Brainteaser Physics: Challenging Physics Puzzlers

Index

Index airport, walkway in, 108 air pressure: effect on window, 74; in Mariotte’s bottle, 50–53; in sauna, 73–76; variation of, 39–40 air resistance, 96–103, 114–15, 141 alternating current, 47, 56, 60, 93 Ampère, André-Marie, 47 anthropometric data, 111 anthropomorphic argument, 120 aqueduct, 1, 7–8 Archimedes, 65–66 Archimedes’ principle, 5–7, 65–66, 76, 78 artwork, mirror shown in, 130, 138, 145 atmospheric pressure. See air pressure atoms, number in grain of sand, 109, 115–16, 126 Avogadro’s constant, 115, 124 balance, faulty, 127, 134, 144 ball, air resistance on, 96–103, 114–15 balloon, 81, 90–92 bar magnet, 127, 132 barrel, filling with water, 57–58, 67– 68 bathymetry, 50 Benford’s law, 142–43 Bernoulli’s equation, 8, 51, 68 Betz theorem, 38 bicycle: with low tire pressure, 32, 41–42, 54; pedal motion of, 31, 34–36, 59; pulled by rope, 55, 59; track from, 131, 139 billion, meaning of word, 116–17 Biot-Savart’s formula, 61 black body radiation, 117–18 boat: in lock, 55–56, 60; in pond, 1, 5–6 books: in pile, 2–3, 14–17; sliding, 79, 85–86 bottle, Mariotte’s, 33–34, 50–53 Boyle’s law, 52 box, forces on, 79, 83–84, 128, 136– 37 brass, data for, 110 brick stones, stability of, 17, 29–30 Brunelleschi, 80 building code for elevators, 77 buoyancy, 7, 76–78, 90–91 calorie, 118 candle, floating, 2, 8–9 ? ≥ Ω + √ > cm ? π < = ≈ ≤ AB = 1 Ω = ? capacitance: of Earth, 61; symbol for, 62; the unit pF, 56–57, 61 capacitor, energy of, 4, 23–24 car: filling fuel tank in, 32, 45–46; worn tires and odometer reading, 42 Carroll, Lewis, 29 catenary, 129, 137 center of gravity: of book pile, 14–15; of candle, 2; of chain, 129, 137; of hammer (sports implement), 129; of L-shaped figure, 128, 135–36; of pendulum with shoe, 141; of shot-putting shot, 109, 113–14; of yin and yang symbol, 95 chain, center of gravity of, 129, 137 characteristic quantity: length, 25, 70, 101, 103; speed, 103; time, 27, 119, 122 charge, electric, 61–62 Charles, J. A. C., 92 cloud droplets, 102 coffee cooling, 109, 117–20 collision time, 109, 120–23 Columbus, egg of, 79–80, 87 compass, magnetic, 33, 46–48 conductivity, thermal, in gas, 24–25 contact time, in collision, 109, 120–23 continuity equation, 38 convection, cooling effect of, 117, 119–20 convergence rate, exponential, 21 cooling law, Newton’s, 119 cube, of resistors, 3, 17–19 cycloid, 36 damping: in electric circuit, 23–24; of pendulum, 141–42 density: of Earth, 26–28; of elements ,6; of human body, 110; of ice, 65; of water, 46, 65; of wood, 63–64 digit, first in data sets, 142–44 dimensional analysis, 27–28, 71, 105, 122–23 dinghy: in high gravity, 78; in pool, 1, 5–6, 29 distance in networks, 18 drag coefficient, 96–103, 114–15 Earth: capacitance of, 61; density of, 26–28; magnetic field from, 33, 46–48, 54; shape of, 33, 48–49; tunnel through, 4, 25–29 educated guess, 27, 121–22 efficiency of turbines, 38–39 egg, boiling on Mount Everest, 39 egg of Columbus, 79–80, 87 Einstein, on thought experiment, 122 elastic wave, 120–21 electric network. See network, electric electromagnetic wave, 23 electron: charge of, 61; mean free path of, 126 elevator, 59, 76–77, 83, 103–7 emissivity, 118 Empire State Building, dropped penny from, 102–103 energy: in sauna, 58, 73–76; stored in capacitor, 4, 23–24 energy data in EU, 132–33, 143 entropy: absolute value of, 76; of mixing in gas, 124–25 estimation of quantities: air resistance on ball, 98; atoms in sand grain, 115–17; brick falling on elevator , 