ETEA Engineering Test flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's second law

The net force on a body equals the rate of change of its momentum; for constant mass this becomes F = ma, with force in newtons, mass in kilograms and acceleration in m/s².

Work-energy theorem

The net work done by all forces acting on an object equals its change in kinetic energy: W_net = ½mv² − ½mu². Work is measured in joules.

Projectile maximum range

For a projectile launched and landing at the same height with speed u, range R = u² sin 2θ / g, which reaches its maximum at a launch angle of 45 degrees.

Centripetal acceleration

A body moving in a circle of radius r at speed v has acceleration v²/r directed toward the centre; the required force mv²/r is supplied by tension, gravity or friction.

Photoelectric equation

Einstein's photoelectric equation is hf = φ + K_max, where hf is the incident photon energy, φ the metal's work function and K_max the maximum kinetic energy of emitted electrons.

Ohm's law

For a metallic conductor kept at constant temperature, the current is directly proportional to the potential difference: V = IR, with V in volts, I in amperes and R in ohms.

Simple pendulum period

The period of a simple pendulum is T = 2π√(L/g), where L is the length and g the gravitational acceleration; for small swings it does not depend on the mass of the bob.

Snell's law

At the boundary between two transparent media, n₁ sin θ₁ = n₂ sin θ₂, where both angles are measured from the normal and n is the refractive index of each medium.

Mole concept

One mole contains 6.022 × 10²³ particles, its mass in grams equals the molar mass, and one mole of any gas occupies 22.4 dm³ at standard temperature and pressure.

Le Chatelier's principle

When a system at equilibrium is disturbed by a change in concentration, pressure or temperature, the equilibrium position shifts in the direction that opposes that change.

pH definition

pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol per dm³; lowering the pH by one unit means a tenfold rise in acidity.

Hess's law

The enthalpy change of a reaction is the same whether it takes place in one step or in several, so the enthalpy changes of the individual steps can simply be added.

Empirical formula

The simplest whole-number ratio of atoms in a compound; it is calculated by dividing percentage composition by atomic masses, then dividing each result by the smallest quotient.

Oxidation number

The apparent charge an atom would carry if shared bonding electrons were assigned to the more electronegative atom; free elements are zero and monatomic ions equal their charge.

Ideal gas equation

PV = nRT relates the pressure, volume, amount and absolute temperature of a gas, with R = 8.314 J mol⁻¹ K⁻¹; temperature must always be expressed in kelvin.

Atomic radius periodic trend

Atomic radius decreases across a period because nuclear charge increases while electrons enter the same shell, and increases down a group as extra shells are added.

Quadratic formula

For ax² + bx + c = 0 with a not equal to zero, x = (−b ± √(b² − 4ac)) / 2a, and the discriminant b² − 4ac determines the type of roots.

Discriminant of a quadratic

For ax² + bx + c = 0, D = b² − 4ac: D > 0 gives two distinct real roots, D = 0 gives two equal real roots, and D < 0 gives complex conjugate roots.

Chain rule

If y = f(g(x)), then dy/dx = f′(g(x)) · g′(x); the rule differentiates a composite function by multiplying the outer derivative by the inner derivative.

Sum of geometric series

For a geometric series with first term a and common ratio r, S_n = a(1 − rⁿ)/(1 − r), and the infinite sum is a/(1 − r) provided |r| < 1.

General term of binomial

In the expansion of (a + b)ⁿ, the term containing b^r is given by T_(r+1) = ⁿC_r a^(n−r) b^r, where the coefficient is a combination.

Slope of a line

For two points (x₁, y₁) and (x₂, y₂), m = (y₂ − y₁)/(x₂ − x₁); parallel lines have equal slopes and perpendicular lines have slopes whose product is −1.

Integration by parts

The rule ∫u dv = uv − ∫v du reverses the product rule; choose u as the factor that becomes simpler when differentiated, such as a power of x.

Determinant of 2×2 matrix

For the matrix with rows (a, b) and (c, d), the determinant is ad − bc; the matrix possesses an inverse only when this determinant is non-zero.

Subject-verb agreement

A singular subject takes a singular verb and a plural subject takes a plural verb; words between them do not alter number, as in 'The box of pens is heavy'.

Present perfect tense

Formed with has or have plus the past participle, this tense links a past action to the present and is used with since for a starting point and for with duration.

Third conditional

This sentence type describes an unreal past situation using if plus the past perfect, followed by would have and a past participle, as in 'If she had studied, she would have passed'.

Passive voice

Formed with a suitable form of the verb be plus a past participle, the passive shifts emphasis from the doer to the action, as in 'The bridge was built in 1990'.

Uses of the definite article

'The' precedes a specific or previously mentioned noun, a superlative or a unique object, but it is omitted before general plurals and uncountable nouns used in a general sense.

Tense shift in reported speech

When the reporting verb is past, present tenses normally shift one step back and past tenses become past perfect, while pronouns and time expressions are also adjusted.

Synonym and antonym

A synonym is a word sharing a similar meaning with another, such as rapid and swift; an antonym carries the opposite meaning, such as rapid and slow.

Time prepositions in, on, at

'At' marks clock times, 'on' marks days and dates, and 'in' marks months, years and longer periods, so we say at 5 pm on Monday in July.