A GUIDE TO PHYSICS PROBLEMS
PART I: PROBLEMS L MECHANICS 1 1 1 2 1 3 1 4 FALLING CHAIN (MIT, STANFORD) CAT AND MOUSE TUG OF WAR (MOSCOW PHYS-TECH, MIT) CUBE BOUNCING OFF WALL (MOSCOW PHYS-TECH) CUE-STRUCK BILLIARD BALL (RUTGERS, MOSCOW PHYS-TECH, WISCONSIN- MADISON (A)) STABILITY ON ROTATING ROLLERS (PRINCETON) 1 5 1 6 1 7 1 8 1 9 SWAN AND CRAWFISH (MOSCOW PHYS-TECH) MUD FROM TIRE (STONY BROOK) CAR DOWN RAMP UP LOOP (STONY BROOK) PULLING STRINGS (MIT) THRU-EARTH TRAIN (STONY BROOK, BOSTON (A), WISCONSIN- 1 10 MADISON (A)) 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 STRING OSCILLATIONS (MOSCOW PHYS-TECH) HOVERING HELICOPTER (MOSCOW PHYS-TECH) ASTRONAUT TETHER (MOSCOW PHYS-TECH, MICHIGAN) SPIRAL ORBIT (MIT) CENTRAL FORCE WITH ORIGIN ON CIRCLE (MIT, MICHIGAN STATE) CENTRAL FORCE ORBIT (PRINCETON) DUMBBELL SATELLITE (MARYLAND, MIT, MICHIGAN STATE) YUKAWA FORCE ORBIT (STONY BROOK) PARTICLE COLLIDING WITH REFLECTING WALLS (STANFORD) EARTH–COMET ENCOUNTER (PRINCETON) CONTENTS CONTENTS 1 21 1 22 1 23 1 24 1 25 1 26 NEUTRON SCATTERING (MOSCOW PHYS-TECH) COLLISION OF MASS–SPRING SYSTEM (MIT) DOUBLE COLLISION OF MASS–SPRING SYSTEM (MOSCOW PHYS-TECH) SMALL PARTICLE IN BOWL (STONY BROOK) FAST PARTICLE IN BOWL (BOSTON) MASS ORBITING ON TABLE (STONY BROOK, PRINCETON, MARYLAND, MICHIGAN) 1 27 1 28 1 29 1 30 1 31 1 32 1 33 1 34 1 35 1 36 FALLING CHIMNEY (BOSTON, CHICAGO) SLIDING LADDER (PRINCETON, RUTGERS, BOSTON) UNWINDING STRING (MIT, MARYLAND (A,B), CHICAGO (A,B)) SIX UNIFORM RODS (STONY BROOK) PERIOD AS FUNCTION OF ENERGY (MIT) ROTATING PENDULUM (PRINCETON, MOSCOW PHYS-TECH) FLYBALL GOVERNOR (BOSTON, PRINCETON, MIT) DOUBLE PENDULUM (STONY BROOK, PRINCETON, MIT) TRIPLE PENDULUM (PRINCETON) THREE MASSES AND THREE SPRINGS ON HOOP (COLUMBIA, STONY BROOK, MIT) 1 37 1 38 1 39 1 40 1 41 1 42 1 43 1 44 1 45 1 46 1 47 1 48 1 49 1 50 1 51 1 52 NONLINEAR OSCILLATOR (PRINCETON) SWING (MIT, MOSCOW PHYS-TECH) ROTATING DOOR (BOSTON) BUG ON GLOBE (BOSTON) ROLLING COIN (PRINCETON, STONY BROOK) UNSTABLE TOP (STONY BROOK) PENDULUM CLOCK IN NONINERTIAL FRAME (MARYLAND) BEER CAN (PRINCETON, MOSCOW PHYS-TECH) SPACE HABITAT BASEBALL (PRINCETON) VIBRATING STRING WITH MASS (STONY BROOK) SHALLOW WATER WAVES (PRINCETON (A,B)) SUSPENSION BRIDGE (STONY BROOK) CATENARY (STONY BROOK, MIT) ROTATING HOLLOW HOOP (BOSTON) PARTICLE