PHYS. 131 Final Exam Cheatsheet by Gina Plett | Cheat Sheets Hero

gina-plett / PHYS. 131 Final Exam

Science / Physics

April 16, 2025 20:10

fluids

nuclear

physics

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Fluids: Statics and Dynamics

Fluid Properties

Density (ρ): Mass per unit volume `ρ = m/V` Water Density: 1000 kg/m³ Air Density: 1.29 kg/m³	Pressure (P): Force per unit area `P = F/A` Units: Pascals (Pa) = N/m²
Macroscopic Differences: Solids: Fixed shape and volume. Liquids: Fixed volume, variable shape. Gases: Variable shape and volume.	Microscopic Differences: Solids: Atoms/molecules tightly packed. Liquids: Atoms/molecules closely packed, can move past each other. Gases: Atoms/molecules widely dispersed, move randomly.
Absolute Pressure: Total pressure including atmospheric pressure. `P_absolute = P_gauge + P_atm`	Gauge Pressure: Pressure relative to atmospheric pressure. `P_gauge = P - P_atm`
Pressure in a Static Fluid: `P = P₀ + ρgh` where: `P₀` = pressure at surface, `ρ` = density, `g` = gravity, `h` = depth.	Suction: Created by pressure difference. Fluid moves from high to low pressure.
Manometers: Measure pressure differences using fluid columns.	Barometers: Measure atmospheric pressure.

Pascal's Principle & Buoyancy

Pascal’s Principle: Pressure applied to a confined fluid is transmitted undiminished throughout the fluid. `F₁/A₁ = F₂/A₂`	Hydraulic Systems: Utilize Pascal’s Principle for force amplification.
Blood Pressure: Measured using a sphygmomanometer. Systolic/Diastolic pressure (e.g., 120/80 mmHg).	Buoyancy: Upward force exerted by a fluid on an immersed object.
Archimedes’ Principle: Buoyant force equals the weight of the fluid displaced by the object. `F_buoyant = ρ_fluid * V_displaced * g`	Apparent Weight: `W_apparent = W_true - F_buoyant`
Floating Objects: Buoyant force equals object’s weight.	Immersed Objects: Buoyant force can be greater than, less than, or equal to object’s weight (determining if object floats, sinks, or is neutrally buoyant).

Fluid Dynamics

Streamlines: Paths of fluid particles in steady flow.	Flow Rate (Q): Volume of fluid passing a point per unit time. `Q = Av` where `A` is cross-sectional area and `v` is flow speed.
Equation of Continuity: Conservation of mass in fluid flow. `A₁v₁ = A₂v₂`	Bernoulli’s Equation: Conservation of energy in fluid flow. `P + ½ρv² + ρgh = constant`
Viscosity: Resistance to flow. Increases energy losses.	Turbulence: Irregular flow with eddies. Increases energy losses.

Simple Harmonic Motion & Waves

Simple Harmonic Motion (SHM)

SHM Definition: Periodic motion where restoring force is proportional to displacement.	Displacement: `x(t) = A cos(ωt + φ)` where: `A` = Amplitude `ω` = Angular frequency `φ` = Phase constant
Velocity: `v(t) = -Aω sin(ωt + φ)`	Acceleration: `a(t) = -Aω² cos(ωt + φ) = -ω²x(t)`
Hooke’s Law: `F = -kx` where: `k` = Spring constant	Natural Frequency: `ω = √(k/m)`
Elastic Potential Energy: `U = ½kx²`	Conservation of Energy: `½kA² = ½mv² + ½kx²`
Pendulum Period: `T = 2π√(L/g)` where: `L` = Length `g` = Gravity	Damped Oscillations: Amplitude decreases over time due to damping force.
Critical Damping: Returns to equilibrium fastest without oscillation.	Resonance: Large amplitude oscillations when driving frequency matches natural frequency.

