric function defined in a right triangle as the ratio of the opposite side to the hypotenuse: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Cosine Function

A primary trigonometric function defined in a right triangle as the ratio of the adjacent side to the hypotenuse: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$.

Tangent Function

A primary trigonometric function defined in a right triangle as the ratio of the opposite side to the adjacent side: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

Angle of Elevation

The angle formed between an observer's horizontal line of sight and an object located upward at a higher elevation.

Angle of Depression

The angle formed between an observer's horizontal line of sight and an object located below; equal in magnitude to the corresponding angle of elevation by alternate interior angles.

Material Properties

Physical, chemical, dimensional, or mechanical components of a specific substance that determine its capabilities, functionality, performance limits, and manufacturability.

Mechanical Properties

Characteristics of materials that govern their behavior under the action of external loads, specifically describing their capacity to resist deformation.

Modes of Applied Stress

The three primary ways external loads are applied: compression (pushing inward), tension (pulling outward along the axis), and shear (forces acting parallel to adjacent internal planes).

Strength

The mechanical property and capacity of a material to withstand destruction or resist deformation when subjected to external loads.

Elasticity

The power or ability of a material to return to its original shape and dimension after deformation when the applied load or stress is released.

Plasticity

The ability of a material to undergo permanent deformation without rupture or brittle failure, occurring after the elastic limit has been exceeded.

Hardness

The resistance of a material to force penetration, indentation, bending, scratching, abrasion, or cutting.

Toughness

The property enabling a material to withstand shock or impact without breaking; considered a combination of strength and plasticity and the opposite of brittleness.

Brittleness

The tendency of a material to fracture under shock or impact rather than bend or undergo permanent deformation; typically associated with high compressive strength and low tensile strength.

Stiffness

The mechanical resistance of a material or structure to elastic deformation or deflection when subjected to an applied load.

Ductility

The mechanical property of a material that enables it to be permanently drawn out or elongated into a thin wire.

Malleability

The property of a material permitting it to be hammered, rolled, or pressed into sheets of different shapes and thicknesses.

Cohesion

The property of a solid body by virtue of which its constituent particles resist being pulled apart or broken into fragments.

Impact Strength

The ability of a metal or material to withstand suddenly applied loads without fracturing.

Fatigue

The progressive damage and weakening that causes strain or breakage of a material under the action of repeatedly applied or cyclic forces.

Creep

The slow, progressive, and time-dependent permanent deformation of a material subjected to a constant mechanical force, often accelerated at high temperatures.

Creep Strength

The constant applied force required to produce a specified rate of strain in a material held at a constant temperature.

Stress ($\sigma$)

The internal resisting force per unit cross-sectional area that a material withstands: $\sigma = \frac{F}{A}$, identical in dimensions to pressure.

Strain ($\varepsilon$)

The fractional change in length or total displacement divided by the original length of a material under load: $\varepsilon = \frac{\Delta L}{L}$.

Engineering Stress ($\sigma_{eng}$)

The ratio of an applied axial load ($F$) to the original, undeformed cross-sectional area ($A_0$): $\sigma_{eng} = \frac{F}{A_0}$.

Engineering Strain ($\varepsilon_{eng}$)

The ratio of the change in length ($\Delta L = L_f - L_0$) to the initial undeformed length ($L_0$): $\varepsilon_{eng} = \frac{L_f - L_0}{L_0}$.

Stress-Strain Curve

A graphical plot of applied stress versus corresponding strain that describes the mechanical deformation behavior of a material throughout its loading history.

Proportional Limit

The region on a stress-strain curve up to which stress remains strictly proportional to strain according to Hooke's Law, with Young's modulus acting as the proportionality constant.

Elastic Limit

The point on a stress-strain graph up to which a material completely returns to its original dimension upon removal of the applied load; exceeding it produces permanent plastic deformation.

Yield Point

The transition point where plastic deformation initiates without an increase in load; categorized into an upper yield point and a lower yield point.

Ultimate Stress Point

The point on the stress-strain curve representing the maximum stress that a material can withstand before localized necking and failure begin.

Fracture Point (Breaking Point)

The point on a stress-strain curve at which physical separation, complete rupture, or material failure takes place.

Young's Modulus ($E$)

The measure of rigidity or ability to resist elastic deformation on force application, defined as the ratio of tensile/compressive stress to strain: $E = \frac{\sigma}{\varepsilon}$, typically given in $\text{N/m}^2$ or $\text{GPa}$.

Pascal ($\text{Pa}$)

The SI unit of stress and pressure, defined as one newton of force pressing uniformly over a surface area of one square meter: $1.0\,\text{Pa} = \frac{1.0\,\text{N}}{1.0\,\text{m}^2}$.

Pound per Square Inch ($\text{psi}$)

The British unit of stress ($\text{lb/in}^2$); relates to SI units through the equivalence $1\,\text{psi} = 6895\,\text{Pa}$ and $1\,\text{Pa} = 1.450 \times 10^{-4}\,\text{psi}$.

Physical Properties

Observable and measurable attributes of a material's state independent of external loads or chemical reactions, such as density, color, melting point, boiling point, and thermal or electrical conductivity.

Avogadro's Number

The fundamental constant defining the number of particles (atoms or molecules) in one mole of any substance, equal to $6.022 \times 10^{23}\,\text{mol}^{-1}$.

Mole

The standard SI unit for amount of substance; one mole contains exactly Avogadro's number ($6.022 \times 10^{23}$) of elementary entities.

Molar Mass

The mass in grams of one mole of a chemical element or compound ($\text{g/mol}$), used to convert mass values to molar amounts.

Mole-Particle Conversion Pathway

The two-step conversion method in stoichiometry: grams are divided by molar mass to obtain moles, and moles are multiplied by Avogadro's number to determine the number of atoms or molecules.