IN MAGNETIC FIELD (STONY BROOK) ADIABATIC INVARIANTS (BOSTON (A)) AND DISSOLVING SPRING (PRINCETON, MIT (B)) 1 53 SUPERBALL IN WEAKENING GRAVITATIONAL FIELD (MICHIGAN STATE) 2 RELATIVITY 2 1 2 2 MARKING STICKS (STONY BROOK) ROCKETS IN COLLISION (STONY BROOK) CONTENTS 2 3 2 4 2 5 2 6 2 7 PHOTON BOX (STONY BROOK) CUBE’S APPARENT ROTATION (STANFORD, MOSCOW PHYS-TECH) RELATIVISTIC ROCKET (RUTGERS) RAPIDITY (MOSCOW PHYS-TECH) CHARGE IN UNIFORM ELECTRIC FIELD (STONY BROOK, MARYLAND, COLORADO) CHARGE IN ELECTRIC FIELD AND FLASHING SATELLITES (MARYLAND) 2 8 2 9 UNIFORMLY ACCELERATED MOTION (STONY BROOK) COMPTON SCATTERING (STONY BROOK, MICHIGAN STATE) 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 MOSSBAUER EFFECT (MOSCOW PHYS-TECH, MIT, COLORADO) POSITRONIUM AND RELATIVISTIC DOPPLER EFFECT (STONY BROOK) TRANSVERSE RELATIVISTIC DOPPLER EFFECT (MOSCOW PHYS-TECH) PARTICLE CREATION (MIT) ELECTRON–ELECTRON COLLISION (STONY BROOK) INVERSE COMPTON SCATTERING (MIT, MARYLAND) PROTON–PROTON COLLISION (MIT) PION CREATION AND NEUTRON DECAY (STONY BROOK) ELASTIC COLLISION AND ROTATION ANGLE (MIT) 3 ELECTRODYNAMICS 3 1 3 2 3 3 3 4 CHARGE DISTRIBUTION (WISCONSIN-MADISON) ELECTROSTATIC FORCES AND SCALING (MOSCOW PHYS-TECH) DIPOLE ENERGY (MIT, MOSCOW PHYS-TECH) CHARGED CONDUCTING SPHERE IN CONSTANT ELECTRIC FIELD (STONY BROOK, MIT) 3 5 3 6 3 7 3 8 3 9 CHARGE AND CONDUCTING SPHERE I (MIT) CHARGE AND CONDUCTING SPHERE II (BOSTON) CONDUCTING CYLINDER AND LINE CHARGE (STONY BROOK, MICHIGAN STATE) SPHERICAL VOID IN DIELECTRIC (PRINCETON) CHARGE AND DIELECTRIC (BOSTON) 3 10 3 11 3 12 3 13 3 14 DIELECTRIC CYLINDER IN UNIFORM ELECTRIC FIELD (PRINCETON) POWDER OF DIELECTRIC SPHERES (STONY BROOK) CONCENTRIC SPHERICAL CAPACITOR (STONY BROOK) NOT-SO-CONCENTRIC SPHERICAL CAPACITOR (MICHIGAN TECH) PARALLEL PLATE CAPACITOR WITH SOLID DIELECTRIC (STONY BROOK, MICHIGAN TECH, MICHIGAN) 3 15 3 16 3 17 PARALLEL PLATE CAPACITOR IN DIELECTRIC BATH (MIT) NOT-SO-PARALLEL PLATE CAPACITOR (PRINCETON (A), RUTGERS (B)) CYLINDRICAL CAPACITOR IN DIELECTRIC BATH (BOSTON, MARYLAND) CONTENTS 3 18 3 19 3 20 3 21 3 22 3 23 3 24 3 25 3 26 3 27 3 28 3 29 3 30 3 31 3 32 3 33 3 34 3 35 3 36 3 37 3 38 3 39 3 40 3 41 3 42 3 43 3 44 3 45 3 46 3 47 3 48 3 49 3 50 3 51 3 52 3 53 3 54 ITERATED CAPACITANCE (STONY BROOK) RESISTANCE VS CAPACITANCE (BOSTON, RUTGERS (A)) CHARGE DISTRIBUTION IN INHOMOGENEOUS MEDIUM (BOSTON) GREEN’S RECIPROCATION THEOREM (STONY BROOK) COAXIAL CABLE AND SURFACE CHARGE (PRINCETON) POTENTIAL OF CHARGED ROD (STONY BROOK) PRINCIPLE OF CONFORMAL MAPPING (BOSTON) POTENTIAL ABOVE HALF PLANES (PRINCETON) POTENTIAL OF HALVED CYLINDER (BOSTON, PRINCETON, CHICAGO) RESISTANCE OF A WASHER (MIT) SPHERICAL RESISTOR (MICHIGAN STATE) INFINITE RESISTOR LADDER (MOSCOW PHYS-TECH) SEMI-INFINITE PLATE (MOSCOW PHYS-TECH) MAGNETIC FIELD IN CENTER OF CUBE (MOSCOW PHYS-TECH) MAGNETIC DIPOLE AND PERMEABLE MEDIUM (PRINCETON) MAGNETIC SHIELDING (PRINCETON) ELECTROMOTIVE FORCE IN SPIRAL (MOSCOW PHYS-TECH) SLIDING COPPER ROD (STONY BROOK, MOSCOW PHYS-TECH) LOOP IN MAGNETIC FIELD (MOSCOW PHYS-TECH, MIT) CONDUCTING SPHERE IN CONSTANT MAGNETIC FIELD (BOSTON) MUTUAL INDUCTANCE OF LINE AND CIRCLE (MICHIGAN) FARADAY’S HOMOPOLAR GENERATOR (STONY BROOK, MICHIGAN) CURRENT IN WIRE AND POYNTING VECTOR (STONY BROOK, MIT) BOX AND IMPULSIVE MAGNETIC FIELD (BOSTON) COAXIAL CABLE AND POYNTING VECTOR (RUTGERS) ANGULAR MOMENTUM OF ELECTROMAGNETIC FIELD (PRINCETON) PLANE WAVE IN DIELECTRIC (STONY BROOK, MICHIGAN) X-RAY MIRROR (PRINCETON) PLANE WAVE IN METAL (COLORADO, MIT) WAVE ATTENUATION (STONY BROOK) ELECTRONS AND CIRCULARLY POLARIZED WAVES (BOSTON) CLASSICAL ATOMIC SPECTRAL LINE (PRINCETON, WISCONSIN-MADISON) LIFETIME OF CLASSICAL ATOM (MIT, PRINCETON, STONY BROOK) LORENTZ TRANSFORMATION OF FIELDS (STONY BROOK) FIELD OF A MOVING CHARGE (STONY BROOK) RETARDED POTENTIAL OF MOVING LINE CHARGE (MIT) ORBITING CHARGES AND MULTIPOLE RADIATION (PRINCETON, MICHIGAN STATE, MARYLAND) 3 55 3 56 3 57 3 58 ELECTRON AND RADIATION REACTION (BOSTON) RADIATION OF ACCELERATING POSITRON (PRINCETON, COLORADO) HALF-WAVE ANTENNA (BOSTON) RADIATION (STONY BROOK) CONTENTS 3 59 3 60 3 61 STABILITY OF PLASMA (BOSTON) CHARGED PARTICLE IN UNIFORM MAGNETICFIELD (PRINCETON) LOWEST MODE OF RECTANGULAR WAVE GUIDE (PRINCETON, MIT, MICHIGAN STATE) 3 62 3 63 TM MODES IN RECTANGULAR WAVE GUIDE (PRINCETON) BETATRON (PRINCETON, MOSCOW PHYS-TECH, COLORADO, STONY BROOK (A)) 3 64 3 65 SUPERCONDUCTING FRAME IN MAGNETIC FIELD (MASCOW PHYS-TECH) SUPERCONDUCTING SPHERE IN MAGNETIC FIELD (MICHIGAN STATE, MOSCOW PHYS- TECH) 3 66 3 67 LONDON PENETRATION DEPTH (MOSCOW PHYS-TECH) THIN SUPERCONDUCTING PLATE