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, l Equations Chapter 2 Motion in One Dimension ~X= DISPLACEMENT Xf- Xi ~X- Xf-Xi Vavg= ~t- tf- ti AVERAGE VELOCITY ~ AVERAGE SPEED average speed distance traveled time of travel AVERAGE ACCELERATION ~V Vf-Vi aavg= ~t- tf- ti DISPLACEMENT ~ = -i_Cvi These equations are valid only for constantly accelerated, straight-line motion. ~ = vi ~ t + 2a(~t) FINAL VELOCITY Vf= Vi+ a~t These equations are valid only for constantly accelerated, straight-line motion. Vf =vi +2a~ Chapter 3 1 + Vf)~t 1 2 J 2 2 Two-Dimensional Motion and Vectors PYTHAGOREAN THEOREM c2 = a2 + b2 This equation is valid only for right triangles. TANGENT, SINE, AND COSINE FUNCTIONS tan () = opp adj sin () = opp hyp These equations are valid only for right triangles. VERTICAL MOTION OF A PROJECTILE THAT FALLS FROM REST These equations assume that air resistance is negligible, and apply only when the initial vertical velocity is zero. On Earth's surface, ay=-g=-9.81 2 Vy,f = 2ay~Y ~y = ~ay(~t) 2 mil. HORIZONTAL MOTION OF A Vx = Vx,i = constant PROJECTILE ~=Vx ~ t These equations assume that air resistance is negligible. Append ix D : Equations Vy,f = ay~t cos () = adj hyp PROJECTILES LAUNCHED ATAN ANGLE These equations assume that air resistance is negligible. On Earth's surface, ay=-g=-9.81 m/s 2. Vx =Vi cos()= constant Ax= (vi cos B)~t Vy,f = Vi sin () + ay~t 2 2 Vy,f = v?(sin 8) + 2ay~Y ~y =(vi sin B)~t + ~ay(~t) 2 RELATIVE VELOCITY Chapter 4 Vac = Vab + Vbc Forces and the Laws of Motion NEWTON'S FIRST LAW An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line) unless the object experiences a net external force. NEWTON'S SECOND LAW IF=ma I.F is the vector sum of all external forces acting on the object. NEWTON'S THIRD LAW If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force exerted on object 2 by object 1, and these two forces are opposite in direction. WEIGHT Fg= mag On Earth's surface, ag= g= 9.81 m!/. COEFFICIENT OF STATIC FRICTION Fs,max Jls=----p; COEFFICIENT OF KINETIC FRICTION Fk flk=Fn The coefficient of kinetic friction varies with speed, but we neglect any such variations here. FORCE OF FRICTION Ft = J1Fn Appendix D: Equations 855 Chapter 5 Work and Energy ~ NET WORK This equation applies only when the force is constant. W net= Fnetd COS KINETIC ENERGY KE= 2 mv WORK-KINETIC ENERGY THEOREM Wnet =ME GRAVITATIONAL POTENTIAL ENERGY PEg= mgh 1 () 2 1 ~ 2 ELASTIC POTENTIAL ENERGY PEelastic = 2kx MECHANICAL ENERGY ME=KE+'LPE CONSERVATION OF MECHANICAL ENERGY MEi =MEt This equation is valid only if non mechanical forms of energy (such as friction) are disregarded. w POWER Chapter 6 P=-=Fv flt Momentum and Collisions MOMENTUM p =m v IMPULSE-MOMENTUM THEOREM Fflt = flp = mvf - mvi This equation is valid only when the force is constant. CONSERVATION OF MOMENTUM These equations are valid for a closed system, that is, when no external forces act on the system during the collision. When such external forces are either negligibly small or act for too short a time to make a significant change in the momentum, these equations represent a good approximation. The second equation is valid for two-body collisions. 856 Append ix 0: Equations Pi = Pt m1 v1,i + m2v2,i = m1v1,f+ m2v2,f 1 CONSERVATION OF MOMENTUM FOR A PERFECTLY INELASTIC COLLISION This is a simplified version of the conservation of momentum equation valid only for perfectly inelastic collisions between two bodies. mlvl,i + m2v2,i = (ml + m2) Vf CONSERVATION OF KINETIC ENERGY FOR AN ELASTIC COLLISION No collision is perfectly elastic; some kinetic energy is always converted to other forms of energy. But if these losses are minimal, this equation can provide a good approximation. Chapter 7 1 2ml vl,i 2 1 + 2m2v2,i 1 2m 1 vl,f 2 2 1 + 2m2v2,f 2 Circular Motion and Gravitation 2 Vt CENTRIPETAL ACCELERATION ac=~ CENTRIPETAL FORCE Fe= mvt r 2 NEWTON'S LAW OF UNIVERSAL GRAVITATION The constant of universal gravitation (G) equals 6.673x 10- 11 N·m 2!kg2. KEPLER'S LAWS OF PLANETARY MOTION Fg= Gmlm2 r2 First Law: Each planet travels in an elliptical orbit around the sun, and the sun is at one of the focal points. Second Law: An imaginary line drawn from the sun to any planet sweeps out equal areas in equal time intervals. Third Law: The square of a planet's orbital period ( T 2 ) is proportional to the cube of the average distance ( r 3 ) between the planet and the sun, or T 2 oc r 3. PERIOD AND SPEED OF AN OBJECT IN CIRCULAR ORBIT T~21C.jfm 6.673X 10 The constant of universal gravitation (G) equals 11 N•m 2 /kg 2 . v,~fcS TORQUE r= Fdsin () Appendix D: Equations 85 7 MECHANICAL ADVANTAGE This equation disregards friction. EFFICIENCY This equation accounts for friction. Chapter 8 MA =Pout- din F· --d m out eft= Wout Win Fluid Mechanics m MASS DENSITY p =- BUOYANT FORCE FE= Fg (displaced fluid)= mfg The first equation is for an object that is completely or partially submerged. The second equation is for a floating object. FE= Fg(object) = mg PRESSURE F P=- v A PASCAL'S PRINCIPLE Pressure applied to a fluid in a closed container is transmitted equally to every point of the fluid and to the walls of the container. HYDRAULIC LIFT EQUATION F2 =-F1 Al FLUID PRESSURE AS A FUNCTION P=Po+ pgh A2 OF DEPTH CONTINUITY EQUATION A 1v 1 =A2 v2 BERNOULLI'S PRINCIPLE The pressure in a fluid decreases as the fluid's velocity increases. Chapter 9 Heat TEMPERATURE CONVERSIONS 9 Tp= 5Tc+ 32.0 T= Tc+273.15 858 Appendix D: Equations , CONSERVATION OF ENERGY L1PE + L1KE + L1 U = 0 SPECIFIC HEAT CAPACITY Q Cp = mi1T CALORIMETRY Qw=-Qx These equations assume that the energy transferred to the surrounding container is negligible. Cp,wmwi1Tw = -cp,xmxi1Tx LATENT HEAT Q =mL Chapter 10 Thermodynamics WORK DONE BY A GAS This equation is valid only when the pressure is constant. When the work done by the gas (W) is negative, positive work is done on the gas. W= PAd= PL1V THE FIRST LAW OF THERMODYNAMICS i1U= Q - W Q represents the energy added to the system as heat and W represents the work done by the system. CYCLIC PROCESSES L1Unet= 0 and Qnet= Wnet EFFICIENCY OF A HEAT ENGINE eff = Wnet = Qh - Qc = 1 _ Qc Qh Chapter 11 Qh Qh Vibrations and Waves HOOKE'S LAW Felastic= - kx PERIOD OF A SIMPLE PENDULUM IN SIMPLE HARMONIC MOTION This equation is valid only when the amplitude is small (less than about 15°). T=2rcjf IN SIMPLE HARMONIC MOTION T=2rcj¥ SPEED OF A WAVE v=JA- PERIOD OF A MASS-SPRING SYSTEM Appendix D: Equations 859 Chapter 12 Sound p INTENSITY OF A SPHERICAL WAVE J This equation assumes that there is no absorption in the medium. intensity= nr2 HARMONIC SERIES OF A VIBRATING v fn = n- n = 1, 2, 3, ... 2L STRING OR A PIPE OPEN AT BOTH 4 l ENDS HARMONIC SERIES OF A PIPE CLOSED AT ONE END v fn = n L BEATS frequency difference = number of beats per second Chapter 13 n = 1, 3, 5, ... 4 Light and Reflection SPEED OF ELECTROMAGNETIC WAVES c=fA 8 This book uses the value c = 3.00 x 10 m/s for the speed of EM waves in a vacuum or in air. LAW OF REFLECTION ~ angle of incidence ((}) = angle of reflection ((}') MIRROR EQUATION This equation is derived assuming that the rays incident on the mirror are very close to the principal axis of the mirror. MAGNIFICATION OF A CURVED MIRROR Chapter 14 Appendix D: Equations 1 1 h' !i M=-,;=- p Refraction INDEX OF REFRACTION 860 1 -+-=p q f For any material other than a vacuum, the index of refraction varies with the wavelength of light. c n=v SNELL'S LAW ni sin (}i = nr sin Br THIN-LENS EQUATION This equation is derived assuming that the thickness of the lens is much less than the focal length of the lens. 1 1 1 - +-=- p MAGNIFICATION OF A LENS This equation can be used only when the index of refraction of the first medium (nJ is greater than the index of refraction of the second medium (nr)· f q h' h q p M=-=-- (forni>nr) CRITICAL ANGLE This equation can be used only when the index of refraction of the first medium (nJ is greater than the index of refraction of the second medium (nr)· Chapter 15 sin ec=nrn-· (for ni > nr) l Interference and Diffraction CONSTRUCTIVE AND DESTRUCTIVE INTERFERENCE The grating spacing multiplied by the sine of the angle of deviation is the path difference between two waves. To observe interference effects, the sources must be coherent and have identical wavelengths. Constructive Interference: dsin B=±mAm = 0, 1, 2, 3, . .. Destructive Interference: dsin B =±(m+~)A m = 0, 1, 2, 3, ... DIFFRACTION GRATING See the equation above for constructive interference. LIMITING ANGLE OF RESOLUTION e = 1.22-A. This equation gives the angle e in radians and applies only to circular apertures. Chapter 16 D Electric Forces and Fields COULOMB'S LAW This equation assumes either point charges or spherical distributions of charge. ELECTRIC FIELD STRENGTH DUE TO A POINT CHARGE 7qlq2) Felectric= kc ( q E=kc2 r Appendix D: Equations 861 Chapter 17 I Electrical Energy and Current ELECTRICAL POTENTIAL ENERGY The displacement, d, is from the reference point and is parallel to the field. This equation is valid only for a uniform electric field. PEezectric = -qEd POTENTIAL DIFFERENCE The second half of this equation is valid only for a uniform electric field, and !1d is parallel to the field. !J. v = MEelectric = -E!J.d q POTENTIAL DIFFERENCE BETWEEN A POINT AT INFINITY AND A POINT q r !J. V= kc- NEAR A POINT CHARGE CAPACITANCE c = _g_ !J.V CAPACITANCE FOR A PARALLELPLATE CAPACITOR IN A VACUUM The permittivity in a vacuum (co) equals 8.85x 10-12 C 2!(N· m2). A c =cod j ELECTRICAL POTENTIAL ENERGY STORED IN A CHARGED CAPACITOR . - 1 2 1 2C There is a limit to the maximum energy (or charge) that can be stored in a capacitor because electrical breakdown ultimately occurs between the plates of the capacitor for a sufficiently large potential difference. ELECTRIC CURRENT I= !J.Q !J.t RESISTANCE R=!J.V I OHM'S LAW Ohm's law is not universal, but it does apply to many materials over a wide range of applied potential differences. !J.V -=constant ELECTRIC POWER P = I!J. V = I2R = (!J. V) I 2 R 862 Appendix D: Equations Q2 PEelectnc - 2Q!J. V = 2C (!J. V) = - Chapter 18 Circuits and Circuit Elements RESISTORS IN SERIES: EQUIVALENT RESISTANCE AND CURRENT RESISTORS IN PARALLEL: EQUIVALENT RESISTANCE AND CURRENT Chapter 19 Req = R 1 + R2 + R3 ... The current in each resistor is the same and is equal to the total current. 1 1 1 Req R1 R2 1 -=-+-+- R3 ... The sum of the current in each resistor equals the total current. Magnetism <PM= AB cos () MAGNETIC FLUX MAGNITUDE OF A MAGNETIC FIELD The direction ofFmagnetic is always perpendicular to both B and v, and can be found with the righthand rule. FORCE ON A CURRENT-CARRYING CONDUCTOR PERPENDICULAR TO B Fmagnetic qv Fmagnetic= BI f A MAGNETIC FIELD This equation can be used only when the current and the magnetic field are at right angles to each other. Chapter 20 Electromagnetic Induction FARADAY'S LAW OF MAGNETIC INDUCTION emf = _ NL1<PM 11t N is assumed to be a whole number. EMF PRODUCED BY A GENERATOR emf= NAB OJ sin mt N is assumed to be a whole number. maximum emf= NABOJ FARADAY'S LAW FOR MUTUAL INDUCTANCE emf=-M/11 11t Appendix D: Equations 863 RMS CURRENT AND POTENTIAL Imax = 0.707 Imax \12 Irms= DIFFERENCE ~Vrms= TRANSFORMERS N2 ~V2=-~Vl N is assumed to be a whole number. Chapter 21 ~Vmax= \12 0.707 ~V Nl Atomic Physics ENERGY OF A LIGHT QUANTUM E=hf MAXIMUM KINETIC ENERGY KEmax = hf- hft OF A PHOTOELECTRON WAVELENGTH AND FREQUENCY h h p mv li = - = - OF MATTER WAVES 34 Planck's constant (h) equals 6. 63 X 10- J•s. E f=h Chapter 22 Subatomic Physics RELATIONSHIP BETWEEN REST ER = mc 2 ENERGY AND MASS BINDING ENERGY OF A NUCLEUS Ebind MASS DEFECT ~m =~mc 2 = Z( atomic mass of H) + Nmn- atomic mass ACTIVITY (DECAY RATE) .. ~ activity=--= liN ~t HALF-LIFE 864 Appendix D: Equations T112 = 0.693 -li j Appendix J Advanced Topics CONVERSION BETWEEN RADIANS n AND DEGREES 8(rad) =-8(deg) 180° ANGULAR DISPLACEMENT 118= !1s This equation gives 118 in radians. r !18 AVERAGE ANGULAR VELOCITY Wavg=M AVERAGE ANGULAR ACCELERATION aavg=--;;; ROTATIONAL KINEMATICS m1 = mi These equations apply only when the angular acceleration is constant. The symbol m represents instantaneous rather than average angular velocity. !1m + a!J.t !18 = mi!J.t + ~a(!1t) m/ = m? 2 + 2a(!18) 1 !18 = 2( mi + mf)!J.t TANGENTIAL SPEED Vt= rm For this equation to be valid, m must be in rad/s. TANGENTIAL ACCELERATION at= ra For this equation to be valid, a must be in rad!s 2. NEWTON'S SECOND LAW FOR r=Ia ROTATING OBJECTS ANGULAR MOMENTUM L=Im ROTATIONAL KINETIC ENERGY KErot=im IDEAL GAS LAW PV=NkBT 1 2 Boltzmann's constant (kB) equals 1.38 x 10-23 J/K. BERNOULLI'S EQUATION p + ~pv 2 + pgh =constant Appendix D: Equations 865 ~ SI Units Sl Base Units Used in This Book Sl Prefixes Symbol Name Quantity A ampere current a atto 10-18 K kelvin absolute temperature f femto 10-15 kg kilogram mass p pico 10-12 m meter length time n nano 10-9 second ~ micro 10-6 m milli 10-3 c centi 10-2 d deci 10-1 k kilo 10 3 M mega 106 G giga 109 T tera 1012 p peta 1015 E exa 1018 Symbol Name Numerical equivalent j I J Other Commonly Used Units Symbol Name Quantity atm standard atmosphere pressure Btu British thermal unit energy 1.013 250 X 10 5 Pa 1.055 X 10 3 J Cal food calorie energy = 1 kcal = 4.186 x 103 J cal calorie energy 4.186 Ci curie decay rate or activity 3.7 x 10 10 s- 1 op degree Fahrenheit temperature 0.5556°C ft foot length 0.3048 m ft · lb foot-pound work and energy 1.356 J g gram mass 0.001 kg gal gallon volume 3.785 x 10-3 m 3 hp horsepower power 746W in inch length 2.54 x 10-2 m kcal kilocalorie energy 4.186 lb pound force 4.45 N mi mile length 1.609 x 10 3 m rev revolution angular displacement 2nrad 0 degrees angular displacement Appendix E: Sl Units Conversions =( I J X ! 