Equation Sheet Sept 2005

Conversions 1000 mg = 1 g 1000 g = 1 kg 100 cm = 1 m 1000 m = 1 km 1000 anythings = 1 kilo anything 1000 milli anythings = 1 anything To change micro (µ) to base unit tack on E-6 To change nano (n) to base unit tack on E-9 To change pico tack on E-12 To change mega (M) to base unit tack on E6 To change giga (G) to base unit tack on E9 To change tera (T) to base unit tack on E12 3 ft = 1 yd 12 in = 1 ft 1 mi = 5280 ft 1 mi = 1760 yd 3.28 ft = 1 m 1.61 km = 1 mi 2.54 cm = 1 inch 1 ft = 30.48 cm 1 min = 60 s 1 h = 60 min 1 h = 3600 s 1 yr = 365.24 days 2.20 lb = 1 kg 454 g = 1 lb 1cm3 = 1 mL (for water @ 4°C) 0.264 gal = 1 L 1 calorie = 4.186 J 1 hp = 745.7 W 1 eV = 1.6 E –19 J 1 u = 1.6605 E –27 kg 1 u = 931.49 MeV 1 N = 1 kg•m/s2 1 J = 1 N•m = 1 kg•m2/s2 1 W = 1 J/s = 1 kg•m2/s3 1 Pa = 1 N/m2 = kg/(m•s2) CONSTANTS Gravitational acceleration g=9.8 m/s2=32.2 ft/s2 Speed of sound = 343 m/s Speed of light c = 2.9979 X 108 m/s e- or p+ charge = 1.6 E –19 C k (electricity) 9 E 9 mass of a proton = 1.67 E –27 kg mass of an electron = 9.11 E –31 kg µ0 = 4πE-7 T•m/A = 1.2566 E-6 T•m/A Avogadro’s number = 6.022 E 23 B field of the Earth = 5 E–5 T Absolute zero = -273.15 °C = 0 K Atmospheric pressure: 1 atm= 1 X 105 Pa= 760 mm Hg= 14.70 lb/in2 Gas constant R = 8.31 J/mol•K

Kinematics , avg v = ∆x/∆t = (x - x0)/(t- t0) , avg a = ∆v/∆t = (v - v0)/(t- t0) , v = x/t (constant velocity/speed) , v = v0 + a t No x , x = ½ (v + v0)t No a , x = v0t + ½ a t2 No v , v2 = v02 + 2 a x No t

Units ,v (m/s) ,v0 (m/s) a (m/s2) x (m) t (s)

Newton’s Law/Forces Fg = mg = 9.8 m (on Earth) Fnet = ma = (+)’s – (-)’s Ffriction = µ FN Fgx = F = Fg sinθ Fgy= F⊥ = Fg cosθ For level ground Ffriction= µmg

F (N) ,m (kg) g (m/s2) µ (none) θ (°)

Circular motion T = 1/f v = 2πr/T , ac = v2/r Fc = m(v2/r) Universal Law of Gravitation Fg = GMm/r2 G = 6.67 X10-11 N•m2/kg2 v = 2πrf ac = 4π2r/T2 Fc = m4π2r/T2 g = GM/r2 v2 = rµg v2 = GM/r 2 3 4π r = GMT2 (Granddaddy!) Work and Energy K = ½ mv2 U = mgh W = Fx (F&x ||) P = W/t Wdone + U0 + K0 = U + K + Wfriction *** WE theorem: Fx + ½ mv02 = ½ mv2 (W = ∆K) Famous height velocity conversion: v = 2

2 gh

T (s) ,f (Hz, rps, s-1) r (m)

K (J) U (J) W (J) P (W)

2

Fpx + mgh0 + ½ mv0 = mgh + ½ mv + Ffx Fpx+mgh0+½mv02 = mgh+½mv2 + Wlost due to friction Impulse and Momentum p = mv Ft = mv – mv0 Conservation of momentum p00 = p OR ∆p = 0 v10 +v1 = v20 +v2 (for perfectly elastic collisions) Waves and Simple Harmonic Motion (1) total time*frequency #waves = (2) total time/period (3) total distance/λ Speed of sound = 343 m/s Speed of light c = 2.9979 X 108 m/s v = λf f = 1/T T = 1/f I = P/4πr2 β = 10 log (I/I0) I = I0 10(β/10) I0 = 1 E -12 W/m2 vsound = 331 + 0.6T f” = f (v vo)/(v vs) Fs = -kx Us = ½ kx2 Ts = 2π Ts2 = 4π2m/k

m k

Tp = 2π

l g

Tp2 = 4π2l/g

, p (kg•m/s) Ft (N•s)

λ (m) I (W/m2) β(dB)

k is the spring constant (N/m) l (m)

Geometry/Trigonometry hyp2 = adj2 + opp2 Or C2 = A2 + B2 Sin θ = opp/hyp Cos θ = adj/hyp Tan θ = opp/adj = Ry/Rx Standard vector notation A units θ° (N or S) of (E or W) Components if θ measured from horizontal Ax = A cos θ Ay = A sin θ If θ is measured from vertical switch sin & cos Law of cosines = R2 = A2 + B2 - 2ABcosθ Algebraic Addition of Vectors by Components 1. Find the components of all vectors to be added, i.e. Ax and Ay. 2. Assign +/- signs + is right/East, - is left/West. + is up/North. - is down/South. 3. Add x components together to get Rx. 4. Add y components together to get Ry. 5. Add Rx and Ry together to get R using the Pythagorean theorem. 6. Find θ. θ = tan-1Ry/Rx 7. Write the resultant in appropriate vector form. Planet

Avg radius-m

Mass-kg

Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Earth’s moon

696 E 6 2.44 E6 6.05 E6 6.38 E6 3.40 E6 71.5 E6 60.3 E6 25.6 E6 24.8 E6 1.15 E6 1.74 E6

1.99 E30 3.30 E23 4.87 E24 5.97 E24 6.42 E23 1.90 E27 5.69 E26 8.66 E25 1.03 E26 1.5 E22 7.35 E22

http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html

Electricity # electrons = charge/1.6 E –19 C F = k q1 q2/r2 E = F/q = V/d E = k q/r2 UE = qV = W = Fd = ½ mv2 I = Q/t V = IR P = IV = I2R = V2/R = Energy/time Req (series) = R1 + R2 + R3 + … 1/Req (parallel) = 1/R1 + 1/R2 + 1/R3.. (usual) Req (parallel)= (R1-1 + R2-1 + R3-1+…)-1 (Ms. Walker) Magnetism F = qvB mv = qrB F = BΙϑ B = µ 0 I/2πr = (2 E –7) I/r F =µ 0 Ι1 Ι2 ϑ/2πr = (2 E –7)Ι1 Ι2 ϑ/r ε = V = ∆ (BA)/t = Bϑv Area of a circle = πr2 Area of a square = s2 Nuclear Physics E = ∆mc2 Ideal Gases/Thermodynamics K = °C +273.15 °C = K – 273.15 PV = nRT PV/T = P0V0/T0 QTC = mC∆T QPC = mH Fluids P = F/A = ρhg Fbuoyant = ρVg ∆L = αL1 (T2 - T1) Avg distance from sun – m -5.79 E10 1.08 E11 1.50 E11 2.28 E11 7.78 E 11 1.43 E12 2.87 E 12 4.50 E 12 5.91 E12 ~same as Earth ROYGBIV

Units q or Q (C) E (N/C) V (V) I (A) P (W) still! R (Ω)

B (T) ϑ (m) ε (V) A (m2) E (J) still! P (Pa) V (m3) Q (J) ρ (kg/m3)