Equation List Constant Velocity x = position v=x/t Δ x = vaverage t

Physics - Berg t = time xf - xo = Δ x vaverage = (vo + vf ) / 2

Accelerated Motion a = acceleration v f = v0 + a t (vf ) 2 = (vo )2 + 2 a Δx

xo = original position x = xo + vt

a=v/t a = (vf – vo)/  t 2 Δ x = vo t + ½ a t Δ x = ½ (vf + vo ) t Acceleration due to gravity on Earth = 9.8 m/s 2

Forces And Newton’s Laws F = force m = mass Tan θ = Opposite side / Adjacent side Sin θ = Opposite side / hypotenuse Cos θ = Adjacent side / hypotenuse Fnet = m a Fg = m (9.8 m/s2) Ff = μk Fn Ff ≤ μs Fn

Opposite side

θ k = spring constant μs > μk

Ft = m v p = mv

Energy E = energy Work = (Force)(distance)

Adjacent side

F = k x (Hooke’s Law)

r = radius (distance) Fc = (m v2)/ r G = 6.67 x 10-11 Nm2 / kg2

Ft = impulse Va – Vb = Vb’ – Va’

Ek = ½ mv 2 Power = change in Energy/ time

Static Electricity Felectric = electric force q = charge 2 Felectric = (k q1 q2) / r k = 9x10 9 Nm2 / c2 E = V / d (parallel plates = constant field) V = Eelectric / q V x q = Eelectric Electric Circuits R = resistance R = R1 +R2 + R3 + … P = IV 1 kWh = 3,600,000 J

v = vf – vo

hypotenuse

Circular Motion and Universal Gravitation ac = centripetal acceleration Fc = centripetal force 2 ac = v / r Fc = ( 42 r m )/ T2 v = 2r / T Fg = (G m1 m2)/ r2 Momentum p = momentum (p)before = (p)after

v = velocity xf = final position

r = distance

V = voltage I = current 1/R = 1/R1 +1/R2 + 1/R3 + … P = I2R P = V2 / R v = I (R + r)

Eg = mgΔy Ee = ½ kx2 Power = work / time

E = Electric Field E = Fe / q Eelectric = Electric Potential Energy Eelectric = Fe x distance

P = Power V= IR

Mechanical Waves, SHM and Sound λ = wavelength f = frequency Speed = λf Speed = λ / T Speed of sound = 331 m/s + 0.6 m/s/ºC (temp) f'’ = f (vwave  v obs) / (vwave ∓ vsource) T = 2(L/g) T = 2(m/k)

T = period f = 1/ T T = 1/f f beat = f1 – f2

Optics n = index of refraction n = (speed of light in vacuum / Speed of light in material) n1 sini = n2 sint i = r Speed of light = 3x 10 8 m/s f = focal length do = object distance di = image distance M = magnification factor ho = object height hi = image height 1/f = 1/do + 1/di M = -di / do = hi/ ho sin  = / b (single slit interference) b =slit width d sin  = m (constructive Interference) m = 0,1,2,3,4… d = distance between slits d sin  = (m+ ½) (destructive Interference) Thermal Physics Q = Thermal Energy c = specific heat T = temperature (K) Hf = Heat of Fusion Hv = Heat of Vaporization Pressure = force/ area Q = mcΔT Q = mHf Q = mHv PV = nrT Constants Csilver = 230 J / kg K Csteam = 2010 J/ kg K Cice = 2100 J/ kg K Cwater = 4180 J / kg K Ccopper = 390 J / kg K Ciron = 450 J / kg K Cglass = 840 J / kg K CAluminum = 900 J/kg K Clead = 130 J / kg K Cprotein = 1700 J / kg K Water Silver Iron

Hf = 334,000 J/kg Hf = 88,000 J/kg Hf = 289,000 J/kg

Projectile Motion Range = [Vo2 sin(2)] / g All motion equations

Hv =2,260,000 J/kg Hv =2,300,000 J/kg Hv =6,340,000 J/kg