10 3 J 2'360:.) rad = I. 745 x w-2 rad Other Units Acceptable with Sl Symbol Name Quantity Conversion Bq becquerel decay rate or activity c oc coulomb electric charge degree Celsius temperature 1K dB decibel relative intensity (sound) (unitless) eV electron volt energy 1.60 X 10- 19 J F farad capacitance H henry inductance A2•s4 c 1--= 12 V kg•m 2 kg•m J 1--=1A2•s2 A2 h hour time Hz hertz frequency 1 A•s 3.600 X 10 3 S s joule work and energy 2 kg•m 1 - 2--= 1 N•m s kW•h kilowatt-hour energy 3.60 X 10 L liter volume 10-3m3 min minute time 6.0x 10 1 s N newton force kg•m 1-s2 Pa pascal pressure kg N 1 - -2= 1 -2 m•s m -6 J - rad radian angular displacement (unitless) T tesla magnetic field strength u unified mass unit mass (atomic masses) kg N V •s 1 - -2= 1 - - = 1 A•s A•m m2 1.660 538 86 X 10-2? kg v volt electric potential difference w watt power Q ohm resistance 2 kg•m J 1 - -3= 1 A•s C 2 kg•m J 1-= 1s3 s --2 V kg•m 1 -2- = 13 A •s A Appendix E: Sl Units 867 Useful Tables Fundamental Constants Symbol Quantity Established value Value used for calculations in this book c speed of light in a vacuum 299 792 458 m/s 3.00 x 10 8 m/s e elementary charge 1.602 176 53 e1 base of natural logarithms 2.718 2818 28 X 1.60 X 10- 19 C 10- 19 C 2.72 12 2 2 8.85 x 10- 12 C2 /(N •m 2 ) eo (Greek epsilon) permittivity of a vacuum 8.854187 817 x 10- G constant of universal gravitation 6.672 59 X 10-ll N•m 2 /kg 2 6.673 g free-fall acceleration at Earth's surface 9.806 65 m/s 2 9.81 m/s 2 h Planck's constant 6.626 0693 x 10-34 J • s 6.63 x 10-34 J •s kB Boltzmann's constant (RINA) 1.380 6505 10-23 J/K 1.38 X 10-23 J/K kc Coulomb constant 8.987 551 787 x 109 N · m 2;c R molar (universal) gas constant 8.314 472 J/(mol• K) 8.31 J/(mol •K) n (Greek pi) ratio of the circumference to the diameter of a circle 3.141 592 654 calculator value X C /(N •m 2 ) X 10-ll N•m 2 /kg 2 8.99 x 109 N •m 2/C 2 Coefficients of Friction (Approximate Values) l's l'k l's steel on steel 0.74 0.57 waxed wood on wet snow aluminum on steel 0.61 0.47 waxed wood on dry snow rubber on dry concrete 1.0 0.8 metal on metal (lubricated) 0.14 l'k 0.1 0.04 0.15 0.06 rubber on wet concrete - 0.5 ice on ice 0.1 0.03 wood on wood 0.4 0.2 Teflon on Teflon 0.04 0.04 glass on glass 0.9 0.4 synovial joints in humans 0.01 0.003 Useful Astronomical Data Symbol Quantity Value used for calculations in this book IE moment of inertia of Earth 8.03 x 10 37 kg•m 2 ME mass of Earth 5.97 X 1024 kg RE radius of Earth 6.38 x 106 m Average Earth-moon distance 3.84 x 108 m Average Earth-sun distance 1.50 X 10 11 m mass of the moon 7.35 mass of the sun 1.99 X 10 30 kg period of Earth's orbit 3.16 X 10 7 S yr Appendix F: Useful Tables X 10 22 kg The Moment of Inertia for a Few Shapes Shape Moment of inertia thin hoop about symmetry axis MR 2 thin hoop about diameter 2 I.MR 2 point mass about axis MR 2 disk or cylin~er about symmetry ax1s I_MR2 Shape gt~ ~ thin rod about perpendicular axis through center _!_M/'2 I thin rod about perpendicular axis through end I.Mf 2 solid sphere about diameter 5MR thin spherical shell about diameter '?:.MR 2 ~I 2 Densities of Some Common Substances* Substance p (kg/m hydrogen Moment of inertia 12 3 2 2 3 Specific Heat Capacities 3 Substance Cp 0.0899 aluminum 8.99 X 102 helium 0.179 copper 3.87 X 102 steam (100°C) 0.598 glass 8.37 X 10 2 air 1.29 gold 1.29 X 10 2 oxygen 1.43 carbon dioxide 1.98 ice 2.09 X 10 3 ethanol 0.806 X 10 3 iron 4.48 X 10 2 ice 0.917 X 10 3 lead 1.28 X 10 2 fresh water (4°C) 1.00 X 10 3 mercury 1.38 X 10 2 sea water (15°C) 1.025 X 10 3 silver 2.34 X 10 2 glycerine 1.26 X 10 3 steam 2.01 X 10 3 aluminum 2.70 X 10 3 water 4.186 X 10 3 iron 7.86 X 10 3 copper 8.92 X 10 3 silver 10.5 X 10 3 lead 11.3 X 10 3 mercury 13.6 X 10 3 gold 19.3 X 10 3 ) (J/kg • °C) "All densities are measured at 0°C and 1 atm unless otherwise noted. Appendix F: Useful Tables 869 Latent Heats of Fusion and Vaporization at Standard Pressure Substance L1 (J/kg) Melting point (OC) Boiling point (OC) Lv (J/kg) 4 -195.81 2.01 10 5 nitrogen -209.97 2.55 X 10 oxygen -2 18.79 1.38 X 104 -182.97 2.13 X 10 5 ethyl alcohol -114 1.04 X 10 5 78 8.54 X 10 5 water 0.00 3.33 100.00 2.26 X 106 lead 327.3 2.45 X 104 1745 8.70 X 10 5 aluminum 660.4 3.97 X 10 5 2467 1.14 X 10 7 X 10 5 X Speed of Sound in Various Media Medium v(m/s) Gases air (0°C) 331 Medium v(m/s) Liquids at 25°C methyl alcohol Medium 1140 Solids aluminum 5100 air (25°C) 346 sea water 1530 copper 3560 air (100°C) 366 water 1490 iron 5130 lead 1320 helium (0°C) hydrogen (0°C) oxygen (0°C) 972 1290 vulcanized rubber Intensity (W/m 2 ) Decibel level (dB) Examples 1.0 X 10- 12 0 1.0 X 10-ll 10 rustling leaves 1.0 X 10- 10 20 quiet whisper 1.0 X 10- 9 30 whisper 1.0 X 10-S 40 mosquito buzzing 1.0 X 10-7 50 normal conversation 1.0 X 10- 6 60 air conditioning at 6 m 1.0 X 10-5 70 vacuum cleaner 1.0 X 10- 4 80 busy traffic, alarm clock 1.0 X 10-3 90 lawn mower 2 100 subway, power motor 1 110 auto horn at 1 m 1.0 X 10° 120 threshold of pain 1.0 X 10 1 130 thunderclap, machine gun 1.0 X 10 3 150 nearby jet airplane 1.0 X 101.0 X 10- I 54 317 Conversion of Intensity to Decibel Level 870 v(m/s) Appendix F: Useful Tables l threshold of hearing I 1 Indices of Refraction for Various Substances* Solids at 20°C n Liquids at 20°C n cubic zirconia 2.20 benzene 1.501 diamond 2.419 carbon disulfide 1.628 fluorite 1.434 carbon tetrachloride 1.461 fused quartz 1.458 ethyl alcohol 1.361 glass, crown 1.52 glycerine 1.473 glass, flint 1.66 water 1.333 ice (at 0°C) 1.309 polystyrene 1.49 sodium chloride 1.544 zircon 1.923 Gases at ooc, 1 atm n air 1.000 293 carbon dioxide 1.000 450 -- *measured with light of vacuum wavelength= 589 nm Useful Atomic Data Symbol Quantity Established value Value used for calculations in this book me mass of electron 9.109 3826 X 10-3 1 kg 5.485 799 0945 X 10-4 u 0.510 998 918 MeV 9.109 X 10-31 kg 5.49 X 10-4 U 5.110 x 10- 1 MeV mn mass of neutron 1.674 927 28 X 10- 27 kg 1.008 664 915 60 u 939.565 360 MeV 1.675 X 10-27 kg 1.008 665 u 9.396 X 102 MeV mp mass of proton 1.672 621 71 X 10-27 kg 1.007 276 466 88 u 938.272 029 MeV 1.673 X 10-27 kg 1.007 276 u 9.383 X 10 2 MeV Appendix F: Useful Tables 871 Periodic Table of the Elements J 1 H Key: Hydrogen 1.007 94 1s 1 n --- Atomic number Group 1 Group 2 3 4 21 Li I u•;,m 6.941 I c Symbol Carbon ~ Name Be Beryllium 9.012182 2 [He~ 6 ~ r~;i~~~;) Average atomic mass Electron configuration I 11 Na 31 11 Sodium 22.989 770 [Ne)3s 1 I I 41 1 L .;.!!!Jj 19 20 K Ca J Group 3 , ~21Sc :I i Potassium 39.0983 Group 4 Group 5 22 23 I Ti Scandium 44.955 910 IArJ3d14s2 [Ar~ v Group 7 Group 6 .I Cr I Mn Group 8 25 24 i I Fe 26 l Group 9 il ~ 27 Co I 37 Rb 51 Rubidium 85.4678 [Kr)5s 1 38 I Sr ... ~ 55 61 71 ... _. _1 I Cs Ba Cesium 132.905 43 [Xej6sl Barium 137.327 (Xe)6s2 88 Fr Ra Francium (223) [Rn)7s 1 Radium (226) _1 I l""J-- 57 56 87 ,--·- -- j I ,.-,.- -- La Hf Ta Hafnium 178.49 Tantalum 180.9479 (Xe)4f'45d~2 (Xe)4f'4stf~2 - _1 I 73 72 lanthanum 138.9055 (Xe)5d 16s2 li' $,2 ' 104 105 Ac Rf Db Actinium (227} (Rn)6d 17s 2 Rutherfordium (261} [Rn)Sf14&# 27s2 Dubnium (262} [Rn)5f 1 4&d~s2 1 ,....._ ., .. _1 I ,..... _- cj I ~·-··-- _1 I ,.... ,._- _j 74 I I 106 107 Sg Bh Seaborgium (266) (Rn)5f14/s 2 Bohrium (264) (Rn)S f 14Js 2 J 108 j ~ 109 Hs Mt Hassium (277) [Rn)5f 14&f'7s 2 Meitnerium (268) (Rn)Sf14&# 77s 2 * The systematic names and symbols for elements greater than 11 0 will be used until the approval of trivial names by IUPAC. I 58 59 60 61 62 Ce Pr Nd Pm Sm Cerium 140.116 (Xe)4 f'S!t'~2 •. "'. Visit the HRW Web site for updates on the periodic table. "'~ 872 ~~~-"""' ---~~ - ~ -.......- 90 '· \.. ,•_....._..., Appendix G: Periodic Table of the Elements I Th Thoriurr J PraseodymitJn 140.907 65 (Xe)4fl&s2 j Neodymium 144.24 (Xe)4f4&s2 j Promethium (145) . [Xe)4f5fis2 J Samanurr, 150.36 [Xe~f'is2 J J Hydrogen Semiconductors (also known as metalloids) Group 18 2 Metals Alkali metals Alkaline-earth metals Transition metals Other metals He Helium 4.002 602 Group 13 Nonmetals Halogens Noble gases Other nonmetals B Boron ~~~~· Group 14 Group 12 Group 11 28 29 Ni Cu 46 47 I 30 Zn Pd 1 I Carbon 14 Si Aluminum Silicon 26.98~ 5~8 J 28.0~5~3p [NeJ3s 3p [NeJ3s . Ga i I ~ Auorine ' 50 51 Sn Sb Tin 118.710 (Kr)4tf105sl5p2 Antimony 121.760 [KrJ4d'ossl5pJ I I 33 As 49 18 34 Se , Ne Neon 32 ~~ 17 18 Cl Ar Chlorine 35.4535 Argon 39.948, (Ne)3sl]p I uz 35 Br f 53 J I I I lNells~ 36 Kr 54 Xe Xenon 131.293 (Krl4d"Ss~ I 85 At W" II 86 Rn Gold 966 55 ~''6s' [XeJ4f'~' Ds I 32 Ge Au Platinum 195.078 ji l l l6 J 80 Pt Darmstadtium (281) 1Rnl5f'4&1'7s' 15 I In (Kr)4d~ 110 Oxygen Group 17 I P . S Phosphorus · Sulfur J . 30.973..761__ , ' '·'' 3~ .• ':· .;.: •!~~ 48 Palladium 106.42 78 l0 N Nitrogen Cd I Group 16 I i;l +,i~J.tflOI",:':1 "i l'~~-i ;·-~,ilfm.~ ~,!>s AI 31 t C 1 I 13 Group 10 Group 15 j 111 Uuu* Unununium (272) (Rn)5f14&# 107s 1 A team at Lawrence Berkeley National Laboratories reported the discovery of elements 116 and 118 in June 1999. The same team retracted the discovery in July 2001. The discovery of elements 113, 114, and 115 has been reported but not confirmed. 63 i Eu ' 95 Am ~ {243) (Rn)5f7s2 64 65 Gd Tb Gadolinium 157.25 [Xe)4f5d'6sz Terbium 158.925 34 txeJ41'&s2 96 l; i 97 Cm Bk 1Rn)Sf76d17s2 (Rn)5f'7s 2 ~ ~ ~ {247) {247) I 1 j 66 Dy 67 I Ho I 68 69 70 Er Tm Yb Erbium 167.259 [Xe)4fl'fs2 Thulium 168.934 21 [Xel4f'36f2 Ytterbium 173.04 [Xe)41'46f2 101 102 Dysprosium 162.500 (Xe)4110fisl Holmium 164.930 32 (Xe)41n6Sz 98 99 Cf Es Fm Md No . (Rn)Sf...,s2 {Rn)Sf117s1 (Rn)51'~s2 [RnJ5f'7s 2 (Rn)5f'fJs2 I ~ j ~ j {251) {252) 100 I ~ j ~ j ~ {257) {258) {259) I~1 Lu Lutetium 174.967 [Xe)41'~'6sz l~ I 103 Lr {262) (Rn)5f1"6d17s 2 The atomic masses listed in this table reflect the precision of current measurements. (Values listed in parentheses are those of the element's most stable or most common isotope.) Appendix G: Periodic Table of the Elements 873 Abbreviated Table of Isotopes and Atomic Masses Z 0 2 Element Symbol (Neutron) n Hydrogen Deuterium Tritium H D T Helium He Average atomic mass (u) Mass number ( * indicates Atomic mass (u) Percent abundance radioactive) A 10.4 m 1* 1.008 665 1.0079 1 2 3* 1.007 825 2.014 102 3.016 049 99.985 0.015 4.002 60 3 4 6* 3.016 029 4.002 602 6.018 886 0.000 14 99.999 86 7.5 92.5 3 Lithium Li 6.941 6 7 6.015 121 7.016 003 4 Beryllium Be 9.0122 7* 8* 9 10* 7.016 928 8.005 305 9.012 174 10.013 584 12.33 y 0.81 s 53.3 d 6.7 X 10-l ? S 100 5 Boron B 10.81 10 11 10.012 936 11.009 305 6 Carbon c 12.011 10* 11 * 12 13 14* 10.016 854 11.011433 12.000 000 13.003 355 14.003 242 13* 14 15 16* 13.005 738 14.003 074 15.000 108 16.006 100 99.63 0.37 15* 16 17 18 19* 15.003 065 15.994 915 16.999 132 17.999 160 19.003 577 99.761 0.039 0.200 18* 19 20* 18.000 937 18.998 404 19.999 982 100 19* 20 21 22 19.001 880 19.992 435 20.993 841 21.991 383 22* 23 24* 21.994 434 22.989 767 23.990 961 23* 24 25 26 22.994 124 23.985 042 24.985 838 25.982 594 78.99 10.00 11.01 26* 27 25.986 892 26.981 534 100 7 8 9 Nitrogen Oxygen Fluorine 10 Neon 11 Sodium 12 Magnesium 13 Aluminum N 0 F Ne Na Mg Al 14.0067 15.9994 18.998 40 20.180 22.989 87 24.305 26.981 54 Appendix H: Abbreviated Table of Isotopes and Atomic Masses Half-life (if radioactive) T 112 1.5 X 106 y 19.9 80.1 19.3 s 20.4m ~ ' 98.9 1.10 5715 y 996m 7.13 s 122 s 26.9 s 109.8 m 1l.Os 17.2 s 90.48 0.27 9.25 2.61 y 100 14.96 h 11.3s 7.4 X 10 5 y ~ Z Element Symbol Average atomic mass (u) Mass number ( * indicates Atomic mass (u) Percent abundance radioactive) A T112 14 Silicon Si 28.086 28 29 30 27.976 927 28.976 495 29.973 770 92.23 4.67 3.10 15 Phosphorus p 30.973 76 30* 31 32* 29.978 307 30.973 762 31.973 907 100 32 33 34 35* 31.972 071 32.971 459 33.967 867 34.969 033 95.02 0.75 4.21 75.77 16 Sulfur s 32.066 2.50m 14.263 d 87.5 d 17 Chlorine Cl 35.453 35 36* 37 34.968 853 35.968 307 36.975 893 18 Argon Ar 39.948 36 37* 38 39* 40 35.967 547 