---------------------Science----------------- Distance = velocity*time + acceleration*time^2/2 velocity = acceleration*time ______ | MASS |__\ Force_Newtons=Mass_Kgm*Accelerate_m/s^2 |______| / Force_lbf=Mass_Slugs*Aceler_ft/s^2 ENERGY_kinetic= Mass*Velocity^2/2 | Force_tan \|/ FRICTION __V___ Force_Friction |coef_u|__\ |______| / Force_Friction =coef_u*Force_tan ^^^^^^^^^^^^^^ metal_u =0.5 glass_u =1 telfon_u =0.04 ____ _____ |__ \______________/ ___| / \ / \//_/ ______________ \___ //____/ \_____| ||// ||/___ ----- Torque = Radius*Force ___ / \ \___/ Acceleration_gravity = g = 9.8m/sec^2 | Force_Newtons=Mass_Kgm*Accelerate_m/s^2 \|/ V 100Kgm = 220.46lbs Man ENERGY_potential_Joule= Force_Newtons*Distance_m Joule = 1_Newton*1_meter = Kgm*(m/s)^2 Watt = Joule/sec _ | | |~~~~~~~~~~~ | | \___________ / \ | |~~~| | 1KWHr = 1_liter_H20 @ 367meters |___| | (1_liter weights 9.8Kgm) | ~~~~~~~~~~~~| ___________/ ___--- ---___ '------`'------` /()\ ____________ /_||_\ _/ _/ _/ 1KWHr = 220lb_man @ 108ft _/ ____________/ Force_gravity =G_constant*Mass_1*Mass_2/Radius G_constant = 6.670E-11 Newtons*meter^2/Kgm^2 ___ STOKE'S LAW _---_ \ / \ | Force=6*PI*Radius*Velocity*Viscosity | --->| \|/ Force=K_Constant*Velocity \_ R _/ V --- Velocity Free_Fall_velocity = V_terminal*(1-exp(-k_constant*time/mass) centipitcal_Force- Velocity^2/Radius Orbit_earth = Radius_earth*sqrt(g_earth/radius_satelite) T_period = 2*PI*radius_satelite^(3/2)/(Radius_earth*g_earth^(1/2)) Energy_Kinetic = Mass*Velocity/2 Energy_gravity = = - G_constant*Mass_earth*Mass_satellite/Radius Force_spring = K_constant*Distance "elastic force" Energy_spring =K_constant*Distance^2/2 Power = Force*velocity Momentum = Mass*velocity Tangental_speed = angular_velocity*radius Moment_of_interia = Sum_all_i(mass_i*radius_i^2) Torque = Moment_of_interia*angular_acceleration =Force*Radius Lontitudal_strain = delta_length/length "tensile strain" Youngs_modulus = stress/strain Stress = Force/Area for metal Youngs_modulus = 10=>30Meg_lbs/in^2 Lead = 2Meg_lbs/in^2 92 stop ___ X/ / height strear_strain = delta_X/height /__/ strear_modulus = (Force_Tangent/Area)/(delta_X/height) for metal strear_modulus = 3=>10Meg_lbs/in^2 Lead = .8Meg_lbs/in^2 Volume_strain = delta_volume/volume Bulk_modulus = (delta_pressure)/(delta_volume/volume) Bulk_modulus =~ Youngs_modulus compressablity = 1/Bulk water =(34lbs/in^2)^-1 Spring_harmonic = Mass*Velocity/2 + K_constant*Distance^2/2 period = 2*PI*Mass/K_constant Suspended_spring_period = 2*PI*Mass/K_constant pendulum_period = 2*PI*sqrt(Length/gravity) _ /_/_/_ / / _/_ | | |___| Tidal waves shallow depth c = sqrt(g*h) Tidal waves shallow depth c = sqrt(g*h/2*PI) Density Gold/Silver = 10=>20 gm/cc Alum/Iron = 3=>8 gm/cc water = 1 gm/cc /\ / \ / \ _/ \_ (_) (_) __________/ \______/ \________ Surface_tension = force to lift a loop of wire = Force/(2*length) water = 70dynes/cm oil/alcohol =~30dynes/cm Pressure_inside_soap_bubble = 4*Surface_tension/radius... bigger bubble=more pressure Bernoullis equation constant = pressure +density*gravity*height +density*velocity^2/2 viscocity "stokes law" Force = viscocity*Area*(delta_velocity/delta_length) one poise - 1dyne*sec/cm^2 oil = 10 poise water = 1centipoise air = 181micro poise Pipe_fuild_Quantity = = (PI/8)*(Radius^4/viscocity)*(delta_pressure/length) Velocity_terminal = (2/9)*(radius^2)*(gravity/viscocity)*(density_differnce) Lift_force= (1/2)*Wing_Area*density*(V_1^2 -V_2^2) Reynolds_Number = above is turbulent Reynolds_Number = density*velocity*diameter/viscocity Reynolds_Number = 216 for air, 1000 for water Temperature_expansion = delta_volume/delta_temperature metals = 40 to 70 ppm quartz is 1ppm liquid is 200 to 