AP® physics 1 and 2 inquiry based lab investigations, teacher’s manual

AP® Physics 1 and 2 Inquiry Based Lab Investigations, Teacher’s Manual AP ® Physics 1 and 2 Inquiry Based Lab Investigations Teacher’s Manual Effective Fall 2021 A P P E N D IX E S Appendix C AP Physi[.]

AP Physics and Inquiry-Based Lab Investigations ® Teacher’s Manual Effective Fall 2021 APPENDIXES Appendix C: AP Physics and Constants and Equations Table of information and equation Tables for AP Physics and exams The accompanying Table of Information and equation tables will be provided to students when they take the AP Physics and Exams Therefore, students may NOT bring their own copies of these tables to the exam room, although they may use them throughout the year in their classes in order to become familiar with their content These tables are current as of the May 2015 exam administration; however it is possible for a revision to occur subsequent to that date Check the Physics course home pages on AP Central for the latest versions of these tables (apcentral.collegeboard.org) The Table of Information and the equation tables are printed near the front cover of both the multiple-choice section and the free-response section The Table of Information is identical for both exams except for some of the conventions The equations in the tables express the relationships that are encountered most frequently in the AP Physics and courses and exams However, the tables not include all equations that might possibly be used For example, they not include many equations that can be derived by combining other equations in the tables Nor 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 313 © 2015 The College Board Appendix C Some explanations about notation used in the equation tables: APPENDIXES 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 equation tables Symbols with arrows above them represent vector quantities Subscripts on symbols in the equations are used to represent special cases of the variables defined in the right-hand columns The symbol ∆ before a variable in an equation specifically indicates a change in the variable (e.g., final value minus initial value) 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 314 © 2015 The College Board AP Physics and Constants and Equations ADVANCED PLACEMENT PHYSICS TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS Proton mass, Electron charge magnitude, Neutron mass, Coulomb’s law constant, meter, kilogram, second, ampere, PREFIXES Prefix Symbol tera T m kg s A kelvin, hertz, newton, joule, K Hz N J watt, coulomb, volt, ohm, − pe • − W C V Ω • APPENDIXES Speed of light, Factor × Universal gravitational constant, Acceleration due to gravity at Earth’s surface, Electron mass, UNIT SYMBOLS = ∞C degree Celsius, VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q sinq 12 35 2 45 M cos q 45 2 35 12 tanq 3 34 43 • giga G mega kilo k − centi c − milli m − micro m − nano n − pico p The following conventions are used in this exam I The frame of reference of any problem is assumed to be inertial unless otherwise stated II Assume air resistance is negligible unless otherwise stated III In all situations, positive work is defined as work done on a system IV The direction of current is conventional current: the direction in which positive charge would drift V Assume all batteries and meters are ideal unless otherwise stated 315 © 2015 The College Board Appendix C ADVANCED PLACEMENT PHYSICS EQUATIONS GEOMETRY AND TRIGONOMETRY MECHANICS = Ãx Ãx + a x t APPENDIXES x =x0 + Ãx t + a t x Ãx2 = Ãx20 + a x ( x - x0 )   Fnet  ÂF = a = m m   Ff £ m Fn Ã2 r   p = mv   Dp = F D t ac = mv K = D= = F= E W d Fd cos q DE Dt P= q = q0 + w0 t + at = w w0 + at x = A cos (2 p ft )   t  Ât = a = net I I = t r= rF sin q ^F L = Iw DL = t Dt Iw   Fs = k x K = Us = r= kx m V a A d E f F I K k L  m P p r T t U V v W x y a = = = = = = = = = = = = = = = = = = = = = = = = acceleration amplitude distance energy frequency force rotational inertia kinetic energy spring constant angular momentum length mass power momentum radius or separation period time potential energy volume speed work done on a system position height angular acceleration m q r t w = = = = = coefficient of friction angle density torque angular speed Rectangle A = bh Triangle A = bh Circle A = pr C = pr Rectangular solid V = wh Cylinder V = pr 2 = S pr  + pr Sphere V = pr S = pr A= C= V= S = b = h = = w= r = area circumference volume surface area base height length width radius Right triangle c= a2 + b2 a sin q = c b cos q = c a tan q = b c q a 90 b DUg = mg Dy = T 2p = w f Ts = p m k Tp = p  g  mm Fg = G 2 r   Fg g= m UG = - Gm1m2 r 316 © 2015 The College Board AP Physics and Constants and Equations ADVANCED PLACEMENT PHYSICS TABLE OF INFORMATION CONSTANTS AND CONVERSION FACTORS Proton mass, m p = 1.67 ¥ 10 -27 kg Neutron mass, mn = 1.67 ¥ 10 -27 kg electron volt, eV = 1.60 ¥ 10 -19 J c = 3.00 ¥ 108 m s Speed of light, Universal gravitational constant, Acceleration due to gravity at Earth’s surface, Avogadro’s number, N = 6.02 ¥ 10 23 mol-1 R = 8.31 J (mol iK) APPENDIXES Electron mass, me = 9.11 ¥ 10 -31 kg Universal gas constant, e = 1.60 ¥ 10 -19 C Electron charge magnitude, G = 6.67 ¥ 10 -11 m kg is g = 9.8 m s Boltzmann’s constant, k B = 1.38 ¥ 10 -23 J K u = 1.66 ¥ 10 -27 kg = 931 MeV c unified atomic mass unit, h = 6.63 ¥ 10 -34 Jis = 4.14 ¥ 10-15 eVis Planck’s constant, hc = 1.99 ¥ 10 -25 J i m = 1.24 ¥ 103 eVinm e0 = 8.85 ¥ 10 -12 C2 N i m Vacuum permittivity, Coulomb’s law constant, k = pe0 = 9.0 ¥ 10 N i m C m0 = p ¥ 10 -7 (Ti m) A Vacuum permeability, Magnetic constant, k  = m0 p = Ơ 10 -7 (T i m) A atm = 1.0 ¥ 10 N m = 1.0 ¥ 10 Pa atmosphere pressure, UNIT SYMBOLS Factor 1012 meter, kilogram, second, ampere, kelvin, PREFIXES Prefix Symbol tera T 10 giga G 106 m kg s A K mole, hertz, newton, pascal, joule, mol Hz N Pa J watt, coulomb, volt, ohm, henry, W C V W H farad, tesla, degree Celsius, electron volt, F T ∞C eV VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES q sin q 12 35 2 45 mega M cosq 45 2 35 12 kilo k tan q 33 34 43 • -2 centi c 10 -3 milli m 10 -6 micro m -9 nano n -12 pico p 10 10 10 10 The following conventions are used in this exam I The frame of reference of any problem is assumed to be inertial unless otherwise stated II In all situations, positive work is defined as work done on a system III The direction of current is conventional current: the direction in which positive charge would drift IV Assume all batteries and meters are ideal unless otherwise stated V Assume edge effects for the electric field of a parallel plate capacitor unless otherwise stated VI For any isolated electrically charged object, the electric potential is defined as zero at infinite distance from the charged object 317 © 2015 The College Board Appendix C ADVANCED PLACEMENT PHYSICS EQUATIONS MECHANICS = Ãx Ãx + a x t APPENDIXES = x x + Ãx t + a t x Ãx2 = Ãx20 + 2ax ( x - x0 )  = a   Fnet F  = m m   Ff £ m Fn Ã2 r   p = mv ac =   Dp = F Dt K = mv 2 D= E W = F= d Fd cos q P = DE Dt q =q0 + w0 t + at = w w0 + at = x A = cos ( wt ) A cos (2 p ft ) xcm =  = a  mi xi  mi  I  I = t r= rF sin q ^F L = Iw DL = t Dt K = I w2   Fs = k x a = A = d = E = F = f = I = K = k = L =  = m = P = p = r = T = t = U = v = W= x = y = a = m= q = t = w= acceleration q1q2 amplitude pe0 r distance   FE energy E = q force frequency  q E = rotational inertia pe0 r kinetic energy DU E = qDV spring constant angular momentum q V = length pe0 r mass  DV power E = Dr momentum radius or separation Q DV = period C time A C = ke0 potential energy d speed work done on a system E = Q e0 A