36.966 776 37.962 732 38.964 314 39.962 384 0.337 35.04 d 0.063 269 y 99.600 K 39.0983 39 40* 41 38.963 708 39.964 000 40.961 827 93.2581 0.0117 6.7302 20 Calcium Ca 40.08 40 41 * 42 43 44 39.962 40.962 41.958 42.958 43.955 96.941 41* 45 40.969 250 44.955 911 100 44* 47 48 43.959 691 46.951 765 47.947 947 7.3 73.8 22 Titanium Sc Ti 44.9559 47.88 591 279 618 767 481 60y 50.9415 50* 51 49.947 161 50.943 962 0.25 99.75 24 Chromium Cr 51.996 48* 52 53 47.954 033 51.940 511 52.940 652 83.79 9.50 54* 55 53.940 361 54.938 048 100 54 55* 56 53.939 613 54.938 297 55.934 940 5.9 26 Iron Fe 54.938 05 55.847 l.Oxl0 5 y 0.596 s v Mn 1.28 X 109 y 0.647 0.135 2.086 23 Vanadium 25 Manganese 3.0xl0 5 y 24.23 19 Potassium 21 Scandium Half-life (if radioactive) 1.5 X 10 17 y 21.6 h 312.1 d 2.7y 91.72 27 Cobalt Co 58.933 20 59 60* 58.933 198 59.933 820 100 28 Nickel Ni 58.793 58 59* 60 57.935 345 58.934 350 59.930 789 68.077 5.27y 7.5xl0 4 y 26.223 29 Copper Cu 63.54 63 65 62.929 599 64.927 791 69.17 30.83 30 Zinc Zn 65.39 64 66 67 68 63.929 144 65.926 035 66.927 129 67.924 845 48.6 27.9 4.1 18.8 Appendix H: Abbreviated Table of Isotopes and Atomic Masses 875 Z Element Symbol Average atomic mass (u) Mass number ( * indicates radioactive) A Percent abundance 31 Gallium Ga 69.723 69 71 68.925 580 70.924 703 60.108 39.892 32 Germanium Ge 72.61 70 72 73 74 76 69.924 250 71.922 079 72.923 462 73.921 177 75.921402 21.23 27.66 7.73 35.94 7.44 33 Arsenic As 74.9216 75 74.921 594 100 34 Selenium Se 78.96 76 77 78 80 82* 75.919 212 76.919 913 77.917 397 79.916 519 81.916 697 9.36 7.63 23.78 49.61 8.73 50.69 49.31 35 Bromine Br 79.904 79 81 78.918 336 80.916 287 36 Krypton Kr 83.80 81* 82 83 84 85* 86 80.916 589 81.913 481 82.914 136 83.911 508 84.912 531 85.910 615 85 87* 84.911 793 86.909 186 72.17 27.83 86 87 88 9.86 7.00 82.58 90* 85.909 266 86.908 883 87.905 618 89.907 737 37 Rubidium 38 Strontium Rb Sr 85.468 87.62 89 88.905 847 100 91.224 90 91 92 93* 94 89.904 702 90.905 643 91.905 038 92.906 473 93.906 314 51.45 11.22 17.15 93 94* 92.906 376 93.907 280 100 92 93* 94 95 96 97 98 100 91.906 807 92.906 811 93.905 085 94.905 841 95.904 678 96.906 020 97.905 407 99.907 476 14.84 97* 96.906 363 97.907 215 98.906 254 Mo 95.94 Tc 98* 99* I 4.75 X 10 10 1.5 X 10 6 y 17.38 2 X 104 y y ~ f ~ 3.5 X 10 3 y 9.25 15.92 16.68 9.55 24.13 9.63 2.6 X 106 y 4.2 X 106 y 2.1 X 10 5 y 44 Ruthenium Ru 101.07 99 100 101 102 104 98.905 939 99.904 219 100.905 558 101.904 348 103.905 558 12.7 12.6 17.1 31.6 18.6 45 Rhodium Rh 102.9055 103 102.905 502 100 Appendix H: Abbreviated Table of Isotopes and Atom ic M asses 10 5 y 29.1 y 88.9058 42 Molybdenum X 10.76 y Zr 92.9064 1.4 X 1020 y 17.3 40 Zirconium Nb T 1;2 2.1 y 41 Niobium Half-life (if radioactive) 11.6 11.4 57.0 39 Yttrium 43 Technetium 876 Atomic mass (u) 4 ~ Z Element Symbol Average atomic mass (u) Mass number ( * indicates radioactive) A Atomic mass (u) Percent abundance 46 Palladi urn Pd 106.42 104 105 106 108 110 103.904 033 104.905 082 105.903 481 107.903 898 109.905 158 11.14 22.33 27.33 26.46 11.72 47 Silver Ag 107.868 107 109 106.905 091 108.904 754 51.84 48.16 48 Cadmium Cd 112.41 109* 110 111 112 113* 114 108.904 984 109.903 004 110.904 182 111.902 760 112.904 401 113.903 359 12.49 12.80 24.13 12.22 28.73 113 115* 112.904 060 114.903 876 4.3 95.7 116 117 118 119 120 121* 115.901 743 116.902 953 117.901 605 118.903 308 119.902 197 120.904 237 14.53 7.58 24.22 8.58 32.59 49 Indium 50 Tin In Sn 114.82 118.71 121.76 121 123 120.903 820 122.904 215 57.36 42.64 52 Tellurium Te 127.60 125 126 128* 130* 124.904 429 125.903 309 127.904 468 129.906 228 7.12 18.93 31.79 33.87 126.9045 127 129* 126.904 474 128.904 984 100 131.29 129 131 132 134 136* 128.904 779 130.905 069 131.904 141 133.905 394 135.907 214 26.4 21.2 26.9 10.4 8.9 100 54 Xenon Xe 9.3 X 10 15 y 4.4 X 10 14 y 55 y Sb I T 1; 2 462 d 51 Antimony 53 Iodine Half-life (if radioactive) 55 Cesium Cs 132.9054 133 135* 137* 132.905 436 134.905 891 136.907 078 56 Barium Ba 137.33 133* 137 138 132.905 990 136.905 816 137.905 236 11.23 71.70 24 > 8 X 10 Y.: < 1.25 X 10 21 y 1.6Xl0 7 y > 2.36 X 10 21 y 2 X 10 6 y 30 y 10.5 y 57 Lanthanum La 138.905 138* 139 137.907 105 138.906 346 0.0902 99.9098 58 Cerium Ce 140.12 138 140 142* 137.905 986 139.905 434 141.909 241 0.25 88.43 11.13 59 Praseodymium Pr 140.9076 141 140.907 647 100 60 Neodymium Nd 144.24 142 143 144* 145 146 141.907 718 142.909 809 143.910 082 144.912 568 145.913 113 27.13 12.18 23.80 8.30 17.19 1.05 X 10 11 y >5Xl0 16 y 2.3 X 10 15 y Appendix H: Abbreviated Table of Isotopes and Atomic Masses 877 Z 878 Element Symbol 61 Promethium Pm 62 Samarium Sm 63 Europium Eu Average atomic mass (u) Mass number ( * indicates radioactive) A Atomic mass (u) Percent abundance 145* 146* 144.912 745 145.914 968 150.36 147* 148* 149* 150 152 154 146.914 894 147.914 819 148.917 180 149.917 273 151.919 728 153.922 206 15.0 11.3 13.8 7.4 26.7 22.7 151.96 151 152* 153 150.919 846 151.921 740 152.921 226 47.8 14.80 20.47 15.65 24.84 21.86 64 Gadolinium Gd 157.25 155 156 157 158 160 154.922 618 155.922 119 156.923 957 157.924 099 159.927 050 T112 17.7y 5.5 y 1.06 X lOlly 7 X 10 15 Y >2x10 15 y 13.5 y 52.2 65 Terbium Tb 158.9253 159 158.925 345 100 66 Dysprosium Dy 162.5 161 162 163 164 160.926 930 161.926 796 162.928 729 163.929 172 18.9 25.5 24.9 28.2 67 Holmium Ho 164.9303 165 164.930 316 100 68 Erbium Er 167.26 166 167 168 170 165.930 292 166.932 047 167.932 369 169.935 462 33.6 22.95 27.8 14.9 69 Thulium Tm 168.9342 169 171* 168.934 213 170.936 428 100 1.92 y 70 Ytterbium Yb 173.04 171 172 173 174 176 170.936 324 171.936 379 172.938 209 173.938 861 175.942 564 14.3 21.9 16.12 31.8 12.7 71 Lutetium Lu 174.967 175 176* 174.940 772 175.942 679 97.41 2.59 72 Hafnium Hf 178.49 177 178 179 180 176.943 218 177.943 697 178.945 813 179.946 547 18.606 27.297 13.029 35.100 73 Tantalum Ta 180.9479 181 180.947 993 99.988 74 Tungsten w 183.85 182 183 184 186 181.948 202 182.950 221 183.950 929 185.954 358 26.3 14.28 30.7 28.6 75 Rhenium Re 186.207 185 187* 184.952 951 186.955 746 37.40 62.60 76 Osmium Os 190.2 188 189 190 192 187.955832 188.958 139 189.958 439 191.961 468 13.3 16.1 26.4 41.0 77 Iridium Ir 192.2 191 193 190.960 585 192.962 916 37.3 62.7 Appendix H: Abbreviated Table of Isotopes and Atomic Masses Half-life (if radioactive) 3.78 X 10 10 y 4.4 X 10 10 y Z Element 78 Platinum Symbol Pt Average atomic mass (u) Mass number ( * indicates radioactive) A Atomic mass (u) Percent abundance 32.9 33.8 25.3 195.08 194 195 196 193.962 655 194.964 765 195.964 926 79 Gold Au 196.9665 197 196.966 543 100 80 Mercury Hg 200.59 198 199 200 201 202 197.966 743 198.968 253 199.968 299 200.970 276 201.970 617 9.97 16.87 23.10 13.10 29.86 81 Thallium Tl 204.383 203 204* 205 208* 202.972 320 203.073 839 204.974 400 207.981 992 29.524 Half-life (if radioactive) T 1; 2 3.78 y 70.476 3.053 m 82 Lead Pb 207.2 206 207 208 212* 205.974 440 206.974 871 207.976 627 211.991 872 24.1 22.1 52.4 83 Bismuth Bi 208.9803 209 212* 208.980 374 211.991 259 100 84 Polonium Po 209* 212* 216* 208.982 405 211.988 842 216.001 889 102 y 0.30 flS 0.145 s 85 Astatine At 218* 219* 218.008 685 219.01l 294 1.6s 0.9m 86 Radon Rn 220* 222* 220.011 369 222.017 571 55.6 s 3.823 d 10.64 h 60.6m 87 Francium Fr 223* 223.019 733 22m 88 Radium Ra 224* 226* 228* 224.020 187 226.025 402 228.031 064 3.66 d 1.6X 10 3 y 5.75y 89 Actinium Ac 227* 228* 227.027 701 228.028 716 18.72 y 1.913 y 90 Thorium Th 232* 234* 232.038 051 234.043 593 91 Protactinium Pa 231* 234* 231.035 880 234.043 300 92 Uranium u 234* 235* 238* 234.040 946 235.043 924 238.050 784 93 Neptunium Np 236* 237* 236.046 560 237.048 168 1.15 X 10 5 y 2.14 X 10 6 y 94 Plutonium Pu 239* 244* 239.052 157 244.064 200 2.412 X 10 5 y 8.1 X 10 7 y 100 1.40 X 10 10 y 24.1 d 32.760 y 6.7h 0.0055 0.720 99.2745 2.46 X 10 5 y 7.04 X 10 8 y 4.47 X 10 9 y Appendix H: Abbreviated Table of Isotopes and Atomic Masses 879 Additional Problems Chapter 1 The S cience of Physics 1. Mt. Waialeale in Hawaii gets 1.168 x 10 3 em of rainfall per year. Express this quantity in meters. 2. An acre is equal to about 4.0469 x 10 3 m 2. Express this area in square kilometers. 4 3 3. A group drinks about 6.4 x 10 cm of water per person per year. Express this in cubic meters. 16. A small rocket launched from rest travels 12.4 m upward in 2.0 s. What is the rocket's net acceleration? 17. A jet slows uniformly from 153 km/h to 0 km/h over 42.0 m. What is the jet's acceleration? 18. A softball thrown straight up at 17.5 m/s is caught 3.60 slater. How high does the ball rise? 4. The largest stone jar on the Plain of Jars in Laos has a mass of 6.0 x 10 3 kg. Express this mass in milligrams. 19. A child, starting from rest, sleds down a snow- 5. Half of a sample of the radioactive isotope beryllium-8 decays in 6.7 x 10-l? s. Express this time in picoseconds. 20. A sky diver opens her parachute and drifts down covered slope in 5.50 s. If the child's final speed is 14.0 m/s, what the length of the slope? for 34.0 s with a constant velocity of 6.50 m/s. What is the sky diver's displacement? 21. In a race, a tortoise runs at 10.0 cm/s and a hare Chapter 2 Motion in One Dimension 6. The fastest airplane is the Lockheed SR-71. If an SR-71 flies 15.0 km west in 15.3 s, what is its average velocity in kilometers per hour? 7. Except for a 22.0 min rest stop, Emily drives with a constant velocity of 89.5 km/h, north. How long does the trip take if Emilis average velocity is 77.8 km/h, north? 8. A spaceship accelerates uniformly for 1220 km. How much time is required for the spaceship to increase its speed from 11.1 km/s to 11.7 km/s? 9. A polar bear initially running at 4.0 m/s accelerates uniformly for 18 s. If the bear travels 135m in this time, what is its maximum speed? 10. A walrus accelerates from 7.0 km/h to 34.5 km/h over a distance of 95 m. What is the magnitude of the walrus's acceleration? 11. A snail can move about 4.0 min 5.0 min. What is the average speed of the snail? 12. A crate is accelerated at 0.035 m!s 2 for 28.0 s along a conveyor belt. If the crate's initial speed is 0.76 m/s, what is its final speed? 13. A person throws a ball vertically and catches it after 5.10 s. What is the balrs initial velocity? 14. A bicyclist accelerates -0.870 m!s 2 during a 3.80 s interval. What is the change in the velocity of the bicyclist and bicycle? 15. A hockey puck slides 55.0 min 1.25 s with a uniform acceleration. If the puck's final speed is 43.2 m/s, what was its initial speed? Appendix 1: Additional Problems runs at 200.0 cm/s. Both start at the same time, but the hare stops to rest for 2.00 min. The tortoise wins by 20.0 em. At what time does the tortoise cross the finish line? 22. What is the length of the race in problem 21? 23. The cable pulling an elevator upward at 12.5 m/s breaks. How long does it take for the elevator to come to rest? 24. A disk is uniformly accelerated from rest for 0.910 s over 7.19 km. What is its final speed? 25. A tiger accelerates 3.0 m!s 2 for 4.1 s to reach a final speed of 55.0 km/h. What was its initial speed in kilometers per hour? 26. A shark accelerates uniformly from 2.8 km/h to 32.0 km/h in 1.5 s. How large is its acceleration? 27. The 1903 Wright flyer was accelerated at 4.88 m/s 2 along a track that was 18.3 m long. How long did it take to accelerate the flyer from rest? 28. A drag racer starts at rest and reaches a speed of 386.0 km/h with an average acceleration of 16.5 m /s2• How long does this acceleration take? 29. A hummingbird accelerates at -9.20 m/s 2 such that its velocity changes from +50.0 km/h to 0 km/h. What is its displacement? 30. A train backs up from an initial velocity of -4.0 m /s and an average acceleration of 2 -0.27 m/s • What is the train's velocity after 17 s? 31. A cross-country skier skiing with an initial velocity of +4.42 m/s slows uniformly at -0.75 m/s 2. How long does it take the skier to stop? 32. What is the skier's displacement in problem 31? 47. Find the displacement direction in problem 46. 33. A speedboat uniformly increases its speed from 48. A train travels 478 km southwest along a straight 25 m/s west to 35 m/s west. How long does it take the boat to travel 250 m west? 34. A ship accelerates at -7.6 x 10-2 m!s 2 so that it comes to rest at the dock 255 m away in 82.0 s. What is the ship's initial speed? 35. A student skates downhill with an average acceleration of 0.85 m!s 2 . Her initial speed is 4.5 m/s, and her final speed is 10.8 m/s. How long does she take to skate down the hill? 36. A wrench dropped from a tall building is caught in a safety net when the wrench has a velocity of -49.5 m/s. How far did it fall? 37. A rocket sled comes to a complete stop from a speed of 320 km/h in 0.18 s. What is the sled's average acceleration? 