1000ppm one calorie = 1/860 watt*hours one BTU = 251.996 cal Heat capacity metal is 30 to 200 millical/(gm*C) water is 1000 millical/(gm*C) defined.. Heat of fusion water is 79cal/gm Heat of vapor water is 539cal/gm Thermal_conductance metal_copper_alum = 1/2 to 1 (cal/sec)/(cm*deg_C) ice/concrete = 1 to 2 milli (cal/sec)/(cm*deg_C) wood = 100micro (cal/sec)/(cm*deg_C) air = 60micro (cal/sec)/(cm*deg_C) Planks_spectral_emission = W_f = (2*PI*h/c^2)*(f^3)/(exp(h*f/Kt)-1) c = speed_light Radiation_black_body = Wbb = universal_constant*Temp^4 universal_constant = 5.672E-8 watts/(m^2*K^4) pressure*volume = Number_atom*R_constant*Temp Volume = 22.4 liters 1atm = 1.01E6dynes/cm^2 Adiabatic = no heat enters or leaves isochoric = volume the same iso thermal = constant temperature isobaric = constant presssure effeciency_carrot = 1-Tc/Th Entropy = delta_heat/temperature =1cal/deg_K heat 1kgm water 0 to 100 C /373 S2 -S1 = | mc*(dt/T) =mc*ln(373/273) /273 Travelling wave = string on tension tension = s mass_per_unit = u velocity = sqrt(tension/mass_per_unit) tranverse_impulse = s*delta_x*time/c tranverse_momentum = u*c*delta_x*time Fluid_wave c = sqrt(gravity*height) = fuild c = sqrt(youngs_module/density) = bar c = sqrt(Bulk_module/density) = bulk c = sqrt(alpha*K*T/M ) = M_molecular_wave c =sqrt(1/(e0*u0)) phi=u0*H eo*E H ^ /|\- | - |______\ E \ /- \ - \ - - \ - \ E /______\ -\ |\ - | \ -\|/ \ V H \- _\| S Electrical c =sqrt(1/(e0*u0)) phi=u0*H eo*E Z = E/H = sqrt(u0/e0) = 377ohms Columbs_law force = K_coul*q1_coul*2_coul/radius^2 K_coul = 8.98E9Newtons*meter^6/coul^2 Energy_density = e0*E/2 Cap = e0*A/length Magnetic Force = q_coul*(velocity X B_field) B_field = d_Phi/d_area circular orbit radius = mass*velocity/(B_field*q_coul) B_field= u0*number_turns*H = uo*H L_inductance = Number*Phi/current Energy = L_inductance*current^2/2 Sound_intensity =Pressure_Amplitude/(2*density*velocity) max_tolerable_loudness = 94uW/cm^2 (280dynes/cm^2)/(2*(1.22E-3gm/cc)*3.46E4cm/sec) softest = 10E-16W/cm^2 conversation =10uW/cm^2 shouting =30uW/cm^2 120dB =200dynes/cm^2 80dB = 2dynes/cm^2 1Gev = gamma rays = Proton rest mass 1Mev = gamma rays = electron rest mass 1Kev = X rays 1ev = light 1mV = short wave 1uV = broadcast bremsstahlung "braking radiation" Xrays | __ | / \ Nucleus \ \__/ \ \__________\ electron | Xray / |/__ Compton_effect light is scatterred by electrons __ /| lower frequency Photon ___\ (e) ==> / Photon / (e) _\| momemtum of photon = p = m*c =E*c/c^2 = h/wave_length Energy = h*v Pair production, cannot happen in empty space photon needs to be near a massive particle __ __ __ Nucleus / \ Nucleus / \ /| \__/ = => \__/ (e) Photon______\ (-e) / |/_ Pair anilihation, can happen in empty space Photoelectric effect Full energy of photon goes into "bounded system" delta_E*delta_time >= h delta_p*delta_x >= h stationary waves require whole number of wavelengths in a orbit. A free electron cannot absorb a free photon, it must be bounded A free electron cannot emmit a free photon, it needs to be near a photon. Large molecules 10E-6cm atom 10E-8cm proton 10E-13cm quark 10E-16cm electron 10E-16cm ^ L /|\ _ momentum __|-------__ /| / | Radius \/ \_ _/ -------- Angular_mometum =Radius X mometum |<-----2a--->| _------_ energy only depends / \ on "a" __----/ --__ \ / 2a | \--->| \__ | _ / a | ----\--- / min_angular_mom_orbit \_ _/max_angular_mom_orbit ------ 1 watch batterie draws 40u Snell's law n1*sin(theta_1) = n2*sin(theta_2) exp(j*X) cos(x) +j*sin(x) Maxwell's Equations __ \/ dot J = -delta_p/dt __ \/ cross E = -delta_B/dt V=delta_Phi/dt __ \/ cross H = J+ delta_D/dt H =I*N __ \/ dot D = p __ \/ dot B = 0 -----------------------------------------------