IN MAGNETIC FIELD (STONY BROOK) PART II: SOLUTIONS L MECHANICS 1 1 1 2 1 3 1 4 FALLING CHAIN (MIT, STANFORD) CAT AND MOUSE TUG OF WAR (MOSCOW PHYS-TECH, MIT) CUBE BOUNCING OFF WALL (MOSCOW PHYS-TECH) CUE-STRUCK BILLIARD BALL (RUTGERS, MOSCOW PHYS-TECH, WISCONSIN- 1 5 1 6 1 7 1 8 1 9 MADISON (A)) STABILITY ON ROTATING ROLLERS (PRINCETON) SWAN AND CRAWFISH (MOSCOW PHYS-TECH) MUD FROM TIRE (STONY BROOK) CAR DOWN RAMP UP LOOP (STONY BROOK) PULLING STRINGS (MIT) 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 THRU-EARTH TRAIN (STONY BROOK, BOSTON (A), WISCONSIN-MADISON (A)) STRING OSCILLATIONS (MOSCOW PHYS-TECH) HOVERING HELICOPTER (MOSCOW PHYS-TECH) ASTRONAUT TETHER (MOSCOW PHYS-TECH, MICHIGAN) SPIRAL ORBIT (MIT) CENTRAL FORCE ORBIT (PRINCETON) DUMBBELL SATELLITE (MARYLAND, MIT, MICHIGAN STATE) YUKAWA FORCE ORBIT (STONY BROOK) PARTICLE COLLIDING WITH REFLECTING WALLS (STANFORD) EARTH–COMET ENCOUNTER (PRINCETON) NEUTRON SCATTERING (MOSCOW PHYS-TECH) CENTRAL FORCE WITH ORIGIN ON CIRCLE (MIT, MICHIGAN STATE) CONTENTS 1 22 1 23 1 24 1 25 1 26 COLLISION OF MASS–SPRING SYSTEM (MIT) DOUBLE COLLISION OF MASS–SPRING SYSTEM (MOSCOW PHYS-TECH) SMALL PARTICLE IN BOWL (STONY BROOK) FAST PARTICLE IN BOWL (BOSTON) MASS ORBITING ON TABLE (STONY BROOK, PRINCETON, MARYLAND, MICHIGAN) 1 27 1 28 1 29 1 30 1 31 1 32 1 33 1 34 1 35 1 36 FALLING CHIMNEY (BOSTON, CHICAGO) SLIDING LADDER (PRINCETON, RUTGERS, BOSTON) UNWINDING STRING (MIT, MARYLAND (A,B), CHICAGO (A,B)) SIX UNIFORM RODS (STONY BROOK) PERIOD AS FUNCTION OF ENERGY (MIT) ROTATING PENDULUM (PRINCETON, MOSCOW PHYS-TECH) FLYBALL GOVERNOR (BOSTON, PRINCETON, MIT) DOUBLE PENDULUM (STONY BROOK, PRINCETON, MIT) TRIPLE PENDULUM (PRINCETON) THREE MASSES AND THREE SPRINGS ON HOOP (COLUMBIA, STONY BROOK, MIT) 1 37 1 38 1 39 1 40 1 41 1 42 1 43 1 44 1 45 1 46 1 47 1 48 1 49 1 50 1 51 1 52 NONLINEAR OSCILLATOR (PRINCETON) SWING (MIT, MOSCOW PHYS-TECH) ROTATING DOOR (BOSTON) BUG ON GLOBE (BOSTON) ROLLING COIN (PRINCETON, STONY BROOK) UNSTABLE TOP (STONY BROOK) PENDULUM CLOCK IN NONINERTIAL FRAME (MARYLAND) BEER CAN (PRINCETON, MOSCOW PHYS-TECH) SPACE HABITAT BASEBALL (PRINCETON) VIBRATING STRING WITH MASS (STONY BROOK) SHALLOW WATER WAVES (PRINCETON (A,B)) SUSPENSION BRIDGE (STONY BROOK) CATENARY (STONY BROOK, MIT) ROTATING HOLLOW HOOP (BOSTON) PARTICLE IN MAGNETIC