38. A racehorse uniformly accelerates 7.56 m!s 2 , reaching its final speed after running 19.0 m. If the horse starts at rest, what is its final speed? 39. An arrow is shot upward at a speed of 85.1 m/s. How long does the archer have to move from the launching spot before the arrow returns to Earth? 40. A handball strikes a wall with a forward speed of 13.7 m/s and bounces back with a speed of 11.5 m/s. If the ball changes velocity in 0.021 s, what is the handball's average acceleration? stretch. If the train is displaced south by 42 km, what is the train's displacement to the west? 49. Find the displacement direction in problem 48. 50. A ship's total displacement is 7400 km at 26° south of west. If the ship sails 3200 km south, what is the western component of its journey? 51. The distance from an observer on a plain to the top of a nearby mountain is 5.3 km at 8.4° above the horizontal. How tall is the mountain? 52. A skyrocket travels 113m at an angle of 82.4° with respect to the ground and toward the south. What is the rocket's horizontal displacement? 53. A hot-air balloon descends with a velocity of 55 km/h at an angle of 37° below the horizontal. What is the vertical velocity of the balloon? 54. A stretch of road extends 55 km at 37° north of east, then continues for 66 km due east. What is a driver's resultant displacement along this road? 55. A driver travels 4.1 km west, 17.3 km north, and finally 1.2 km at an angle of 24.6° west of north. What is the driver's displacement? 56. A tornado picks up a car and hurls it horizontally 125m with a speed of 90.0 m/s. How long does it take the car to reach the ground? 41. A ball accelerates at 6.1 m/s 2 from 1.8 m/s to 9.4 m!s. How far does the ball travel? 57. A squirrel knocks a nut horizontally at a speed of 42. A small sandbag is dropped from rest from a 58. A flare is fired at an angle of 35° to the ground at hovering hot-air balloon. After 2.0 s, what is the sandbag's displacement below the balloon? 43. A hippopotamus accelerates at 0.678 m!s 2 until it reaches a speed of 8.33 m/s. If the hippopotamus runs 46.3 m, what was its initial speed? 44. A ball is hit upward with a speed of 7.5 m/s. How long does the ball take to reach maximum height? 45. A surface probe on the planet Mercury falls 17.6 m downward from a ledge. If free-fall acceleration near Mercury is -3.70 m/s2, what is the probe's velocity when it reaches the ground? Chapter 3 Two-Dimensional M otio n a nd Vectors 46. A plane moves 599 m northeast along a runway. If the northern component of this displacement is 89 m, how large is the eastern component? 10.0 cm/s. If the nut lands at a horizontal distance of 18.6 em, how high up is the squirrel? an initial speed of 250 m/s. How long does it take for the flare to reach its maximum altitude? 59. A football kicked with an initial speed of 23.1 m/s reaches a maximum height of 16.9 m. At what angle was the ball kicked? 60. A bird flies north at 58.0 km/h relative to the wind. The wind is blowing at 55.0 km/h south relative to Earth. How long will it take the bird to fly 1.4 km relative to Earth? 61. A race car moving at 286 km/h is 0.750 km behind a car moving at 252 km/h. How long will it take the faster car to catch up to the slower car? 62. A helicopter flies 165m horizontally and then moves downward to land 45 m below. What is the helicopter's resultant displacement? 63. A toy parachute floats 13.0 m downward. If the parachute travels 9.0 m horizontally, what is the resultant displacement? Appendix 1: Additional Problems 881 64. A billiard ball travels 2.7 mat an angle of 13° with respect to the long side of the table. What are the components of the ball's displacement? 65. A golf ball has a velocity of 1.20 m/s at 14.0° east of north. What are the velocity components? 66. A tiger leaps with an initial velocity of 55.0 km/h at an angle of 13.0° with respect to the horizontal. What are the components of the tiger's velocity? 67. A tramway extends 3.88 km up a mountain from a station 0.8 km above sea level. If the horizontal displacement is 3.45 km, how far above sea level is the mountain peak? 68. A bullet travels 850 m, ricochets, and moves another 640 mat an angle of 36° from its previous forward motion. What is the bullet's resultant displacement? 79. What is the range of an arrow shot horizontally at 85.3 m/s from 1.50 m above the ground? 80. A drop of water in a fountain takes 0.50 s to travel 1.5 m horizontally. The water is projected upward at an angle of 33°. What is the drop's initial speed? 81. A golf ball is hit up a 41.0° ramp to travel4.46 m horizontally and 0.35 m below the edge of the ramp. What is the ball's initial speed? 82. A flare is fired with a velocity of 87 km/h west from a car traveling 145 km/h north. With respect to Earth, what is the flare's resultant displacement 0.45 s after being launched? 83. A sailboat travels south at 12.0 km/h with respect to the water against a current 15.0° south of east at 4.0 km/h. What is the boat's velocity? 69. A bird flies 46 km at 15° south of east, then 22 km at 13° east of south, and finally 14 km at 14° west of south. What is the bird's displacement? 70. A ball is kicked with a horizontal speed of 9.37 m/s off the top of a mountain. The ball moves 85.0 m horizontally before hitting the ground. How tall is the mountain? 71. A ball is kicked with a horizontal speed of 1.50 m/s from a height of 2.50 x 102 m. What is its horizontal displacement when it hits the ground? 72. What is the velocity of the ball in problem 71 when it reaches the ground? 73. A shingle slides off a roof at a speed of 2.0 m!s and an angle of 30.0° below the horizontal. How long does it take the shingle to fall45 m? 74. A ball is thrown with an initial speed of 10.0 m/s and an angle of 37.0° above the horizontal. What are the vertical and horizontal components of the ball's displacement after 2.5 s? 75. A rocket moves north at 55.0 km/h with respect to the air. It encounters a wind from 17.0° north of west at 40.0 km/h with respect to Earth. What is the rocket's velocity with respect to Earth? 76. How far to the north and west does the rocket in problem 75 travel after 15.0 min? 77. A cable car travels 2.00 x 10 2 m on level ground, then 3.00 x 10 2 m at an incline of 3.0°, and then 2 2.00 x 10 m at an incline of 8.8°. What is the final displacement of the cable car? 78. A hurricane moves 790 km at 18° north of west, then due west for 150 km, then north for 470 km, and finally 15° east of north for 240 km. What is the hurricane's resultant displacement? 882 Appendix 1: Additional Problems Chapter 4 Forces and the Laws of Motion 84. A boat exerts a 9.5 x 104 N force 15.0° north of west on a barge. Another exerts a 7.5 x 104 N force north. What direction is the barge moved? 85. A shopper exerts a force on a cart of 76 Nat an angle of 40.0° below the horizontal. How much force pushes the cart in the forward direction? 86. How much force pushes the cart in problem 85 against the floor? 87. What are the magnitudes of the largest and smallest net forces that can be produced by combining a force of 6.0 N and a force of 8.0 N? 88. A buoyant force of 790 N lifts a 214 kg sinking boat. What is the boat's net acceleration? 89. A house is lifted by a net force of 2850 N and moves from rest to an upward speed of 15 cm/s in 5.0 s. What is the mass of the house? 90. An 8.0 kg bag is lifted 20.0 em in 0.50 s. If it is initially at rest, what is the net force on the bag? 91. A 90.0 kg skier glides at constant speed down a 17.0° slope. Find the frictional force on the skier. 92. A snowboarder slides down a 5.0° slope at a constant speed. What is the coefficient of kinetic friction between the snow and the board? 93. A 2.00 kg block is in equilibrium on a 36.0° incline. What is the normal force on the block? 94. A 1.8 x 10 3 kg car is parked on a hill on a 15.0° incline. A 1.25 x 104 N frictional force holds the car in place. Find the coefficient of static friction. 95. The coefficient of kinetic friction between a jar 109. A traffic signal is supported by two cables, each slid across a table and the table is 0.20. What is the magnitude of the jar's acceleration? of which makes an angle of 40.0° with the vertical. If each cable can exert a maximum force 2 of 7.50 x 10 N, what is the largest weight they can support? 96. A force of 5.0 N to the left causes a 1.35 kg book 2 to have a net acceleration of 0.76 m!s to the left. What is the frictional force on the book? 97. A child pulls a toy by exerting a force of 15.0 N at an angle of 55.0° with respect to the floor. What are the components of the force? 98. A car is pulled by three forces: 600.0 N to the north, 750.0 N to the east, and 675 N at 30.0° south of east. What direction does the car move? 99. Suppose a catcher exerts a force of -65.0 N to stop a baseball with a mass of 0.145 kg. What is the ball's net acceleration as it is being caught? 100. A 2.0 kg fish pulled upward by a fisherman rises 1.9 min 2.4 s, starting from rest. What is the net force on the fish during this interval? 101. An 18.0 N force pulls a cart against a 15.0 N frictional force. The speed of the cart increases 1.0 m/s every 5.0 s. What is the cart's mass? 110. A certain cable of an elevator is designed to exert a force of 4.5 x 104 N. If the maximum acceleration that a loaded car can withstand is 3.5 m/s 2, what is the combined mass of the car and its contents? 11 I. A frictional force of 2400 N keeps a crate of machine parts from sliding down a ramp with an incline of 30.0°. The coefficient of static friction between the box and the ramp is 0.20. What is the normal force of the ramp on the box? 112. Find the mass of the crate in problem 111. 113. A 5.1 x 102 kg bundle of bricks is pulled up a ramp at an incline of 14° to a construction site. The force needed to move the bricks up the ramp is 4.1 x 10 3 N. What is the coefficient of static friction between the bricks and the ramp? 102. A 47 kg sled carries a 33 kg load. The coefficient of kinetic friction between the sled and snow is 0.075. What is the magnitude of the frictional force on the sled as it moves up a hill with a 15° incline? 103. Ice blocks slide with an acceleration of 1.22 m/s 2 down a chute at an angle of 12.0° below the horizontal. What is the coefficient of kinetic friction between the ice and chute? 104. A 1760 N force pulls a 266 kg load up a 17° incline. What is the coefficient of static friction between the load and the incline? 105. A 4.26 x 10 7 N force pulls a ship at a constant speed along a dry dock. The coefficient of kinetic friction between the ship and dry dock is 0.25. Find the normal force exerted on the ship. 106. If the incline of the dry dock in problem 105 is 10.0°, what is the ship's mass? 107. A 65.0 kg skier is pulled up an 18.0° slope by 2 a force of 2.50 x 10 N. If the net acceleration uphill is 0.44 m/s 2, what is the frictional force between the skis and the snow? 108. Four forces are acting on a hot-air balloon: F1 = 2280.0 N up, F2 = 2250.0 N down, F3 = 85.0 N west, and F4 = 12.0 N east. What is the direction of the net external force on the balloon? Chapter 5 Work and Energy 114. If 2.13 x 106 J of work must be done on a 2 roller-coaster car to move it 3.00 x 10 m, how large is the net force acting on the car? 115. A force of 715 N is applied to a roller-coaster 4 car to push it horizontally. If 2.72 x 10 J of work is done on the car, how far has it been pushed? 116. In 0.181 s, through a distance of 8.05 m, a test pilot's speed decreases from 88.9 m/s to 0 m/s. If the pilot's mass is 70.0 kg, how much work is done against his body? 117. What is the kinetic energy of a disk with a mass of 0.20 g and a speed of 15.8 km/s? 118. A 9.00 x 10 2 kg walrus is swimming at a speed of 35.0 km/h. What is its kinetic energy? 119. A golf ball with a mass of 47.0 g has a kinetic energy of 1433 J. What is the ball's speed? 120. A turtle, swimming at 9.78 m/s, has a kinetic energy of 6.08 x 104 J. What is the turtle's mass? 121. A 50.0 kg parachutist is falling at a speed of 47.00 m/s when her parachute opens. Her speed upon landing is 5.00 m/s. How much work is done by the air to reduce the parachutist's speed? 122. An 1100 kg car accelerates from 48.0 km/h to 59.0 km/h over 100.0 m. What was the magnitude of the net force acting on it? Appendix 1: Additional Problems 883 123. What is the gravitational potential energy of a 64.0 kg person at 5334 m above sea level? 124. A spring has a force constant of 550 N/m. What is the elastic potential energy stored in the spring when the spring is compressed 1.2 em? 125. What is the kinetic energy of a 0.500 g raindrop that falls 0.250 km? Ignore air resistance. 126. A 50.0 g projectile is fired upward at 3.00 x 10 2 m/sand lands at 89.0 m/s. How much mechanical energy is lost to air resistance? 127. How long does it take for 4.5 x 106 J of work to be done by a 380.3 kW engine? 