PHYS 40B Physics Lab Equation Reference

Posted on Jun 19, 2026 in Physical Activity and Sports Sciences

PHYS 40B — Complete Equation Cheat Sheet

All equations, rearrangements, and symbol definitions for laboratory coursework.

Lab 1 – Buoyancy

Core Equations

Fluid Forces

• F_top = ρ_fluid · g · h₁ · A
• F_bottom = ρ_fluid · g · h₂ · A

Net Force Equilibrium

• ΣF = F_bottom – F_top – F_g = 0

Buoyant Force Definition

• F_B = F_bottom – F_top = ρ_fluid · g · V_disp

Floating Fraction

• ρ_object / ρ_fluid = V_sub / V_object

Lab 2 – Simple Harmonic Oscillation

Core Equations

Hooke’s Law

• F = -k · x
• m · (d²x/dt²) = -k · x

Angular Frequency and Period

• ω = √(k / m)
• T = 2π√(m / k)

Massive Spring Correction

• T = 2π√((m + M/3) / k)
• T = A · √(m + B) where B = M/3

Lab 3 – Waves

Core Equations

• Wave Speed: v = λ · f
• Wave Equation: y(x,t) = y₀ · sin(kx – ωt)
• Standing Waves: λ_n = 2L / n; f_n = nv / 2L

Lab 4 – Resonance

Core Equations

• Wave Speed: v = √(T / μ)
• Speed of Sound: c = √(γP / ρ)
• Open–Closed Tube: f_n = nv / 4L (n = 1, 3, 5…)

Lab 6 – Diffraction & Interference

Core Equations

• Single Slit Minimum: a · sin(θ) = λ
• Double Slit Maxima: d · sin(θ) = mλ
• Small Angle Approximation: sin(θ) ≈ y / L

Lab 6 – Lenses

Core Equations

• Thin Lens Equation: 1/f = 1/s + 1/s’
• Magnification: m = -s’/s = h’/h

Lab 7 – Ideal Gas Law

Core Equations

• Ideal Gas Law: PV = nRT
• Two-State Relation: (P₁V₁) / T₁ = (P₂V₂) / T₂

Lab 8 – Specific Heat of Solids

Core Equations

• Heat Capacity: Q = mcΔT
• Latent Heat: Q = mL
• Molar Specific Heat: C_molar = c · M
• Dulong–Petit Law: C_v,molar ≈ 3R