FIELD (STONY BROOK) ADIABATIC INVARIANTS (BOSTON (A)) AND DISSOLVING SPRING (PRINCETON, MIT (B)) 1 53 SUPERBALL IN WEAKENING GRAVITATIONAL FIELD (MICHIGAN STATE) 2 RELATIVITY 2 1 2 2 2 3 MARKING STICKS (STONY BROOK) ROCKETS IN COLLISION (STONY BROOK) PHOTON BOX (STONY BROOK) CONTENTS 2 4 2 5 2 6 2 7 CUBE’S APPARENT ROTATION (STANFORD, MOSCOW PHYS-TECH) RELATIVISTIC ROCKET (RUTGERS) RAPIDITY (MOSCOW PHYS-TECH) CHARGE IN UNIFORM ELECTRIC FIELD (STONY BROOK, MARYLAND, COLORADO) 2 8 2 9 CHARGE IN ELECTRIC FIELD AND FLASHING SATELLITES (MARYLAND) UNIFORMLY ACCELERATED MOTION (STONY BROOK) 2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 COMPTON SCATTERING (STONY BROOK, MICHIGAN STATE) MÖSSBAUER EFFECT (MOSCOW PHYS-TECH, MIT, COLORADO) POSITRONIUM AND RELATIVISTIC DOPPLER EFFECT (STONY BROOK) TRANSVERSE RELATIVISTIC DOPPLER EFFECT (MOSCOW PHYS-TECH) PARTICLE CREATION (MIT) ELECTRON–ELECTRON COLLISION (STONY BROOK) INVERSE COMPTON SCATTERING (MIT, MARYLAND) PROTON–PROTO N COLLISION (MIT) PION CREATION AND NEUTRON DECAY (STONY BROOK) ELASTIC COLLISION AND ROTATION ANGLE (MIT) 3 ELECTRODYNAMICS 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 CHARGE DISTRIBUTION (WISCONSIN-MADISON) ELECTROSTATIC FORCES AND SCALING (MOSCOW PHYS-TECH) DIPOLE ENERGY (MIT, MOSCOW PHYS-TECH) CHARGED CONDUCTING SPHERE IN CONSTANT ELECTRIC FIELD (STONY BROOK, MIT) CHARGE AND CONDUCTING SPHERE I (MIT) CHARGE AND CONDUCTING SPHERE II (BOSTON) CONDUCTING CYLINDER AND LINE CHARGE (STONY BROOK, MICHIGAN STATE) SPHERICAL VOID IN DIELECTRIC (PRINCETON) CHARGE AND DIELECTRIC (BOSTON) DIELECTRIC CYLINDER IN UNIFORM ELECTRIC FIELD (PRINCETON) POWDER OF DIELECTRIC SPHERES (STONY BROOK) CONCENTRIC SPHERICAL CAPACITOR (STONY BROOK) NOT-SO-CONCENTRIC SPHERICAL CAPACITOR (MICHIGAN TECH) PARALLEL PLATE CAPACITOR WITH SOLID DIELECTRIC (STONY BROOK, MICHIGAN TECH, MICHIGAN) PARALLEL PLATE CAPACITOR IN DIELECTRIC BATH (MIT) NOT-SO-PARALLEL PLATE CAPACITOR (PRINCETON (A), RUTGERS (B)) CYLINDRICAL CAPACITOR IN DIELECTRIC BATH (BOSTON, MARYLAND) ITERATED CAPACITANCE (STONY BROOK) CONTENTS 3 19 3 20 3 21 3 22 3 23 3 24 3 25 3 26 3 27 3 28 3 29 3 30 3 31 3 32 3 33 3 34 3 35 3 36 3 37 3 38 3 39 3 40 3 41 3 42 3 43 3 44 3 45 3 46 3 47 3 48 3 49 3 50 3 51 3 52 3 53 3 54 3 55 3 56 3 57 3 58 3 59 RESISTANCE VS CAPACITANCE (BOSTON, RUTGERS (A)) CHARGE DISTRIBUTION IN INHOMOGENEOUS MEDIUM (BOSTON) GREEN’S RECIPROCATION THEOREM (STONY BROOK) COAXIAL CABLE AND SURFACE CHARGE (PRINCETON) POTENTIAL OF CHARGED ROD (STONY BROOK) PRINCIPLE OF CONFORMAL MAPPING (BOSTON) POTENTIAL ABOVE HALF PLANES (PRINCETON) POTENTIAL OF HALVED CYLINDER (BOSTON, PRINCETON, CHICAGO) RESISTANCE OF A WASHER (MIT) SPHERICAL RESISTOR (MICHIGAN STATE) INFINITE RESISTOR LADDER (MOSCOW PHYS-TECH) SEMI-INFINITE PLATE (MOSCOW PHYS-TECH) MAGNETIC FIELD IN CENTER OF CUBE (MOSCOW PHYS-TECH) MAGNETIC DIPOLE AND PERMEABLE MEDIUM (PRINCETON) MAGNETIC SHIELDING (PRINCETON) ELECTROMOTIVE FORCE IN SPIRAL (MOSCOW PHYS-TECH) SLIDING COPPER ROD (STONY BROOK, MOSCOW PHYS-TECH) LOOP IN MAGNETIC FIELD (MOSCOW PHYS-TECH, MIT) CONDUCTING SPHERE IN CONSTANT MAGNETIC FIELD (BOSTON) MUTUAL INDUCTANCE OF LINE AND CIRCLE (MICHIGAN) FARADAY’S HOMOPOLAR GENERATOR (STONY BROOK, MICHIGAN) CURRENT IN WIRE AND POYNTING VECTOR (STONY BROOK, MIT) BOX AND IMPULSIVE MAGNETIC FIELD (BOSTON) COAXIAL CABLE AND POYNTING VECTOR (RUTGERS) ANGULAR MOMENTUM OF ELECTROMAGNETIC FIELD (PRINCETON) PLANE WAVE IN DIELECTRIC (STONY BROOK, MICHIGAN) X-RAY MIRROR (PRINCETON) PLANE WAVE IN METAL (COLORADO, MIT) WAVE ATTENUATION (STONY BROOK) ELECTRONS AND CIRCULARLY POLARIZED WAVES (BOSTON) CLASSICAL ATOMIC SPECTRAL LINE (PRINCETON, WISCONSIN-MADISON) LIFETIME OF CLASSICAL ATOM (MIT, PRINCETON, STONY BROOK) LORENTZ TRANSFORMATION OF FIELDS (STONY BROOK) FIELD OF A MOVING CHARGE (STONY BROOK) RETARDED POTENTIAL OF MOVING LINE CHARGE (MIT) ORBITING CHARGES AND MULTIPOLE RADIATION (PRINCETON, MICHIGAN STATE,MARYLAND) ELECTRON AND RADIATION REACTION (BOSTON) RADIATION OF ACCELERATING POSITRON (PRINCETON, COLORADO) HALF-WAVE ANTENNA (BOSTON) CERENKOV RADIATION (STONY BROOK) STABILITY OF PLASMA (BOSTON) CONTENTS 3 60 3 61 CHARGED PARTICLE IN UNIFORM MAGNETIC FIELD (PRINCETON) LOWEST MODE OF RECTANGULAR WAVE GUIDE (PRINCETON, MIT, MICHIGAN STATE) 3 62 3 63 TM MODES IN RECTANGULAR WAVE GUIDE (PRINCETON) BETATRON (PRINCETON, MOSCOW PHYS-TECH, COLORADO, STONY BROOK (A)) 3 64 3 65 3 66 3 67 SUPERCONDUCTING FRAME IN MAGNETIC FIELD (MOSCOW PHYS-TECH) SUPERCONDUCTING SPHERE IN MAGNETIC FIELD (MICHIGAN STATE, MOSCOW PHYS-TECH) LONDON PENETRATION DEPTH (MOSCOW PHYS-TECH) THIN SUPERCONDUCTING PLATE IN MAGNETIC FIELD (STONY BROOK)