128. A ship's engine has a power output of 13.0 MW. How much work can it do in 15.0 min? 129. A catcher picks up a baseball from the ground with a net upward force of 7.25 X 1o- 2 N so that 4.35 x 10-2 J of net work is done. How far is the ball lifted? 130. A crane does 1.31 x 10 3 Jof net work when lifting cement 76.2 m. How large is the net force doing this work? 131. A girl exerts a force of 35.0 Nat an angle of 20.0° to the horizontal to move a wagon 15.0 m along a level path. What is the net work done on it if a frictional force of 24.0 N is present? 132. The Queen Mary had a mass of 7.5 x 10 7 kg and a top cruising speed of 57 km/h. What was the kinetic energy of the ship at that speed? 133. How fast is a 55.0 kg sky diver falling when her kinetic energy is 7.81 x 104 J? 134. A hockey puck with an initial speed of 8.0 m/s coasts 45 m to a stop. If the force of friction on the puck is 0.12 N, what is the puck's mass? 139. A ball falls 3.0 m down a vertical pipe, the end of which bends horizontally. How fast does the ball leave the pipe if no energy is lost to friction? 140. A spacecraft's engines do 1.4 x 10 13 Jof work in 8.5 min. What is the power output of these engines? 141. A runner exerts a force of 334 N against the ground while using 2100 W of power. How long does it take him to run a distance of 50.0 m? 142. A high-speed boat has four 300.0 kW motors. How much work is done in 25 s by the motors? 143. A 92 N force pushes an 18 kg box of books, initially at rest, 7.6 m across a floor. The coefficient of kinetic friction between the floor and the box is 0.35. What is the final kinetic energy of the box of books? 144. A guardrail can be bent by 5.00 em and then restore its shape. What is its force constant if struck by a car with 1.09 x 104 Jof kinetic energy? 145. A 25.0 kg trunk strikes the ground with a speed of 12.5 m/s. If no energy is lost from air resistance, what is the height from which the trunk fell? 146. Sliding a 5.0 kg stone up a frictionless ramp with a 25.0° incline increases its gravitational potential energy by 2.4 x 102 J. How long is the ramp? 147. A constant 4.00 x 102 N force moves a 2.00 x 2 10 kg iceboat 0.90 km. Frictional force is negligible, and the boat starts at rest. Find the boat's final speed. 148. A 50.0 kg circus clown jumps from a platform into a net 1.00 m above the ground. The net is stretched 0.65 m and has a force constant of 3.4 x 104 N/m. What is the height of the platform? 135. How far does a 1.30 x 104 kg jet travel if it is slowed from 2.40 x 10 2 km/h to 0 km/h by an acceleration of -30.8 m/s 2? 136. An automobile is raised 7.0 m, resulting in an increase in gravitational potential energy of 6.6 x 104 J. What is the automobile's mass? 137. A spring in a pogo stick has a force constant of 1.5 x 10'1 N/m. How far is the spring compressed when its elastic potential energy is 120 J? 138. A 100.0 g arrow is pulled back 30.0 em against a bowstring. The bowstring's force constant is 1250 N/m. What speed will the arrow leave the bow? Chapter 6 Momentum and Collisions 149. If a 50.0 kg cheetah, initially at rest, runs 274m north in 8.65 s, what is its momentum? 150. If a 1.46 x 10 5 kg whale has a momentum of 9.73 x 10 5 kg•m/s to the south, what is its velocity? 151. A star has a momentum of 8.62 x 10 36 kg•m/s and a speed of 255 km/s. What is its mass? 152. A 5.00 g projectile has a velocity of 255 m/s right. Find the force to stop this projectile in 1.45 s. 153. How long does it take a 0.17 kg hockey puck to decrease its speed by 9.0 mls if the coefficient of kinetic friction is 0.050? 884 Appendix 1: Additional Problems I 154. A 705 kg race car driven by a 65 kg driver moves with a velocity of 382 km/h right. Find the force to bring the car and driver to a stop in 12.0 s. 155. Find the stopping distance in problem 154. 156. A 50.0 g shell fired from a 3.00 kg rifle has a speed of 400.0 m!s. With what velocity does the rifle recoil in the opposite direction? 157. A twig at rest in a pond moves with a speed of 0.40 cm/s opposite a 2.5 g snail, which has a speed of 1.2 cm/s. What is the mass of the twig? 158. A 25.0 kg sled holding a 42.0 kg child has a speed of 3.50 m/s. They collide with and pick up a snowman, initially at rest. The resulting speed of the snowman, sled, and child is 2.90 m!s. What is the snowman's mass? 159. An 8500 kg railway car moves right at 4.5 m/s, and a 9800 kg railway car moves left at 3.9 m/s. The cars collide and stick together. What is the final velocity of the system? 160. What is the change in kinetic energy for the two railway cars in problem 159? 161. A 55 g clay ball moving at 1.5 m/s collides with a 55 g clay ball at rest. By what percentage does the kinetic energy change after the inelastic collision? 162. A 45 g golf ball collides elastically with an identical ball at rest and stops. If the second ball's final speed is 3.0 m!s, what was the first ball's initial speed? 163. A 5.00 X 10 2 kg racehorse gallops with a momentum of 8.22 x 10 3 kg•m/s to the west. What is the horse's velocity? 164. A 3.0 x 10 7 kg ship collides elastically with a 2.5 x 10 7 kg ship moving north at 4.0 km/h. After the collision, the first ship moves north at 3.1 km/h and the second ship moves south at 6.9 km/h. Find the unknown velocity. 165. A high-speed train has a mass of 7.10 x 10 5 kg and moves at a speed of 270.0 km/h. What is the magnitude of the train's momentum? 166. A bird with a speed of 50.0 km/h has a momentum of magnitude of 0.278 kg •m/s. What is the bird's mass? 167. A 75 N force pulls a child and sled initially at rest down a snowy hill. If the combined mass of the sled and child is 55 kg, what is their speed after 7.5 s? 168. A student exerts a net force of -1.5 N over a period of 0.25 s to bring a falling 60.0 g egg to a stop. What is the egg's initial speed? 169. A 1.1 x 10 3 kg walrus starts swimming east from rest and reaches a velocity of 9.7 m/s in 19 s. What is the net force acting on the walrus? 170. A 12.0 kg wagon at rest is pulled by a 15.0 N force at an angle of 20.0° above the horizontal. If an 11.0 N frictional force resists the forward force, how long will the wagon take to reach a speed of 4.50 m/s? 171. A 42 g meteoroid moving forward at 7.82 x 10 3 m/s collides with a spacecraft. What force is needed to stop the meteoroid in 1.0 x 10-6 s? 172. A 455 kg polar bear slides for 12.2 s across the ice. If the coefficient of kinetic friction between the bear and the ice is 0.071, what is the change in the bear's momentum as it comes to a stop? 173. How far does the bear in problem 172 slide? 17 4. How long will it take a -1.26 x 104 N force to stop a 2.30 x 10 3 kg truck moving at a speed of 22.2 m/s? 175. A 63 kg skater at rest catches a sandbag moving north at 5.4 m/s. The skater and bag then move north at 1.5 m/s. Find the sandbag's mass. 176. A 1.36 x 104 kg barge is loaded with 8.4 x 10 3 kg of coal. What was the unloaded barge's speed if the loaded barge has a speed of 1.3 m/s? 177. A 1292 kg automobile moves east at 88.0 km/h. If all forces remain constant, what is the car's velocity if its mass is reduced to 1255 kg? 178. A 68 kg student steps into a 68 kg boat at rest, causing both to move west at a speed of 0.85 m/s. What was the student's initial velocity? 179. A 1400 kg automobile, heading north at 45 km/h, collides inelastically with a 2500 kg truck traveling east at 33 km/h. What is the vehicles' final velocity? 180. An artist throws 1.3 kg of paint onto a 4.5 kg canvas at rest. The paint-covered canvas slides backward at 0.83 m/s. What is the change in the kinetic energy of the paint and canvas? 181. Find the change in kinetic energy if a 0.650 kg fish leaping to the right at 15.0 m/s collides inelastically with a 0.950 kg fish leaping to the left at 13.5 m/s. 182. A 10.0 kg cart moving at 6.0 m/s hits a 2.5 kg cart moving at 3.0 m/s in the opposite direction. Find the carts' final speed after an inelastic collision. 183. A ball, thrown right 6.00 m/s, hits a 1.25 kg panel at rest, then bounces back at 4.90 m/s. The panel moves right at 1.09 m/s. Find the ball's mass. Appendix 1: Additional Problems 885 184. A 2150 kg car, moving east at 10.0 m/s, collides and joins with a 3250 kg car. The cars move east together at 5.22 m/s. What is the 3250 kg car's initial velocity? 185. Find the change in kinetic energy in problem 184. 186. A 15.0 g toy car moving to the right at 20.0 cm/s collides elastically with a 20.0 g toy car moving left at 30.0 cm/s. The 15.0 g car then moves left at 37.1 cm/s. Find the 20.0 g car's final velocity. 187. A remora swimming right at 5.0 m/s attaches to a 150.0 kg shark moving left at 7.00 m!s. Both move left at 6.25 m/s. Find the remora's mass. 197. A 2.05 x 108 kg asteroid has an orbit with a 7378 km radius. The centripetal force on the asteroid is 3.00 x 10 9 N. Find the asteroid's tangential speed. 198. Find the gravitational force between a 0.500 kg mass and a 2.50 x 10 12 kg mountain that is 10.0 km away. 199. The gravitational force between Ganymede and Jupiter is 1.636 x 10 22 N. Jupiter's mass is 1.90 x 10 27 kg, and the distance between the two bodies is 1.071 x 10 6 km. What is Ganymede's mass? 200. At the sun's surface, the gravitational force on 188. A 6.5 x 10 12 kg comet, moving at 420 m/s, catches up to and collides inelastically with a 1.50 x 10 13 kg comet moving at 250 m/s. Find the change in the comets' kinetic energy. 1.00 kg is 274 N. The sun's mass is 1.99 x 1030 kg. If the sun is assumed spherical, what is the sun's radius? 189. A 7.00 kg ball moves east at 2.00 m/s, collides 20 I. At the surface of a red giant star, the gravitational with a 7.00 kg ball at rest, and then moves 30.0° north of east at 1.73 m/s. What is the second ball's final velocity? 190. A 2.0 kg block moving at 8.0 m/s on a frictionless surface collides elastically with a block at rest. The first block moves in the same direction at 2.0 m/s. What is the second block's mass? force on 1.00 kg is only 2.19 x 10-3 N. If its mass equals 3.98 x 1031 kg, what is the star's radius? 202. Uranus has a mass of 8.6 x 1025 kg. The mean distance between the centers of the planet and its moon Miranda is 1.3 x 10 5 km. If the orbit is circular, what is Miranda's period in hours? 203. What is the tangential speed in problem 202? 204. The rod connected halfway along the 0.660 m radius of a wheel exerts a 2.27 x 10 5 N force. How large is the maximum torque? Chapter 7 Circular Motion and Gravitation 205. A golfer exerts a torque of 0.46 N •m on a golf 191. A pebble that is 3.81 m from the eye of a tornado has a tangential speed of 124 m/s. What is the magnitude of the pebble's centripetal acceleration? 192. A race car speeds along a curve with a tangential speed of 75.0 m/s. The centripetal acceleration on the car is 22.0 m!s2. Find the radius of the curve. 193. A subject in a large centrifuge has a radius of 8.9 m and a centripetal acceleration of 20g (g = 9.81 m/s 2 ). What is the tangential speed of the subject? 194. A 1250 kg automobile with a tangential speed of 48.0 km/h follows a circular road that has a radius of 35.0 m. How large is the centripetal force? 195. A rock in a sling is 0.40 m from the axis of rotation and has a tangential speed of 6.0 m!s. What is the 2 rock's mass if the centripetal force is 8.00 x 10 N? 196. A 7.55 x 10 13 kg comet orbits the sun with a speed of 0.173 km/s. If the centripetal force on the comet is 505 N, how far is it from the sun? 886 Appendix 1: Additional Problems club. If the club exerts a force of 0.53 Non a stationary golf ball, what is the length of the club? 206. What is the orbital radius of the Martian moon Deimos if it orbits 6.42 x 1023 kg Mars in 30.3 h? 207. A 4.00 x 10 2 N •m torque is produced applying a force 1.60 m from the fulcrum and at an angle of 80.0° to the lever. How large is the force? 208. A customer 11 m from the center of a revolving restaurant has a speed of 1.92 x 10-2 m/s. How large a centripetal acceleration acts on the customer? 209. A toy train on a circular track has a tangential speed of 0.35 m/s and a centripetal acceleration 2 of 0.29 m!s • What is the radius of the track? 210. A person against the inner wall of a hollow cylinder with a 150m radius feels a centripetal acceleration of 9.81 m/s 2. Find the cylinder's tangential speed. 2 11. The tangential speed of 0.20 kg toy carts is 5.6 m/s when they are 0.25 m from a turning shaft. How large is the centripetal force on the carts? 212. A 1250 kg car on a curve with a 35.0 m radius has a centripetal force from friction and gravity of 8.07 x 10 3 N. What is the car's tangential speed? 228. A block of ebony with a volume of 2.5 x 10-3 m 3 is placed in fresh water. If the apparent weight of the block is 7.4 N, what is the density of ebony? 