# Formulas for Final

## Physics 221 with Spanier at University of Tennessee - Knoxville *

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Trigonometry Sin = opp/hyp Cos = adj/hyp Tan = opp/adj Motion v = Δx/Δt (m/s) a = Δv/Δt (m/s2) speed: not the same as velocity. “distance” over time rather than displacement over time v(t) = vo + at x(t) = xo + vot + (½)at2 a = g = 10 freefall x – xo = vot + (½)at2 or Δx = vot + (½)at2 v = √2gh F = ma Fg = mg Vectors rx = r cos θ ry = r sin θ “easy” angles: sin 30° = ½ cos 60° = ½ sin 90° = 1 cos 90° = 0 sin 0° = 0 cos 0° = 1 table: http://www.clarku.edu/~djoyce/trig/cosines.html Friction: F = m*N m = coefficient, static or kinetic N = normal force Work W = F ∆x Kinetic Energy KE = (1/2) mv2 Potential Energy W = mgh Spring W = ½ kx2 F = -kx Freefall mgh = (½)mv2 m cancels out: v = √2gh Power P = W/∆t = Watts = J/s Momentum p = mv T = p2 /2m (I can’t find this in the notes & I don’t know what it means…) Impulse = FΔt Elastic collision: energy & momentum conserved Circular motion Θ = x ω = v α = a Centripetal accel. ac =v2/r Centripetal force: applied by another force such as tension Fc = mac Inertia I = mr2 or ∑mr2 Torque τ = Fr = Iα Angular Momentum L = Iω (p = mv) Elasticity F/A = M (∆L/L); M = modulus ex: Bulk, Young Density p = m/V PV = Work = A∆x (W = F∆x) Pressure P = F/A Bernoulli’s equation P + (½)pv2 + pgh Oscillation F = mα = - ωx x(t) α sin (ωt) (I don’t understand what this means because the formulas in the book are different! Maybe I’m looking at the wrong part?) Book: x(t) = A cos (ωt) Waves v = λf (f = 1/T) Interference: constructive and destructive (Phase shift) Standing waves: fixed end(s) Temperature 0C = 273 K Heat (Q) Q = mcΔT PV = nRT or NkT n = mass/ molar mass N = # molecules R = 8.32 Jmol-1K-1 k = 1.38 E-23 1 mol of ideal gas: 22.4 L Internal Energy U = 3/2 nRT ∆U = Q – W ∆U = Uf – Ui Isobaric: ∆U = Q – W Adiabatic: Q = 0 ∆U = -W Isovolumetric: W = 0 ∆U = Q Isothermal: ∆U = 0 W = Q Efficiency Qh – Qc / Qh Entropy S = Q/t Q: energy expelled Light Lens equation: 1/i + 1/o = 1/f i = image distance o = object distance f = focal length\ Magnification M = -i/o

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