MTTC Physics (019) flashcards

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

Accuracy and precision

Accuracy is closeness to the accepted value; precision is closeness of repeated measurements to each other. A systematic offset reduces accuracy, while random scatter reduces precision.

Percent error

Percent error compares an experimental result to an accepted value: |experimental − accepted| ÷ accepted × 100. It is usually reported as a positive magnitude with the accepted value in the denominator.

Random and systematic error

Random error scatters readings above and below the true value and shrinks when results are averaged; systematic error shifts every reading the same way and is not reduced by repeating trials.

Dimensional analysis

Checking an equation by comparing the base-unit dimensions of both sides. Both sides must reduce to identical dimensions; this catches algebraic errors but cannot determine dimensionless numerical constants.

Independent and dependent variables

The independent variable is deliberately changed by the experimenter; the dependent variable is measured in response; controlled variables are held fixed so they do not confound the observed relationship.

Uncertainty in a product

For z = xy or z = x/y, fractional uncertainties combine in quadrature: δz/z = √[(δx/x)² + (δy/y)²]. For sums and differences, absolute uncertainties combine in quadrature instead.

Constant-acceleration kinematics

With uniform acceleration a: v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx. These equations fail whenever the acceleration changes during the interval of interest.

Projectile motion

Without air resistance, horizontal velocity stays constant while vertical acceleration is g downward. The components are independent, so time of flight is determined by the vertical motion alone.

Newton's second law

The net force on an object equals mass times acceleration, ΣF = ma. Acceleration points along the net force and is inversely proportional to the object's mass.

Centripetal acceleration

An object moving in a circle at constant speed accelerates toward the center with a = v²/r, requiring net inward force mv²/r. Speed is constant but velocity direction changes continuously.

Work-energy theorem

The net work done on an object equals its change in kinetic energy: W_net = ½mv_f² − ½mv_i². Only the force component along the displacement transfers energy.

Conservation of momentum

If the net external impulse on a system is zero, total momentum Σmv stays constant. This applies to collisions, explosions, and recoil even when kinetic energy is not conserved.

Elastic versus inelastic collisions

Elastic collisions conserve both momentum and kinetic energy. Perfectly inelastic collisions conserve momentum only, with the objects sticking together and losing the maximum possible kinetic energy.

Simple harmonic motion periods

For a mass-spring oscillator T = 2π√(m/k), independent of amplitude. For a small-angle pendulum T = 2π√(L/g), depending only on length and the local gravitational field strength.

Wave equation

Wave speed equals frequency times wavelength, v = fλ. Frequency is set by the source and stays constant across media; speed and wavelength change when the wave enters a different medium.

Standing waves on a string

A string fixed at both ends supports wavelengths λ = 2L/n, giving f_n = nv/(2L), where v = √(T/μ). Nodes always occur at the two fixed ends.

Doppler effect

Observed frequency shifts when source and observer move relative to each other, described by f′ = f(v ± v_o)/(v ∓ v_s). Relative approach raises the observed frequency; recession lowers it.

Sound intensity level

Level β = 10 log₁₀(I/I₀) decibels, with I₀ = 1×10⁻¹² W/m². Intensity from a point source falls as the inverse square of distance, so doubling distance drops the level about 6 dB.

Snell's law

At an interface, n₁ sin θ₁ = n₂ sin θ₂, where n = c/v. Light bends toward the normal entering a denser medium; total internal reflection begins beyond sin θ_c = n₂/n₁.

Thin lens equation

1/f = 1/d_o + 1/d_i with magnification m = −d_i/d_o. A positive image distance means a real image; converging lenses have positive focal length and can form real or virtual images.

Double-slit interference

Constructive interference occurs at d sin θ = mλ, producing bright fringes; destructive interference occurs at half-integer multiples. Fringe spacing on a distant screen is Δy = λL/d.

Coulomb's law

The force between point charges is F = k|q₁q₂|/r², with k ≈ 8.99×10⁹ N·m²/C². Like charges repel, opposite charges attract, and the force falls off as the inverse square of separation.

Electric field and potential

E = F/q is force per unit charge, pointing from positive toward negative. Potential V = kQ/r is scalar; work moving charge q is qΔV, and field equals the negative potential gradient.

Capacitors in circuits

C = Q/V, with parallel plates C = ε₀A/d and stored energy U = ½CV². Capacitors add directly in parallel but reciprocally in series, where 1/C_eq = Σ1/C_i.

Kirchhoff's rules

The junction rule sets the sum of currents entering a node to zero; the loop rule sets the sum of potential changes around any closed loop to zero. Both follow from charge and energy conservation.

Magnetic force on a charge

F = qvB sin θ, perpendicular to both velocity and field, so magnetic force does no work and cannot change a particle's speed. The right-hand rule gives the force direction.

Faraday's law of induction

Induced emf equals the negative rate of change of magnetic flux through a loop: ε = −N dΦ/dt. Lenz's law says the induced current opposes the flux change that produced it.

First law of thermodynamics

ΔU = Q − W, where Q is heat added to the system and W is work done by the system. Internal energy rises when heat is added or work is done on the system.

Ideal gas law

PV = nRT with R = 8.31 J/(mol·K), or PV = NkT with k = 1.38×10⁻²³ J/K. Temperatures must be absolute; at constant volume, pressure is proportional to Kelvin temperature.

Carnot efficiency

No engine operating between reservoirs at T_H and T_C can exceed e = 1 − T_C/T_H, with temperatures in kelvin. Real engines fall short because of friction and irreversible heat flow.

Photoelectric effect

Light above a threshold frequency ejects electrons with maximum kinetic energy K_max = hf − φ, where φ is the work function. Intensity sets the number of electrons, not their maximum energy.

Radioactive half-life

The time for half of a radioactive sample to decay, related to the decay constant by T½ = ln2/λ. Activity and undecayed nuclei both fall exponentially according to N = N₀e^(−λt).