213. Two wrestlers, 2.50 x 10-2 m apart, exert a 2.77 x 229. One piston of a hydraulic lift holds 1.40 x 10 3 kg. 214. A 1.81 x 10 5 kg blue whale is 1.5 m from a 230. A hydraulic-lift piston raises a 4.45 x 104 N 10-3 N gravitational force on each other. One has a mass of 157 kg. What is the other's mass? 4 2.04 x 10 kg whale shark. What is the gravitational force between them? 215. Triton's orbit around Neptune has a radius of 3.56 x 10 5 km. Neptune's mass is 1.03 x 1026 kg. What is Triton's period? The other holds an ice block (p = 917 kg!m 3 ) that is 0.076 m thick. Find the first piston's area. weight by 448 m. How large is the force on the other piston if it is pushed 8.00 m downward? 231. A platinum flute with a density of 21.5 g/cm 3 is submerged in fresh water. If its apparent weight is 40.2 N, what is the flute's mass? 216. Find the tangential speed in problem 215. 217. A moon orbits a 1.0 x 1026 kg planet in 365 days. What is the radius of the moon's orbit? 218. What force is required to produce a 1.4 N •m torque when applied to a door at a 60.0° angle and 0.40 m from the hinge? 219. What is the maximum torque that the force in problem 218 can exert? 220. A worker hanging 65.0° from the vane of a windmill exerts an 8.25 x 10 3 N •m torque. If the worker weighs 587 N, what is the vane's length? Chapter 8 Fluid Mechanics 221. A cube of volume 1.00 m 3 floats in gasoline, 3 which has a density of 675 kg/m . How large a buoyant force acts on the cube? 222. A cube 10.0 em on each side has a density of 4 3 2.053 x 10 kg/m . Its apparent weight in fresh water is 192 N. Find the buoyant force. 223. A 1.47 x 106 kg steel hull has a base that is 2.50 x 10 3 m 2 in area. If it is placed in sea water (p = 1.025 x 10 3 kg!m 3 ), how deep does the hull sink? 224. What size force will open a door of area 1.54 m 2 if the net pressure on the door is 1.013 x 10 3 Pa? 225. Gas at a pressure of 1.50 x 106 Pa exerts a force of 1.22 x 10 4 Non the upper surface of a piston. What is the piston's upper surface area? 226. In a barometer, the mercury column's weight equals the force from air pressure on the mercury's surface. Mercury's density is 13.6 x 10 3 kg/m 3 . What is the air's pressure if the column is 760 mm high? 227. A cube of osmium with a volume of 166 cm 3 is placed in fresh water. The cube's apparent weight is 35.0 N. What is the density of osmium? Chapter 9 Heat 232. Surface temperature on Mercury ranges from 463 K during the day to 93 K at night. Express this temperature range in degrees Celsius. 233. Solve problem 233 for degrees Fahrenheit. 234. The temperature in Fort Assiniboine, Montana, went from -5°F to +37°F on January 19, 1892. Calculate this change in temperature in kelvins. 235. An acorn falls 9.5 m, absorbing 0.85 of its initial potential energy. If 1200 J/kg will raise the acorn's temperature 1.0°C, what is its temperature increase? 236. A bicyclist on level ground brakes from 13.4 m/s to 0 m!s. What is the cyclist's and bicycle's mass if the increase in internal energy is 5836 J? 237. A 61.4 kg roller skater on level ground brakes from 20.5 m/s to 0 m/s. What is the total change in the internal energy of the system? 238. A 0.225 kg tin can (cp = 2.2 x 10 3 J/kg•°C) is 4 cooled in water, to which it transfers 3.9 x 10 J of energy. By how much does the can's temperature change? 239. What mass of bismuth (cp = 121 J/kg•°C) increases temperature by 5.0°C when 25 J are added by heat? 240. Placing a 0.250 kg pot in 1.00 kg of water raises the water's temperature 1.00°C. The pot's temperature drops 17 .5°C. Find the pot's specific heat capacity. 241. Lavas at Kilauea in Hawaii have temperatures of 2192°F. Express this quantity in degrees Celsius. 242. The present temperature of the background radiation in the universe is 2. 7 K. What is this temperature in degrees Celsius? Appendix 1: Additional Problems 887 243. The human body cannot survive at a temperature of 42°C for very long. Express this quantity in kelvins. 4 244. Two sticks rubbed together gain 2.15 x 10 J 245. A stone falls 561.7 m. When the stone lands, the internal energy of the ground and the stone increases by 105 J. What is the stone's mass? floor from 5.7 m/s to 0 m/s. If 3.3 x 105 J cause 1.0 kg of ice to melt, how much of the ice melts? 247. Placing a 3.0 kg skillet in 5.0 kg of water raises the water's temperature 2.25°C and lowers the skillet's temperature 29.6°C. Find the skillet's specific heat. 6 air's temperature increases 55°C when 45 x 10 J are added to it by heat, what is the air's mass? 249. A 0.23 kg tantalum part has a specific heat 0 capacity of 140 J/kg • C. By how much does the part's temperature change if it gives up 4 3.0 x 10 J as heat? Chapter 10 Thermodynamics 250. A volume of air increases 0.227 m 3 at a net pressure of 2.07 x 10 7 Pa. How much work is done on the air? 6 251. The air in a hot-air balloon does 3.29 x 10 J of work, increasing the balloon's volume by 2190 m 3 . What is the net pressure in the balloon? 252. Filling a fire extinguisher with nitrogen gas at a net pressure of 25.0 kPa requires 472.5 J of work on the gas. Find the change in the gas's volume. 253. The internal energy of air in a closed car rises 873 J. How much heat energy is transferred to the air? 254. A system's initial internal energy increases from 39 J to 163 J. If 114 J of heat are added to the system, how much work is done on the system? 255. A gas does 623 J of work on its surroundings when 867 J are added to the gas as heat. What is the change in the internal energy of the gas? 256. An engine with an efficiency of 0.29 takes in 693 J as heat. How much work does the engine do? 257. An engine with an efficiency of 0.19 does 998 J of work. How much energy is taken in by heat? Appendix 1: Additional Problems 259. A 5.4 x 10-4 m 3 increase in steam's volume does 260. A pressure of 655 kPa does 393 J of work inflating a bike tire. Find the change in volume. 261. An engine's internal energy changes from 8093 J to 2.0920 x 104 J. If 6932 J are added as heat, how much work is done on or by the system? 262. Steam expands from a geyser to do 192 kJ of 246. A 2.5 kg block of ice at 0.0°C slows on a level 888 5 71 J as heat and loses 463 J as heat per cycle. 1.3 J of work on a piston. What is the pressure? from kinetic energy and lose 33 percent of it to the air. How much does the sticks' internal energy change? 248. Air has a specific heat of 1.0 x 103 J/kg • 0 C. If 258. Find the efficiency of an engine that receives work. If the system's internal energy increases by 786 kJ, how much energy is transferred as heat? 263. If 632 kJ are added to a boiler and 102 kJ of work are done as steam escapes from a safety valve, what is the net change in the system's internal energy? 264. A power plant with an efficiency of 0.35 percent requires 7.3 7 x 10 8 J of energy as heat. How much work is done by the power plant? 1 265. An engine with an efficiency of 0.11 does 1150 J of work. How much energy is taken in as heat? 266. A test engine performs 128 J of work and receives 581 J of energy as heat. What is the engine's efficiency? Chapter 11 Vibrations and Waves 267. A scale with a spring constant of 420 N/m is compressed 4.3 em. What is the spring force? 268. A 669 N weight attached to a giant spring stretches it 6.5 em. What is the spring constant? 269. An archer applies a force of 52 N on a bowstring with a spring constant of 490 N/m. What is the bowstring's displacement? 270. On Mercury, a pendulum 1.14 m long would have a 3.55 s period. Calculate ag for Mercury. 271. Find the length of a pendulum that oscillates with a frequency of 2.5 Hz. 272. Calculate the period of a 6.200 m long pendulum in Oslo, Norway, where ag= 9.819 m/s 2• 273. Find the pendulum's frequency in problem 272. 274. A 24 kg child jumps on a trampoline with a spring constant of 364 N/m. What is the oscillation period? 275. A 32 N weight oscillates with a 0.42 s period when on a spring scale. Find the spring constant. ~ 276. Find the mass of a ball that oscillates at a period of 0.079 s on a spring with a constant of 63 N/m. 277. A dolphin hears a 280kHz sound with a wave- 295. A 1.53 m long pipe that is closed on one end has a seventh harmonic frequency of 466.2 Hz. What is the speed of the waves in the pipe? 296. A pipe open at both ends has a fundamental length of 0.51 em. What is the wave's speed? 278. If a sound wave with a frequency of 20.0 Hz has a speed of 331 m/s, what is its wavelength? 279. A sound wave has a speed of 2.42 x 104 m/sand a wavelength of 1.1 m. Find the wave's frequency. frequency of 125 Hz. If the pipe is 1.32 m long, what is the speed of the waves in the pipe? 297. Traffic has a power output of 1.57 x 10-3 W. At what distance is the intensity 5.20 x 10-3 W/m 2? 298. If a mosquito's buzzing has an intensity of 9.3 x 280. An elastic string with a spring constant of 65 N/m is stretched 15 em and released. What is the spring force exerted by the string? 281. The spring in a seat compresses 7.2 em under a 620 N weight. What is the spring constant? 282. A 3.0 kg mass is hung from a spring with a spring constant of 36 N/m. Find the displacement. 283. Calculate the period of a 2.500 m long pendu2 lum in Quito, Ecuador, where ag= 9.780 m!s • 10-8 W/m 2 at a distance of 0.21 m, how much sound power does the mosquito generate? 299. A note from a flute (a pipe with a closed end) has a first harmonic of 392.0 Hz. How long is the flute if the sound's speed is 331 m/s? 300. An organ pipe open at both ends has a first harmonic of 370.0 Hz when the speed of sound is 331 m/s. What is the length of this pipe? 284. How long is a pendulum with a frequency of Chapter 13 Light and Reflection 0.50 Hz? 285. A tractor seat supported by a spring with a 3 spring constant of 2.03 x 10 N/m oscillates at a frequency of 0.79 Hz. What is the mass on the spring? 286. An 87 N tree branch oscillates with a period of 0.64 s. What is the branch's spring constant? 287. What is the oscillation period for an 8.2 kg baby in a seat that has a spring constant of 221 N/m? 288. An organ creates a sound with a speed of 331 m/s and a wavelength of 10.6 m. Find the frequency. 289. What is the speed of an earthquakes-wave with a 2.3 x 10 4 m wavelength and a 0.065 Hz frequency? Chapter 12 Sound 290. What is the distance from a sound with 5.88 x 10-s W power if its intensity is 3.9 x 10- 6 W/m 2? 291. Sound waves from a stereo have a power output of 3.5 W at 0.50 m. What is the sound's intensity? 292. What is a vacuum cleaner's power output if the sound's intensity 1.5 m away is 4.5 x 10-4 W/m 2? 293. Waves travel at 499 m/s on a 0.850 m long cello string. Find the string's fundamental frequency. 294. A mandolin string's first harmonic is 392 Hz. How long is the string if the wave speed on it is 329 m/s? 301. A 7.6270 x 108 Hz radio wave has a wavelength of 39.296 em. What is this wave's speed? 302. An X ray's wavelength is 3.2 nm. Using the speed of light in a vacuum, calculate the frequency of the Xray. 303. What is the wavelength of ultraviolet light with a frequency of 9.5 x 10 14 Hz? 304. A concave mirror has a focal length of 17 em. Where must a 2.7 em tall coin be placed for its image to appear 23 em in front of the mirror's surface? 305. How tall is the coin's image in problem 304? 306. A concave mirror's focal length is 9.50 em. A 3.0 em tall pin appears to be 15.5 em in front of the mirror. How far from the mirror is the pin? 307. How tall is the pin's image in problem 306? 308. A convex mirror's magnification is 0.11. Suppose you are 1.75 m tall. How tall is your image? 309. How far in front of the mirror in problem 308 are you if your image is 42 em behind the mirror? 310. A mirror's focal length is -12 em. What is the object distance if an image forms 9.00 em behind the surface of the mirror? 311. What is the magnification in problem 310? 312. A metal bowl is like a concave spherical mirror. You are 35 em in front of the bowl and see an image at 42 em. What is the bowl's focal length? Appendix 1: Additional Problems 889 313. For problem 312, find the bowl's radius of curvature. 314. A concave spherical mirror on a dressing table has a focal length of 60.0 em. If someone sits 35.0 em in front of it, where is the image? 315. What is the magnification in problem 314? 316. An image appears 5.2 em behind the surface of a convex mirror when the object is 17 em in front of the mirror. What is the mirror's focal length? 317. If the object in problem 316 is 3.2 em tall, how tall is its image? 318. In order for someone to observe an object, the wavelength of the light must be smaller than the object. The Bohr radius of a hydrogen atom is 5.291 770 x 10- 11 m. What is the lowest frequency that can be used to locate a hydrogen atom? 319. Meteorologists use Doppler radar to watch the movement of storms. If a weather station uses electromagnetic waves with a frequency of 2.85 x 10 9 Hz, what is the wavelength of the radiation? 