Equation Sheet For Quizzes and Tests

hapter : Aluminum.70 g/cm 3 opper 8.96 g/cm 3 Iron 7.87 g/cm 3 Equation Sheet For Quizzes and Tests You must have memorized the unit prefix values and the formulas related to circles, spheres, and rectangles. density= mass volume ρ= m V Lead.34 g/cm 3 Water.00 g/cm 3 Seawater.03 g/cm 3 Mercury 3.6 g/cm 3 Gasoline 0.680 g/cm 3 hapter : velocity =speed and direction change in position average velocity= change in time v= Δ x Δ t (unit: m/s= m s ) change of velocity average acceleration= time ā= Δ v Δ t acceleration has direction (unit: m/s = m s ) Assuming no acceleration, constant velocity, and initial position=0: distance=(velocity) (time) d=v t Assuming constant acceleration, initial velocity=0 and initial position= 0: velocity =(acceleration) ( time) v=a t distance= (acceleration) (time) d= at net force=(mass) (acceleration) F net =m a force has direction unit: newton, N= kg m s Weight is the downward force caused by gravity: weight=(mass) (acceleration due to gravity ) w=m g g=9.80m/ s at earth surface force on object A due to object B= force on object B due to object A F A due to B = F B due to A Momentum: momentum=(mass) (velocity ) p=m v momentum has direction change of momentum=(average force) (time of interaction ) Δ p= F Δ t conservation of total momentum in an isolated system: p total, before = p total, after ircular motion: centripetal acceleration= ( velocity) radius of circle a c = v r (mass) (velocity ) centripetal force= radius of circle F c = mv r Gravitational force in general: (one mass) (another mass) gravitational force=(constant) F=G m m G=6.67 0 N m (distance) d kg gravitational acceleration= (constant) (mass) distance g=g m d

hapter 3: Assuming constant force: work done by force=(force) (distance moved in direction of force) W=F d unit: joule, J=N m= kg m s power= work time P= W t unit: watt, W=J/s= J s change in gravitational potential energy=work=(weight) (change in height) PE=W =Fd=(m g) h=mgh kinetic energy= (mass) ( velocity) KE= m v If friction can be ignored, total energy is unchanged during free fall from height h: change in KE = change in PE m v =mg h so v= (g h) hapter 4: T F = 9 5 T +3 o F T = 5 9 (T F 3 o F) T K =T +73 o =T +73 K change in heat energy of H O=(mass) (specific heat) (change in temperature) Q=m cδ T c ice =0.50 cal g o c water =.00 cal g o c steam =0.48 cal g o H O fusion heat energy absorbed or released=(mass) (latent heat of H O fusion) Q=m L f L f =80 cal g H O vaporization heat energy absorbed or released=(mass) (latent heat of H O vaporization) Heat and mechanical energy conversion: Q=m L v L v =540 cal g food calorie=000 cal cal=4.86 J hapter 5: period= frequency T = f velocity =(wavelength) (frequency) velocity of sound v at temperature T =33 m/ s+(0.600 m ) T s o v =λ f speed of light in vacuum=c=9979458 m/ s (Using 3.00 0 8 m/s is nearly always OK.) beat frequency=one frequency other frequency f beat =f f sound power sound intensity= area I= P A (an integer ) ( velocity of wave) resonant frequency of a string or an open pipe= (length) (an integer ) ( velocity of wave) resonant frequency of pipe with closed end= (length) f n = nv L f n = n v 4 L n=,, 3,... n=,, 3,...

hapter 6: quantity of charge=(number of electrons) (electron charge) q=ne=n (.60 0 9 ) unit: coulomb, oulomb s Law: (charge on object ) (charge on object ) electrical force=(constant)( (distance between objects) ) F=k q q k=9.00 0 9 N m d work to create potential difference electric potential difference= charge moved V = W q unit: volt, V = N quantity of charge moved electric current= time for the movement I= q t unit: ampere, A= s electric potential resistance= electric current R= V I unit: ohm, Ω= V A electric power consumed=(electric current) (electric potential) P=I V unit: watt, W=J/s= J s hapter 7: (electric power in W) (time in h) (rate in $/kw-h) electric cost= 000W /kw (primary voltage) voltage) =(secondary ( primary loops) (secondary loops) V p N p = V s N s (power in) = (power out) P in =P out (primary voltage) (primary current)=(secondary voltage) (secondary current) R total =R +R +R 3 +... Resistances in series period= frequency T = f R total = R + R + R 3 +... velocity =(wavelength) (frequency) speed of light in vacuum=(wavelength) (frequency) V p I p =V s I s Resistances in parallel c=λ f speed of light in vacuum=c=9979458 m/s 3.00 0 8 m/s (Using 3.00 0 8 m/s is nearly always OK.) angle of incidence=angle of reflection θ i =θ speed of light in vacuum r index of refraction= speed of light in material energy of photon=(planck's constant) (photon frequency) E photon =hf photon =(6.63 0 34 J s)f photon n= c v photon energy Planck's constant=h=6.63 0 34 J s momentum of a photon= speed of light p photon = E photon = h c λ photon hapter 8: wavelength =(constant) ( ) (number) λ =R ( ) n =(.097 07 m ) ( ) n ommon energy unit used in atomic and nuclear physics: ev=.60 0 9 J energy of n th energy of innermost orbit state orbit state= number squared E n = E n Planck's constant wavelength of massive particle= particle momentum n = 3.6 ev =Planck's constant (mass) ( velocity) =.8 0 8 J n λ= h mv n=,, 3,

