Genel Fizik Formülleri ( ingilizce ) Table of Information and Equation Tables for AP Physics Exams The accompanying Table of Information and Equation Tables will be provided to students when they take the AP Physics Exams. Therefore, students may NOT bring their own copies of these tables to the examination room, although they may use them throughout the year in their classes in order to become familiar with their content. Table of Information For both the Physics B and Physics C Exams, the Table of Information is printed near the front cover of the multiple-choice section and on the green insert provided with the free-response section. The tables are identical for both exams except for one convention as noted. Equation Tables For both the Physics B and Physics C Exams, the equation tables for each exam are printed only on the green insert provided with the free-response section. The equation tables may be used by students when taking the free-response sections of both exams, but NOT when taking the multiple-choice sections. The equations in the tables express the relationships that are encountered most frequently in AP Physics Courses and Exams. However, the tables do not include all equations that might possibly be used. For example, they do not include many equations that can be derived by combining other equations in the tables. Nor do they include equations that are simply special cases of any that are in the tables. Students are responsible for understanding the physical principles that underlie each equation and for knowing the conditions for which each equation is applicable. The equation tables are grouped in sections according to the major content category in which they appear. Within each section, the symbols used for the variables in that section are defined. However, in some cases the same symbol is used to represent different quantities in different tables. It should be noted that there is no uniform convention among textbooks for the symbols used in writing equations. The equation tables follow many common conventions, but in some cases consistency was sacrificed for the sake of clarity. Some explanations about notation used in the equation tables: 1. The symbols used for physical constants are the same as those in the Table of Information and are defined in the Table of Information rather than in the right-hand columns of the tables. 2. Symbols in bold face represent vector quantities. 3. Subscripts on symbols in the equations are used to represent special cases of the variables defined in the right-hand columns. 4. The symbol D before a variable in an equation specifically indicates a change in the variable (i.e., final value minus initial value). 5. Several different symbols (e.g. d, r, s, h, ) are used for linear dimensions such as length. The particular symbol used in an equation is one that is commonly used for that equation in textbooks. TABLE OF INFORMATION FOR 2006 and 2007 CONSTANTS AND CONVERSION FACTORS 1 unified atomic mass unit, 27 2 1 u 1.66 10 kg 931 MeV c - =¥ = Proton mass, 27 1.67 10 kg p m - =¥ Neutron mass, 27 1.67 10 kg n m - =¥ Electron mass, 31 9.11 10 kg e m - =¥ Electron charge magnitude, 19 1.60 10 C e - =¥ Avogadro’s number, 23 -1 0 6.02 10 mol N=¥ Universal gas constant, 8.31 J (mol K) R = i Boltzmann’s constant, 23 1.38 10 J K B k - =¥ Speed of light, 8 3.00 10 m s c=¥ Planck’s constant, 34 15 6.63 10 J s 4.14 10 eV s h - - =¥ =¥ i i 25 3 1.99 10 J m 1.24 10 eV nm hc - =¥ =¥ i i Vacuum permittivity, 12 2 2 0 8.85 10 C N m - =¥ i Coulomb’s law constant, 922 0 14 9 . 0 1 0 Nm C k p ==¥ i Vacuum permeability, 7 0 41 0 ( T m ) A mp - =¥ i Magnetic constant, 7 0 41 0 ( T m ) A k mp - == ¢ i Universal gravitational constant, 11 3 2 6.67 10 m kg s G - =¥ i Acceleration due to gravity at Earth’s surface, 2 9.8 m s g = 1 atmosphere pressure, 52 5 1 atm 1.0 10 N m 1.0 10 Pa =¥ =¥ 1 electron volt, 19 1 eV 1.60 10 J - =¥ UNITS Name Symbol meter m kilogram kg second s ampere A kelvin K mole mol hertz Hz newton N pascal Pa joule J watt W coulomb C volt V ohm W henry H farad F tesla T degree Celsius C electron- volt eV PREFIXES Factor Prefix Symbol 9 10 giga G 6 10 mega M 3 10 kilo k 2 10 - centi c 3 10 - milli m 6 10 - micro m 9 10 - nano n 12 10 - pico p VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES ? sin ? cos ? tan ? 0 0 1 0 30 1/2 32 / 33 / 37 3/5 4/5 3/4 45 22 / 22 / 1 53 4/5 3/5 4/3 60 32 / 1/2 3 90 1 0 ? The following conventions are used in this exam. I. Unless otherwise stated, the frame of reference of any problem is assumed to be inertial. II. The direction of any electric current is the direction of flow of positive charge (conventional current). III. For any isolated electric charge, the electric potential is defined as zero at an infinite distance from the charge. *IV. For mechanics and thermodynamics equations, W represents the work done on a system. *Not on the Table of Information for Physics C, since Thermodynamics is not a Physics C topic. ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007 NEWTONIAN MECHANICS ELECTRICITY AND MAGNETISM 0 at uu =+ 2 00 1 2 xxta u =++t 0 () 22 0 2ax x uu =+- net m Â= = FF a fric F N m £ 2 c a r u = sin rtq = F m = pv tDD == J F p 2 1 2 Km u = g Um g D = h cos WFr q D = avg W P t D = PF cos uq = s k =- Fx 2 1 2 s Uk = x 2 s m T k p = 2 p T g p = 1 T f = 12 2 G Gm m F r =- 12 G Gm m U r =- a = acceleration F = force f = frequency h = height J = impulse K = kinetic energy k = spring constant = length m = mass N = normal force P = power p = momentum r = radius or distance T = period t = time U = potential energy u = velocity or speed W = work done on a system x = position m = coefficient of friction q = angle t = torque 2 12 0 1 4 qq F r p = q = F E 12 0 1 4 E qq Uq V r p == avg V E d =- 0 1 4 i i i q V r p = Â Q C V = 0 A C d = 2 11 22 c UQ VC V == avg Q I t D D = R A r = VI R = PI V = pi i CC = Â 11 s i i CC = Â i i s R R = Â 11 i i p R R = Â sin B FqB uq = sin B FB Iq = 0 2 I B r m p = cos m BA fq = m t f e D D =- avg B u e = A = area B = magnetic field C = capacitance d = distance E = electric field e = emf F = force I = current = length P = power Q = charge q = point charge R = resistance r = distance t = time U = potential (stored) energy V = electric potential or potential difference u = velocity or speed r = resistivity q = angle f m = magnetic flux ADVANCED PLACEMENT PHYSICS B EQUATIONS FOR 2006 and 2007 FLUID MECHANICS AND THERMAL PHYSICS WAVES AND OPTICS 0 PPg h r =+ buoy F Vg r = 11 22 AA uu = 2 1 const. 2 Pg y rr u ++= 0 T a DD = kA T H L D = F P A = B PV nRT Nk T == 3 2 avg B Kk T = 3 3 B rms kT RT M u m == WP V D =- UQW D =+ H W e Q = H C c H TT e T - = A = area e = efficiency F = force h = depth H = rate of heat transfer k = thermal conductivity K avg = average molecular kinetic energy = length L = thickness M = molar mass n = number of moles N = number of molecules P = pressure Q = heat transferred to a system T = temperature U = internal energy V = volume u = velocity or speed u rms = root-mean-square velocity W = work done on a system y = height a = coefficient of linear expansion m = mass of molecule r = density f ul = c n u = 1122 sin sin nn qq = 2 1 sin n c n q = 0 111 s sf i += 00 hs ii M hs == - 2 R f = sin dm ql = mL x m d l d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction R = radius of curvature s = distance u = speed x = position l = wavelength q = angle ATOMIC AND NUCLEAR PHYSICS E hf pc == max Kh f f =- h p l = 2 () E mc DD = E = energy f = frequency K = kinetic energy m = mass p = momentum l = wavelength f = work function GEOMETRY AND TRIGONOMETRY Rectangle A bh = Triangle 1 2 Ab h = Circle 2 Ar p = 2 Cr p = Parallelepiped Vw h = Cylinder 2 Vr p = 2 22 Srr p p =+ Sphere 3 4 3 Vr p = 2 4 Sr p = Right Triangle 222 abc += sin a c q = cos b c q = tan a b q = A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius c a b 90° q ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007 MECHANICS ELECTRICITY AND MAGNETISM 0 at uu =+ 2 00 1 2 xx ta t u =++ () 22 00 2ax x uu =+- net m Â= = FF a d dt = p F dt D == Ú JFp m = pv fric FN m £ Wd ? = Ú Fr 2 1 2 Km u = dW P dt = P = Fv g Um g h D = 2 2 c ar r u w == =¥ rF t net I Â= = tt a 22 Ir d mm r == Â Ú cm mm =ÂÂ rr r uw = I =¥= Lrp w 2 1 2 KI w = 0 t wwa =+ 2 00 1 2 tt qqw a =++ a = acceleration F = force f = frequency h = height I = rotational inertia J = impulse K = kinetic energy k = spring constant = length L = angular momentum m = mass N = normal force P = power p = momentum r = radius or distance r = position vector T = period t = time U = potential energy u = velocity or speed W = work done on a system x = position m = coefficient of friction q = angle t = torque w = angular speed a = angular acceleration s k =- Fx 2 1 2 s Uk x = 21 T f p w == 2 s m T k p = 2 p T g p = 12 2 ˆ G Gm m r =- Fr 12 G Gm m U r =- 2 12 0 1 4 qq F r p = q = F E 0 Q d ? = Ú EA dV E dr =- 0 1 4 i i i q V r p = Â 12 0 1 4 E qq Uq V r p == Q C V = 0 A C d k = pi i CC = Â 11 s i i CC = Â dQ I dt = 2 11 22 c UQ VC V == R A r = r = EJ d IN eA u = VI R = i i s R R = Â 11 i i p R R = Â PI V = M q =¥ Fv B A = area B = magnetic field C = capacitance d = distance E = electric field e = emf F = force I = current J = current density L = inductance = length n = number of loops of wire per unit length N = number of charge carriers per unit volume P = power Q = charge q = point charge R = resistance r = distance t = time U = potential or stored energy V = electric potential u = velocity or speed r = resistivity f m = magnetic flux k = dielectric constant 0 dI m ? = Ú B Id d r 0 3 4 m p ¥ = r B Id =¥ Ú FB 0 s Bn I m = m d f ? = Ú BA m d dt f e =- dI L dt e =- 2 1 2 L UL I = ADVANCED PLACEMENT PHYSICS C EQUATIONS FOR 2006 and 2007 GEOMETRY AND TRIGONOMETRY CALCULUS Rectangle Ab h = Triangle 1 2 Ab = h Circle 2 Ar p = 2 Cr p = Parallelepiped Vw h r = Cylinder 2 Vr p = 2 22 Sr p p =+ Sphere 3 4 3 Vr p = 2 4 Sr p = Right Triangle 22 abc += 2 sin a c q = cos b c q = tan a b q = A = area C = circumference V = volume S = surface area b = base h = height = length w = width r = radius c a b 90 ° q df dfdu dx du dx = () 1 nn d x nx dx - = () x x d ee dx = () 1 1n d x dx x = () sin cos d x x dx = () cos sin d x x dx =- 1 1 ,1 1 nn xd x x n n + =? + Ú - x x ed x e = Ú ln dx x x = Ú cos sin xdx x = Ú sin cos xdx x =- Ú