320. PCS cellular phones have antennas that use radio frequencies from 1800-2000 MHz. What range of wavelengths corresponds to these frequencies? 321. Suppose you have a mirror with a focal length of 32.0 em. Where would you place your right hand so that you appear to be shaking hands with yourself? 322. A car's headlamp is made of a light bulb in front of a concave spherical mirror. If the bulb is 5.0 em in front of the mirror, what is the radius of the mirror? 323. Suppose you are 19 em in front of the bell of your friend's trumpet and you see your image at 14 em. If the trumpet's bell is a concave mirror, what would be its focal length? 324. A soup ladle is like a spherical convex mirror with a focal length of 27 em. If you are 43 em in front of the ladle, where does the image appear? If your nose is 6.0 em long, how long does the image appear? 329. How fast does microwave radiation that has a frequency of 1.173 06 x 10 11 Hz and a wavelength of 2.5556 mm travel? 330. Suppose the microwaves in your microwave oven have a frequency of 2.5 x 10 10 Hz. What is the wavelength of these microwaves? 331. You place an electric heater 3.00 min front of a concave spherical mirror that has a focal length of 30.0 em. Where would your hand feel warmest? 332. You see an image of your hand as you reach for a doorknob with a focal length of 6.3 em. How far from the doorknob is your hand when the image appears at 5.1 em behind the doorknob? 333. What is the magnification of the image in problem 332? Chapter 14 Refraction 334. A ray of light in air enters an amethyst crystal (n = 1.553). If the angle of refraction is 35°, what is the angle of incidence? 335. Light passes from air at an angle of incidence of 59.2° into a nephrite jade vase (n = 1.61). Determine the angle of refraction in the jade. 336. Light entering a pearl travels at a speed of 1.97 x 10 8 m/s. What is the pearl's index of refraction? 337. An object in front of a diverging lens of focal length 13.0 em forms an image with a magnification of +5.00. How far from the lens is the object placed? 338. An object with a height of 18 em is placed in front of a converging lens. The image height is -9.0 em. What is the magnification of the lens? 339. If the focal length of the lens in problem 338 is 6.0 em, how far in front of the lens is the object? 325. What is the magnification in problem 324? 340. Where does the image appear in problem 339? 326. Just after you dry a spoon, you look into the con- 341. The critical angle for light traveling from a vex part of the spoon. If the spoon has a focal length of -8.2 em and you are 18 em in front of the spoon, where does the image appear? 327. The base of a lamp is made of a convex spherical mirror with a focal length of -39 em. Where does the image appear when you are 16 em from the base? 890 328. Consider the lamp and location in problem 327. Appendix 1: Additional Problems green tourmaline gemstone into air is 37.8°. What is tourmaline's index of refraction? 342. Find the critical angle for light traveling from ruby (n = 1.766) into air. 343. Find the critical angle for light traveling from emerald (n =1.576) into air. ~ 344. Malachite has two indices of refraction: n 1 = 1.91 and n2 = 1.66. A ray of light in air enters malachite at an incident angle of 35.2°. Calculate both of the angles of refraction. 345. A ray of light in air enters a serpentine figurine (n = 1.555). If the angle of refraction is 33°, what is the angle of incidence? 346. The critical angle for light traveling from an aquamarine gemstone into air is 39.18°. What is the index of refraction for aquamarine? 347. A 15 em tall object is placed 44 em in front of a diverging lens. A virtual image appears 14 em in front of the lens. What is the lens's focal length? 348. What is the image height in problem 347? 349. A lighthouse converging lens has a focal length of 4 m. What is the image distance for an object placed 4 m in front of the lens? 350. What is the magnification in problem 349? 351. Light moves from olivine (n = 1.670) into onyx. If the critical angle for olivine is 62.85°, what is the index of refraction for onyx? 352. When light in air enters an opal mounted on a ring, the light travels at a speed of 2.07 x 108 m/s. What is opal's index of refraction? 353. When light in air enters albite, it travels at a velocity of 1.95 x 10 8 m/s. What is albite's index of refraction? 354. A searchlight is constructed by placing a 500 W bulb 0.5 m in front of a converging lens. The focal length of the lens is 0.5 m. What is the image distance? 355. A microscope slide is placed in front of a converging lens with a focal length of 3.6 em. The lens forms a real image of the slide 15.2 em behind the lens. How far is the lens from the slide? 356. Where must an object be placed to form an image 12 em in front of a diverging lens with a focal length of 44 em? C hapter 1 5 Interference and Diffraction 359. Light with a 587.5 nm wavelength passes through two slits. A second-order bright fringe forms 0.130° from the center. Find the slit separation. 360. Light passing through two slits with a separa- tion of 8.04 X 10-6 m forms a third bright fringe 13.1° from the center. Find the wavelength. 361. Two slits are separated by 0.0220 em. Find the angle at which a first-order bright fringe is observed for light with a wavelength of 527 nm. 362. For 546.1 nm light, the first-order maximum for a diffraction grating forms at 75.76°. How many lines per centimeter are on the grating? 363. Infrared light passes through a diffraction grating of 3600 lines/em. The angle of the third-order maximum is 76.54°. What is the wavelength? 364. A diffraction grating with 1950 lines/em is used to examine light with a wavelength of 497.3 nm. Find the angle of the first-order maximum. 365. At what angle does the second-order maximum in problem 364 appear? 366. Light passes through two slits separated by 3.92 x 10-6 m to form a second-order bright fringe at an angle of 13.1 °. What is the light's wavelength? 367. Light with a wavelength of 430.8 nm shines on two slits that are 0.163 mm apart. What is the angle at which a second dark fringe is observed? 368. Light of wavelength 656.3 nm passes through two slits. The fourth-order dark fringe is 0.548° from the central maximum. Find the slit separation. 369. The first-order maximum for light with a wavelength of 447.1 nm is found at 40.25°. How many lines per centimeter does the grating have? 370. Light through a diffraction grating of 9550 lines/em forms a second-order maximum at 54.58°. What is the wavelength of the light? 357. The critical angle for light traveling from almandine garnet into air ranges from 33.1° to 35.3°. Calculate the range of almandine garnet's index of refraction. 358. Light moves from a clear andalusite (n = 1.64) crystal into ivory. If the critical angle for andalusite is 69.9°, what is the index of refraction for ivory? Chapter 16 Electric Forces and Fields 37 1. Charges of -5.31J.C and +5.31J.C are separated by 4.2 em. Find the electric force between them. 372. A dog's fur is combed, and the comb gains a charge of 8.0 nC. Find the electric force between the fur and comb when they are 2.0 em apart. 11 373. Two equal charges are separated by 6.5 x 10- m. If the magnitude of the electric force between the charges is 9.92 x 10-4 N, what is the value of q? Appendix I: Additional Problems 891 374. Two point charges of -13.0 ~C and -16.0 ~C exert repulsive forces on each other of 12.5 N. What is the distance between the two charges? 375. Three equal point charges of 4.00 nC lie 4.00 m apart on a line. Calculate the magnitude and direction of the net force on the middle charge. 389. Find the electric force vector on a 5.0 nC charge in a 1500 N/C electric field directed along the y-axis. 390. What electric charge experiences an 8.42 X 1o-9 N electric force in an electric field of 1663 N/C? 376. A proton is at each corner of a square with sides 391. Two 3.00 ~C charges lie 2.00 m apart on the x-axis. Find the resultant electric field vector at 1.52 x 10- m long. Calculate the resultant force vector on the proton at the upper right corner. a point 0.250 m on they-axis, above the charge on the left. 9 377. Three 2.0 nC charges are located at coordinates (0 m, 0 m), (1.0 m, 0 m), and (1.0 m, 2.0 m). Find the resultant force on the first charge. 378. Charges of 7.2 nC and 6.7 nC are 32 em apart. Find the equilibrium position for a -3.0 nC charge. 379. A -12.0 ~C charge is between two 6.0 ~C charges, 5.0 em away from each. What electric force keeps the central charge in equilibrium? 380. A 9.0 N/C electric field is directed along the x-axis. Find the electric force vector on a -6.0 C charge. 381. What charge experiences an electric force of 6.43 x 10-9 N in an electric field of 4.0 x 10 3 N/C? 382. A 5.00 ~C charge is 0.500 m above a 15.0 ~C charge. Calculate the electric field at a point 1.00 m above the 15.0 mC charge. 383. Two static point charges of 99.9 ~C and 33.3 ~C exert repulsive forces on each other of 87.3 N. What is the distance between the two charges? 384. Two particles are separated by 9.30 x 10- 11 m. If the magnitude of the electric force between the charges is 2.66 x 10-8 N, what is the value of q? 385. A -23.4 nC charge is 0.500 m below a 4.65 nC charge and 1.00 m below a 0.299 nC charge. Find the resultant force vector on the -23.4 nC charge. 392. Two electrons are 2.00 x 10- 10 m and 3.00 x 10- 10 m, respectively, from a point. Where with respect to that point must a proton be placed so that the resultant electric field strength is zero? 393. A -7.0 C charge is in equilibrium with a 49 C charge 18m to the right and an unknown charge 25 m to the right. What is the unknown charge? 394. Suppose two pions are separated by 8.3 x 10-10 m. If the magnitude of the electric force between the charges is 3.34 x 10-10 N, what is the value of q? 395. Suppose two muons having equal but opposite charge are separated by 6.4 x 1o- 8 m. If the magnitude of the electric force between the charges is 5.62 x 10- 14 N, what is the value of q? 396. Consider four electrons at the corners of a square. Each side of the square is 3.02 x 10-5 m. Find the magnitude and direction of the resultant force on q3 if it is at the origin. 397. A charge of 5.5 nC and a charge of 11 nC are separated by 88 em. Find the equilibrium position for a -22 nC charge. 398. Three charges are on they-axis. At the origin is a charge, q1 = 72 C; an unknown charge, q2, is at y = 15 mm. A third charge, q3 = -8.0 C, is placed at y = -9.0 mm so that it is in electrostatic equilibrium with q1 and q2. What is the charge on ql 386. Three point charges are on the corners of a triangle: q1 =-9.00 nC is at the origin; q2 = -8.00 nC is at x = 2.00 m; and q3 = 7.00 nC is at y = 3.00 m. Find the magnitude and direction of the resultant force on ql. 387. Charges of -2.50 nC and -7.50 nC are 20.0 em apart. Find a 5.0 nC charge's equilibrium position. 388. A -4.6 C charge is in equilibrium with a -2.3 C charge 2.0 m to the right, and an unknown charge 4.0 m to the right. What is the unknown charge? 892 Appendix 1: Additional Problems Chapter 17 Electrical Energy and Current 399. A helium-filled balloon with a 14.5 nC charge rises 290 m above Earth's surface. By how much does the electrical potential energy change if Earth's electric field is -105 N/C? 400. A charged airplane rises 7.3 km in a 3.4 x 10 5 N/C electric field. The electrical potential energy changes by -1.39 X 10 11 J. What is the charge on the plane? j 401. Earth's radius is 6.4 x 106 m. What is Earth's capacitance if it is regarded as a conducting sphere? 402. A 0.50 pF capacitor is connected across a 1.5 V battery. How much charge can this capacitor store? 403. A 76 C charge passes through a wire's crosssectional area in 19 s. Find the current in the wire. 404. The current in a telephone is 1.4 A. How long does 98 C of charge take to pass a point in the wire? 405. What is a television's total resistance if it is plugged into a 120 V outlet and carries 0.75 A of current? 406. A motor with a resistance of 12.2 Q is plugged into a 120.0 V outlet. What is the current in the motor? 407. The potential difference across a motor with a 0.30 Q resistance is 720 V. How much power is used? 408. What is a microwave oven's resistance if it uses 1750 W of power at a voltage of 120.0 V? 409. A 64 nC charge moves 0.95 m with an electrical potential energy change of -3.88 x 10-5 J. What is the electric field strength? 410. A -14 nC charge travels through a 156 N/C electric field with a change of 2.1 x 10-6 J in the electrical potential energy. How far does the charge travel? 5 411. A 5.0 x 10- F polyester capacitor stores 6.0 x 4 10- C. Find the potential difference across the capacitor. 