Traveling Waves

Transverse Waves: Particle motion perpendicular to wave direction.	Longitudinal Waves: Particle motion parallel to wave direction.
Wave Speed on a String: `v = √(T/μ)` where: `T` = Tension `μ` = Linear density	Wave Speed: `v = λf` where: `λ` = Wavelength `f` = Frequency
Snapshot Graph (D vs. x): Displacement as a function of position at a given time.	History Graph (D vs. t): Displacement as a function of time at a given position.
1D Sinusoidal Wave: `D(x, t) = A cos(kx - ωt + φ)` where: `k = 2π/λ` (wave number)	Phase: Argument of the cosine function `(kx - ωt + φ)` Phase Constant: `φ`

Standing Waves

Superposition: Waves combine linearly.	Constructive Interference: Waves add in phase; larger amplitude.
Destructive Interference: Waves add out of phase; smaller amplitude.	Reflection at a Boundary: Wave pulse can be inverted upon reflection if going from less dense to more dense medium.
Standing Waves: Superposition of two waves traveling in opposite directions, creating stationary nodes and antinodes.	String Fixed at Both Ends: `λ_n = 2L/n` `f_n = nv/(2L)` (n=1, 2, 3…)
Open-Open Tube: `λ_n = 2L/n` `f_n = nv/(2L)` (n=1, 2, 3…)	Open-Closed Tube: `λ_n = 4L/n` `f_n = nv/(4L)` (n=1, 3, 5…)
Overtones: Frequencies above the fundamental frequency.	Musical Instruments: Standing waves produce specific tones based on instrument geometry.

Sound & Light: Interference

Sound Waves

Loudness: Subjective perception of sound intensity.	Power (P): Energy per unit time. Intensity (I): Power per unit area. `I = P/A` (W/m²)
Sound Intensity Level (dB): `β = 10 log₁₀(I/I₀)` where: `I₀ = 10⁻¹² W/m²`	Intensity vs. Distance: Intensity decreases with the square of the distance from the source. `I ∝ 1/r²`
Doppler Effect: Change in frequency due to relative motion between source and observer. `f' = f (v ± v_o) / (v ± v_s)` where: `v` = speed of sound, `v_o` = observer speed, `v_s` = source speed	Use (+) when moving toward and (-) when moving away. Apply consistently for observer and source.

Interference

Constructive Interference: Path difference is an integer multiple of the wavelength.	Destructive Interference: Path difference is a half-integer multiple of the wavelength.
Beats: Periodic variations in amplitude due to interference of two sound sources with slightly different frequencies. `f_beat = \|f₁ - f₂\|`	Similarities: Both sound and light exhibit interference phenomena.
Differences: Light interference involves electromagnetic waves, while sound interference involves mechanical waves.	Index of Refraction (n): Ratio of speed of light in vacuum to speed of light in the material. `n = c/v`
Optical Path Length: Product of the physical distance and the index of refraction. `OPL = n * d`	Young’s Double-Slit Experiment: Demonstrates interference of light waves.
Bright Fringes (Constructive Interference): `d sin θ = mλ` (m = 0, ±1, ±2,…)	Dark Fringes (Destructive Interference): `d sin θ = (m + ½)λ` (m = 0, ±1, ±2,…)

Nuclear Physics

Nuclear Structure & Binding Energy

Standard Notation: AZX `A` = Mass number (protons + neutrons) `Z` = Atomic number (protons) `X` = Chemical symbol	Nuclide Mass: Actual mass of the nucleus. Atomic Mass: Mass of the neutral atom (nucleus + electrons).
Mass Defect (Δm): Difference between the mass of the nucleus and the sum of the masses of its individual nucleons. `Δm = (Zm_p + Nm_n) - m_nucleus`	Binding Energy (BE): Energy required to separate a nucleus into its constituent nucleons. `BE = Δmc²`
Binding Energy per Nucleon: `BE/A` Roughly constant for most nuclei, indicating nuclear stability.	Nuclear Stability: Related to the balance between the strong nuclear force and the electromagnetic force.

Radioactive Decay

Decay Rate (λ): Probability of decay per unit time.	Activity (A): Number of decays per unit time. `A = λN` where `N` is the number of radioactive nuclei.
Decay Equation: `N(t) = N₀e^(-λt)` `A(t) = A₀e^(-λt)`	Half-Life (T₁/₂): Time for half of the radioactive nuclei to decay. `T₁/₂ = ln(2) / λ`
Lifetime (τ): Average time for a nucleus to decay. `τ = 1/λ`	Conservation of Energy: Used to determine if a decay process is energetically possible.
Alpha Decay: Emission of an alpha particle (⁴₂He). Reduces mass number by 4 and atomic number by 2.	Beta Decay: Emission of a beta particle (electron or positron). Changes the atomic number by 1 (either +1 or -1).
Gamma Decay: Emission of a gamma ray (high-energy photon). Does not change mass number or atomic number.	Radiation Dose: Measure of energy absorbed by biological tissue.
Radiation Effects: Can cause damage to DNA and other biological molecules.	Dose Equivalent: Measure of biological effect of radiation, taking into account the type of radiation. Measured in Sieverts (Sv).