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Conceptual Physics: Form WSF.0.0A Name ______________________________ FORMULAS Date _________________ Period _____ Metric Prefixes 103 102 101 1 10–1 10–2 10–3 10–4 10–5 10–6 10–7 10–8 k – – none d c m – – µ – – 10–9 10–10 10–11 10–12 n – – Motion Speed: d t distance: d = vt d time: t = v speed: v = • v = speed • d = distance • t = time Acceleration: acceleration: a = time: t = ∆v v f − v i = t t v f − vi a final velocity: v f = vi + at • a = acceleration • ∆v = change in velocity v f = final velocity vi = initial velocity Free Fall: (objects accelerating because of gravity) final speed: vf = gt + vi distance: d = ½at 2 + vit v avg = v f + vi 2 • • • • g = a = 9.8 m/s² = acceleration of gravity d = distance • t = time • vf = final speed vi = initial speed vavg = average speed Units: distance: time: mass: m = meters; km = kilometers; cm = centimeters h = hours; s = seconds g = grams; kg = kilograms Energy Gravitational Energy PE = mgh KE = ½mv2 • The height from which the object falls (h) • The mass of the object (m) • The acceleration of gravity (g) • The mass of the object (m) • The speed (v) p Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 2 Force Net Force: • Forces in the same direction • Fnet = net force Fnet = F1 + F2 + . . . + Fn • F1 + F2 + . . . + Fn = add all the forces • • Forces in opposite directions Fnet = FL – FS • FL = larger force • FS = smaller force • FL – FS = subtract the forces Forces at right angles Pythagorean theorem a2 + b2 = c2 c = c2 • THE NET FORCE IS IN THE DIRECTION OF THE LARGER FORCE • a = one of the forces at right angles • b = one of the forces at right angles • c = the net force Multiple forces Always add all the forces acting in the same direction before subtracting or applying the Pythagorean theorem Newton's Second Law of Motion: F m force: F = ma ( F = m × a ) accleration: a = mass: m = F a • a = acceleration • F = force • m = mass Air Resistance: Fnet = Fweight − Fair resistance • Fnet = net force • m = mass Fweight = mg • Fweight = weight • Fair resistance = air resistance • g = acceleration of gravity (9.8m/s²) Units: distance: m = meters; km = kilometers; cm = centimeters time: h = hours; s = seconds mass: g = grams; kg = kilograms kg • m 1N = 1 2 force: N = newtons; s Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 3 Machines Work: W=F×d • • • W = work (J) F = force (N) d = distance (m) Power: Power = P= Work time W t Mechanical Advantage: mechanical = output force advantage input force F MA = out Fin Efficiency: efficiency = eff = work output × 100% work input Wout × 100% Win (NOTE: Express efficiency as a decimal to calculate Wout or Win.) Inclined Plane: Wout = Fout × Dout Win = Fin × Din Wf = Win – Wout AMA = Fout/Fin IMA = Din/Dout Eff = (Wout/Win) × 100 Eff = (AMA/IMA) × 100 Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 4 Machines (Continued) Levers: AE AR M =F×A • IMA = ideal mechanical advantage • AE = effort arm M = M 1 + M 2 +... Balanced levers • M E = effort moment • M R = resistance moment IMA = ME = MR • AR = resistance arm Wheel and Axle: IMA = input radius output radius IMA = Rin Rout Pulleys: IMA = # of supporting strands IMA (fixed pulley) = 1 IMA (movable pulley) = 2 Units: work: power: MA: J = joules W = watts no units (also units for energy) 1 W = 1 J /s Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 5 Momentum Momentum: p = mv C p = momentum (kg·m/s) C m = mass (kg) C v = velocity (m/s) pTOTAL = p1 + p2 + . . . + pn Change of Momentum and Force: Definitions Substitutions • F = ma ∆v t • ∆p = m∆v • a= m∆v t ∆p F= t F= Waves Speed: v=fλ C v = speed (m/s) C f = frequency (1/s or Hz) C λ = wavelength (m) C pTOTAL = total momentum C p1, p2, pn = momentums of the objects in a system Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 6 Sound M= v v sound C M = mach number C v = speed relative to the medium C vsound = speed of sound in the medium Speed of Sound Through Different Materials Material Speed (m/s) Air 343 Water 1,483 Steel 5,940 Glass 5,640 Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 7 Light Primary Colors Speed in a vacuum Speed in a vacuum = 3.0 × 108 m/s Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 8 Heat Temperature: K = C + 273 C K = Kelvins C = K – 273 C C = Celsius (EC) Heat: q = mCΔT C q = heat (joules) ΔT = Tf – Ti J J or C C = specific heat gK g° C C ΔT = temperature change C Tf = final temperature C Ti = initial temperature Specific Heats of Common Substances: Units: heat temperature specific heat Material Specific Heat (J/g°C) water 4.18 aluminum 0.897 copper 0.385 lead 0.129 nickel 0.444 zinc 0.388 J = joules EC = degrees Celsius; K = Kelvins J J = joules per gram degree Celsius or joules per gram Kelvin or g° C gK Conceptual Physics: Form WSF.0.0A Formulas FORMULAS Page 9 Pressure and Fluids Pressure: F A force: F = PA ( F = P × A) pressure: P = area: A = F P Archimedes' Principle: m V mass: m = D × V m volume: V = D V = L ×W × H (NOTE: Density of water – 1 g/mL density: D = Pascal’s Principle: F1 F2 = A1 A2 • P = pressure • F = force • A = area • D = density • m = mass • V = volume • L = length • W = width • H = height or 1 kg/L ) • F1 = force applied on surface one • F2 = force applied on surface two • A1 = area of surface one • A2 = area of surface two Units: force: N = newtons; 1N = 1 kg • m s2 pressure: Pa = pascals area: m2 = meters squared volume: m3 = meters cubed; cm3 = centimeters cubed (note: 1 mL = 1 cm3); L = liters Conceptual Physics: Form WSF.0.0A FORMULAS Formulas Page 10 Conceptual Physics: Form WSF.0.0A FORMULAS Formulas Page 11 Conceptual Physics: Form WSF.0.0A FORMULAS Formulas Page 12 Conceptual Physics: Form WSF.0.0A FORMULAS Formulas Page 13 Conceptual Physics: Form WSF.0.0A FORMULAS Formulas Page 14