412. Some ceramic capacitors can store 3 x 10-2 C with a potential difference of 30 kV across them. What is the capacitance of such a capacitor? 413. The area of the plates in a 4550 pF parallelplate capacitor is 6.4 x 10- 3 m 2. Find the plate separation. 414. A television receiver contains a 14 )lF capacitor charged across a potential difference of 1.5 x 104 V. How much charge does this capacitor store? 415. A photocopier uses 9.3 A in 15 s. How much charge passes a point in the copier's circuit in this time? 416. A 114 )lC charge passes through a gold wire's cross-sectional area in 0.36 s. What is the current? 417. If the current in a blender is 7.8 A, how long do 56 C of charge take to pass a point in the circuit? 419. A battery-powered lantern has a resistance of 6.4 Q. What potential difference is provided by the battery if the total current is 0.75 A? 420. The potential difference across an electric eel is 650 V. How much current would an electric eel deliver to a body with a resistance of 1.0 x 102 Q? 421. If a garbage-disposal motor has a resistance of 25.0 Q and carries a current of 4.66 A, what is the potential difference across the motor's terminals? 422. A medium-sized oscillating fan draws 545 rnA of current when the potential difference across its motor is 120 V. How large is the fan's resistance? 423. A generator produces a 2.5 x 104 V potential difference across power lines that carry 20.0 A of current. How much power is generated? 424. A computer with a resistance of 91.0 Q uses 230.0 W of power. Find the current in the computer. 425. A laser uses 6.0 x 10 13 W of power. What is the potential difference across the laser's circuit if the current in the circuit is 8.0 x 10 6 A? 426. A blender with a 75 Q resistance uses 350 W of power. What is the current in the blender's circuit? Chapter 18 Circuits and Circuit Elements 427. A theater has 25 surround-sound speakers wired in series. Each speaker has a resistance of 12.0 Q. What is the equivalent resistance? 428. In case of an emergency, a corridor on an airplane has 57 lights wired in series. Each light bulb has a resistance of 2.00 Q. Find the equivalent resistance. 429. Four resistors with resistances of 39 Q, 82 Q , 12 Q, and 42 Q are connected in parallel across a 3.0 V potential difference. Find the equivalent resistance. 430. Four resistors with resistances of 33 Q, 39 Q, 4 7 Q, and 68 Q are connected in parallel across a 1.5 V potential difference. Find the equivalent resistance. 431. A 16 Q resistor is connected in series with another resistor across a 12 V battery. The current in the circuit is 0.42 A. Find the unknown resistance. 432. A 24 Q resistor is connected in series with another resistor across a 3.0 V battery. The current in the circuit is 62 rnA. Find the unknown resistance. 418. A computer uses 3.0 A in 2.0 min. How much charge passes a point in the circuit in this time? Appendix 1: Additional Problems 893 433. A 3.3 Q resistor and another resistor are connected in parallel across a 3.0 V battery. The current in the circuit is 1.41 A. Find the unknown resistance. 445. For the figure above, what is the current in the 3.0 Q resistors? s.on 2.on 434. A 56 Q resistor and another resistor are connected in parallel across a 12 V battery. The current in the circuit is 3.21 A. Find the unknown resistance. 24.0V 435. Three bulbs with resistances of 56 Q , 82 Q, and s.on 24 Q are wired in series. If the voltage across the circuit is 9.0 V, what is the current in the circuit? 436. Three bulbs with resistances of 96 Q, 48 Q, and 29 Q are wired in series. What is the current through the bulbs if the voltage across them is 115V? 437. A refrigerator (R 1 = 75 Q) wired in parallel with an oven (R 2 = 91 Q) is plugged into a 120 V outlet. What is the current in the circuit of each appliance? 438. A computer (R 1 = 82 Q) and printer (R2 = 24 Q) are wired in parallel across a 120 V potential difference. Find the current in each machine's circuit. 5.o n 5.o n 446. For the figure above, calculate the equivalent resistance of the circuit. 447. For the figure above, what is the total current in the circuit? 448. For the figure above, what is the current in either of the 8.0 Q resistors? Chapter 19 Magnetism 449. A proton moves at right angles to a magnetic field of 0.8 T. If the proton's speed is 3.0 x 10 7 m/s, how large is the magnetic force exerted on the proton? 450. A weak magnetic field exerts a 1.9 x 10-22 N force on an electron moving 3.9 x 106 m/s perpendicular to the field. What is the magnetic field strength? 3.o n 1.5 n 451. A 5.0 x 10-5 T magnetic field exerts a 6.1 x 12.0V 439. For the figure above, what is the equivalent resistance of the circuit? 10- 17 N force on a 1.60 x 10- 19 C charge, which moves at a right angle to the field. What is the charge's speed? 452. A 14 A current passes through a 2 m wire. A 440. For the figure above, find the current in the circuit. 441. For the figure above, what is the potential difference across the 6.0 Q resistor? 442. For the figure above, what is the current through the 6.0 Q resistor? 3.6 x 10-4 T magnetic field is at right angles to the wire. What is the magnetic force on the wire? 453. A 1.0 m printer cable is perpendicular to a 1.3 x 10-4 T magnetic field. What current must the cable carry to experience a 9.1 x 10-5 N magnetic force? 454. A wire perpendicular to a 4.6 x 10-4 T magnetic 5.on field experiences a 2.9 x 10-3 N magnetic force. How long is the wire if it carries a 10.0 A current? 455. A 12 m wire carries a 12 A current. What mag- 3.on 15.0V netic field causes a 7.3 x 10-2 N magnetic force to act on the wire when it is perpendicular to the field? 456. A magnetic force of 3.7 x 10- 13 N is exerted on 443. For the figure above, calculate the equivalent resistance of the circuit. 444. For the figure above, what is the total current in the circuit? 894 Appendix 1: Additional Problem s an electron moving at 7.8 x 10 6 m/s perpendicular to a sunspot. How large is the sunspot's magnetic field? 457. An electron moves with a speed of 2.2 x 10 6 m/sat right angles through a 1.1 x 10-2 T magnetic field. How large is the magnetic force on the electron? 458. A pulsar's magnetic field is 1 x 10-8 T. How fast does an electron move perpendicular to this field . c soth at a 3.2 x 10-22 N magnetic 10rce acts on the charge? 459. A levitation device designed to suspend 75 kg uses 10.0 m of wire and a 4.8 x 10-4 T magnetic field, perpendicular to the wire. What current is needed? 460. A power line carries 1.5 x 10 3 A for 15 km. Earth's magnetic field is 2.3 x 10-5 T at a 45° angle to the power line. What is the magnetic force on the line? 470. A step-down transformer converts a 3.6 kV voltage to 1.8 kV. If the primary (input) coil has 58 turns, how many turns does the secondary have? 47 1. A step-up transformer converts a 4.9 kV voltage to 49 kV. If the secondary (output) coil has 480 turns, how many turns does the primary have? 472. A 320-turn coil rotates from 0° to 90.0° in a 0.046 T magnetic field in 0.25 s, which induces an average emf of 4.0 V. What is the area of the coil? 473. A 180-turn coil with a 5.0 x 10-5 m 2 area is in a magnetic field that decreases by 5.2 x 10-4 Tin 1.9 x 10-5 s. What is the induced current if the coil's resistance is 1.0 x 102 W? 474. A generator provides a maximum ac current of 1.2 A and a maximum output emf of 211 V. Calculate the rms potential difference. 475. Calculate the rms current for problem 474. Chapter 20 Electromagnetic Induction 461. A coil with 540 turns and a 0.016 m 2 area is rotated exactly from 0° to 90.0° in 0.050 s. How strong must a magnetic field be to induce an emf of 3.0V? 476. A generator can provide a maximum output emf of 170 V. Calculate the rms potential difference. 477. A step-down transformer converts 240 V across the primary to 5.0 V across the secondary. What is the step-down ratio (N1 :N2 )? 462. A 550-turn coil with an area of 5.0 x 10-5 m 2 is in a magnetic field that decreases by 2.5 X 1o-4 T in 2.1 X 10-5 s. What is the induced emf in the coil? 463. A 246-turn coil has a 0.40 m 2 area in a magnetic field that increases from 0.237 T to 0.320 T. What time interval is needed to induce an emf of -9.1 V? 464. A 9.5 V emf is induced in a coil that rotates from 0.0° to 90.0° in a 1.25 x 10-2 T ma~netic field for 25 ms. The coil's area is 250 em . How many turns of wire are in the coil? 465. A generator provides a rms emf of 320 V across 100 Q. What is the maximum emf? 466. Find the rms current in the circuit in problem 465. 467. Some wind turbines can provide an rms current of 1.3 A. What is the maximum ac current? 468. A transformer has 1400 turns on the primary and 140 turns on the secondary. What is the voltage across the primary if secondaryvoltage is 6.9 kV? 469. A transformer has 140 turns on the primary and 840 turns on the secondary. What is the voltage across the secondary if the primary voltage is 5.6 kV? Chapter 21 Atomic Physics 478. Determine the energy of a photon of green light with a wavelength of 527 nm. 479. Calculate the de Broglie wavelength of an electron with a velocity of 2.19 x 106 m/s. 480. Calculate the frequency of ultraviolet (UV) light having a photon energy of 20.7 eV. 481. X-ray radiation can have an energy of 12.4 MeV. To what wavelength does this correspond? 482. Light of wavelength 240 nm shines on a potassium surface. Potassium has a work function of 2.3 eV. What is the maximum kinetic energy of the photoelectrons? 483. Manganese has a work function of 4.1 eV. What is the wavelength of the photon that will just have the threshold energy for manganese? 484. What is the speed of a proton with a de Broglie wavelength of 2.64 x 10- 14 m? 485. A cheetah can run as fast as 28 m/ s. If the cheetah has a de Broglie wavelength of 8.97 x 10-37 m, what is the cheetah's mass? 486. What is the energy of a photon of blue light with a wavelength of 430.8 nm? Appendix 1: Additional Problems 895 487. Calculate the frequency of infrared (IR) light with a photon energy of 1.78 eV. 488. Calculate the wavelength of a radio wave that has a photon energy of 3.1 x 10-6 eV. 489. Light of frequency 6.5 x 10 14 Hz illuminates a lithium surface. The ejected photoelectrons are found to have a maximum kinetic energy of 0.20 eV. Find the threshold frequency of this metal. 490. Light of wavelength 519 nm shines on a rubidium surface. Rubidium has a work function of 2.16 eV. What is the maximum kinetic energy of the photoelectrons? 491. The smallest known virus moves across a Petri dish at 5.6 x 10-6 m/s. If the de Broglie wavelength of the virus is 2.96 x 10-8 m, what is the virus's mass? 492. The threshold frequency of platinum is 1.36 x 10 15 Hz. What is the work function of platinum? 493. The ship Queen Elizabeth II has a mass of 7.6 x 10 7 kg. Calculate the de Broglie wavelength if this ship sails at 35 m/s. 494. Cobalt has a work function of 5.0 eV. What is the wavelength of the photon that will just have the threshold energy for cobalt? 495. Light of frequency 9.89 x 10 14 Hz illuminates a calcium surface. The ejected photoelectrons are found to have a maximum kinetic energy of 0.90 eV. Find the threshold frequency of this metal. 496. What is the speed of a neutron with a de Broglie wavelength of 5.6 x 10- 14 m? 499. Find the mass defect of i~Ni. 500. Complete this radioactive-decay formula: 212 s4Po ------7 ? + 42He. 501. Complete this radioactive-decay formula: 16 N-----7?+_0e+v. 1 7 502. Complete this radioactive-decay formula: 1 1 ~ism ------7 ~6Nd +? . 503. A 3.29 x 10- 3 g sample of a pure radioactive substance is found after 30.0 s to have only 8.22 x 10-4 g left undecayed. What is the halflife of the substance? 504. The half-life of ~~Cr is 21.6 h. A chromium-48 sample contains 6.5 x 10 6 nuclei. Calculate the activity of the sample in mCi. 505. How long will it take a sample of lead-212 (which has a half-life of 10.64 h) to decay to one-eighth its original strength? 506. Compute the binding energy of 1 ~~Sn. 507. Calculate the difference in the binding energy o f 126C and 1680. 508. What is the mass defect of ~6Zn? 509. Complete this radioactive-decay formula: (. ------7 131 Xe + _0e + -v. 54 1 510. Complete this radioactive-decay formula: +< 16ow 74 ------7 1s6Hf 72 .• 511. Complete this radioactive-decay formula: 4 ? ------7 107 52 Te + 2He. 512. A 4.14 x 10-4 g sample of a pure radioactive substance is found after 1.25 days to have only 2.07 x 10-4 g left undecayed. What is the substance's half-life? 513. How long will it take a sample of cadmium-109 Chapter 22 Subatomic Physics 497. Calculate the binding energy of i§K. 498. Determine the difference in the binding energy 1 of ~~Ag and ~§cu. 896 Appendix 1: Additional Problems with a half-life of 462 days to decay to one-fourth its original strength? 514. The half-life of ~~Fe is 2.7 years. What is the decay constant for the isotope?