hapter 9: (no equations) hapter 0: hapter : atomic weight of element=periodic Table value with units of g/mol formula mass of compound=sum of atomic masses of atoms in the compound with units of g/mol mass in g moles of an element= atomic mass in g/mol mass in g moles of compound= formula mass in g/mol Avogadro's number=6.0 0 3 atoms or molecules per mol atomic mass of element (number of atoms of element) 00=% of element in compound formula mass of compound oncentration by volume: %solute= V solute V solvent 00 By mass: %solute= m solute m solvent 00 number of moles molarity M= L of water hapter : (no equations) unit: M, mol /L= mol L ph= log 0 [H 3 O + ] [H 3 O + ]=0 ph hapter 3: energy=(mass) (speed of light) E=m c

Symbols and Units English letters symbols (Usually shown italicized): x, y, and z mainly used for position r used for radial distance d used for linear distance l used for length w used for width and for weight h used for height s used for speed c used for the speed of light = 9979458 m/s exactly, approximate value 3.00 0 8 m/s c specific heat in J/kg K=J/kg o v used for velocity = speed with direction v average velocity a used for acceleration a average acceleration g used for gravitational acceleration (at the earth surface g= 9.8 m/s ) G used for the universal gravitation constant = 6.674 0 N m /kg A used for area V used for volume and used for electrical potential (voltage) I used for electric current and for intensity (power per unit area) of sound or light R used for electrical resistance, the universal gas constant=8.3 J/mol K and the Rydberg constant=.097 0 7 m - k B used for Boltzmann's constant=gas constant/n A =R/N A =.38 0-3 J/K k coefficient in oulomb's law=9.00 0 7 N m / F used for force N used for normal (perpendicular) force N p, N s used for primary and secondary turn count in a transformer V p, V s used for primary and secondary voltages in a transformer n used for number of electrons and for the index of refraction of an optical medium m used for mass W used for work E used for energy and also for electric field KE kinetic energy PE potential energy U internal energy Q used for heat energy, usually measured in calories (cal) J conversion factor for calories to joules=4.86 J/cal (used in text, but can be confusing) P used for power (energy per unit time) p used for pressure (force per unit area) B used for magnetic field T used for temperature and period of cyclic motion h used for Planck's constant=6.63 0-34 J s f used for frequency q used for electric charge used for electrical capacitance L used for electrical inductance L f, L v used for heat of fusion (melting), and heat of vaporization (condensing) N A used for Avogadro's constant=6.0 0 3 number of atoms/mol or molecules/mol e used for the magnitude of electron charge=.60 0-9 and base of natural logarithms=.787...

Units (NOT italicized, these are easily confused with some of the quantity symbols given above): Unit Symbol Quantity meters m distance gram g mass second s time newton N=kg m/s force joule J=N m=kg m /s energy, work watt W=J/s power, energy per unit time coulomb electric charge celsius o temperature measured from freezing point of water kelvin K temperature measured from absolute zero ampere A=/s electric current, charge per unit time volt V=J/ electric voltage farad F=/V electrical capacitance henry H electrical inductance ohm Ω=V/A electrical resistance tesla T magnetic field hertz Hz=/s frequency, cycles per second radian rad angular measure, full circle has π radians pascal Pa=N/m pressure mole mol N A atoms or molecules Greek letter symbols: pi π 3.45965...= circumference of a circle divided by its diameter rho ρ used for density and resistivity alpha α, beta β, theta θ, and phi φ mainly used for angles alpha α, beta β, and gamma γ used for different kinds of radioactivity sigma σ used for standard deviation, uncertainty capital sigma Σ used to show summation omega ω used for angular frequency capital omega Ω used for the unit of electrical resistance epsilon ε and delta δ used for small changes capital delta Δ used for large changes mu μ used for coefficient of friction, prefix for micro (0-6 ) mu naught μ 0 permeability of free space=4π 0-7 H/m epsilon naught ε 0 permittivity of free space=8.854 0 - F/m lambda λ used for wavelength