position height 1 UC = Q DV C ( DV )2 angular acceleration = 2 coefficient of friction DQ angle I = Dt torque r angular speed R= A U s = kx P = I DV DV R DUg = mg Dy I = 2p = w Rs = = T t t  = net ELECTRICITY AND MAGNETISM  FE = f = = = = = e= F = I =  = P = Q = q = R = r = t = U = A B C d E V = v = k = r= q = F= area magnetic field capacitance distance electric field emf force current length power charge point charge resistance separation time potential (stored) energy electric potential speed dielectric constant resistivity angle flux    FM = qv ¥ B    FM = qv sin q B    FM= I  ¥ B i    FM = I  sin q B   F B = B A  Ri Ts = p m k = Rp  R1i Tp = p  g Cp =  Ci   FB = B cos q A = Cs  C1i e= - e= B v  mm Fg = G 2 r   Fg g= m UG = - B= i i i m0 I 2p r DFB Dt Gm1m2 r 318 © 2015 The College Board AP Physics and Constants and Equations ADVANCED PLACEMENT PHYSICS EQUATIONS FLUID MECHANICS AND THERMAL PHYSICS m V P= F A P = P0 + rgh Fb = rVg A1v1 = A2 v2 P1 + rgy1 + rv 2 = P2 + rgy2 + kA DT Q = Dt L PV = nRT = NkBT K = = area = force = depth = thermal conductivity = kinetic energy = thickness = mass = number of moles = number of molecules = pressure = energy transferred to a system by heating T = temperature t = time U = internal energy V = volume v = speed W = work done on a system y = height r = density A F h k K L m n N P Q rv 2 k T B MODERN PHYSICS l= h p E = mc n= c à n sin q1 = n sin q2 1 + = si so f M = hi s = i ho so DL = m l d sin q = m l E= f = K= m= p = l= f= energy frequency kinetic energy mass momentum wavelength work function d = separation f = frequency or focal length h = height L = distance M = magnification m = an integer n = index of refraction s = distance v = speed l = wavelength q = angle GEOMETRY AND TRIGONOMETRY Rectangle A = bh Circle DU = Q + W K max = hf - f v f Triangle A = bh W = - P DV E = hf l= APPENDIXES r= WAVES AND OPTICS A = pr C = pr Rectangular solid = h Cylinder V =p S = pr + 2p r Sphere V = pr S = pr A= C= V= S = b = h = = w= r = area circumference volume surface area base height length width radius Right triangle c = a + b2 a sin q = c b cos q = c a tan q = b c q a 90° b 319 © 2015 The College Board This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank This page is intentionally left blank collegeboard.org AP Physics and Inquiry-Based Lab Investigations ® Aligned with best practices in science instruction as proposed by the National Science Foundation and America’s Lab Report, AP Physics and Inquiry-Based Lab Investigations: A Teacher’s Manual serves to guide teachers through inquiry-based lab experiments and procedures that are easily tailored to diverse needs and are appropriate for small and large classes ® · Features 15 student-directed, inquiry-based lab investigations (7 for AP Physics and for AP Physics 2) · Emphasizes scientific inquiry, reasoning, and critical thinking · Aligns with the learning objectives in the AP Physics 1: Algebra-Based and AP Physics 2: Algebra-Based Curriculum Framework · Enables students to plan, direct, and integrate a range of science practices, such as designing experiments, collecting data, and applying quantitative skills · Includes lists of supplemental resources 140086110 13b-8127 ... constant, k B = 1. 38 ¥ 10 -23 J K u = 1. 66 ¥ 10 -27 kg = 9 31 MeV c unified atomic mass unit, h = 6.63 ¥ 10 -34 Jis = 4 .14 ¥ 10 -15 eVis Planck’s constant, hc = 1. 99 ¥ 10 -25 J i m = 1. 24 ¥ 10 3 eVinm... number, N = 6. 02 ¥ 10 23 mol -1 R = 8. 31 J (mol iK) APPENDIXES Electron mass, me = 9 .11 ¥ 10 - 31 kg Universal gas constant, e = 1. 60 ¥ 10 -19 C Electron charge magnitude, G = 6.67 ¥ 10 -11 m kg is... FUNCTIONS FOR COMMON ANGLES q sin q 12 35 2 45 mega M cosq 45 2 35 12 kilo k tan q 33 34 43 • -2 centi c 10 -3 milli m 10 -6 micro m -9 nano n - 12 pico p 10 10 10 10 The following conventions are