107; energy consumption in EU, 142; Fermi problem, 125; pendulum period, 141–42; resistivity of tungsten, 93; speed of sound in brass, 121; temperature increase in water fall, 37; water level in pool, 5; water molecules from Socrates’ blood, 124–26 158 index Euclid, 128 EU energy statistics, 132–33, 142– 43 evaporation, cooling effect of, 117, 119–20 expansion, thermal, 5, 7, 45–46 factor of safety in elevator, 77 farad, 56–57, 61–62 Faraday’s cage, 26 Fermat’s principle, 43 Fermi problem, 125 filament, in lightbulb, 93–94 floating body, orientation of, 63–67 Franklin, Benjamin, 92 free fall, 97–98, 102–4 frequency of alternating current, 47, 56, 60 friction, 69–72, 84–87, 128, 136 fuel tank, 32, 45–46 gas: equation of state for, 73: heat capacity of, 75; kinetic theory of, 24, 73, 75; thermal conductivity of, 24 gasoline, 32, 45–46 Gedankenexperiment, 6, 122 generator: on bicycle wheel, 35; in waterfall, 38–39 geometry, Greek, 128, 135 global warming, 7 gradient, 49–50 granular matter, 70 gravitation, Earth’s, 25–29, 48–50 gravity, jolt of, 58–59, 76–78 Greek geometry, 128, 135 hammer throwing (sports), 109, 114–15, 129, 138–39 harbor, best location of, 32–33, 43– 44 heat capacity: of gas molecule, 75; of water, 37, 118 helium in balloon, 81, 90–92 Hertz’s collision formula, 121–23 Hindenburg (airship), 92 Hook, Robert, 28 human body, volume of, 108, 110–11 humming of transformer, 56, 60–61 hydroelectric power, 31, 37–39 hydrogen in balloon, 81, 90–92 IAAF (International Association of Athletics Federations), 109, 129, 138–39 ice: density of, 65; floating in water, 1, 6–7, 29 iceberg, 64–65 idealization in physics models: bricks falling over edge, 17; dinghy in pool, 6; energy from waterfall, 37–40; energy loss in capacitors, 23–25 incandescent lamp, 82, 92–94 inch (unit), 111 instability. See stability iron bar, magnetic, 127, 132 Janssen’s formula, 71–72 jogging shoe, 140 Johns Hopkins University Press, 144 Joule, James Prescott, 40 Kelvin, Lord, 40 kilogram, definition of, 111 kinetic gas theory, 24, 73, 75 lamp, electric, 31–32, 40–41, 62, 94–95, 131–32, 139–40, 145 lift. See elevator lightbulb, 81–82, 92–95, 131–32, 139–40, 145 liquids, thermal expansion of, 5, 7, 45–46 lock for boats, 8, 55, 60 index 159 magnetic field: from Earth, 33, 46– 48, 54; near wire, 33, 46–48 magnetic iron bar, 127, 132 Manet, Édouard (painter), 145 Mariotte, Edme, 52 Mariotte’s bottle, 33–34, 50–53 Maxwell’s screw rule, 47 mean free path: of electron, 126; in gas, 25 Metamorphoses (poem), 116 meter, definition of, 27 metric, for distance in networks, 18 Michelson-Morley experiment, 113 Millikan, Robert A., 61 mirror. See reflection Montgolfier brothers, 91 Mount Everest, boiling egg on, 39 nano, used as prefix, 62–63 network, electric: brightness of three lamps, 31–32, 40–41; connected as Platonic bodies, 18–19; discharging two capacitors, 4, 23–25; resistor cube, 3, 17–19; resistor ladder, 3, 20–23; resistor tetrahedron , 19, 30; rules for simplifying , 19; with unequal lamps in series , 62, 94–95; with unknown wiring, 131–32, 139–40, 145; Wheatstone bridge, 41, 53 Newcomb, Simon, 144 Newton, letter from Hooke to, 28 Newton’s cooling law, 119 Newton’s cradle, 123 Niagara Falls, 31 north pole, 47–48, 54 ocean: density of water in, 65, 111; global warming effect on, 7; shape of surface, 7, 33, 48–50; volume of, 124 odometer, 42 Olympic games, 109, 114 optical reflection, 43–45, 130, 138, 145 order of magnitude, 27–28, 143 orienteering (sports), 47–48 Ørsted, Hans Christian, 47 oscillatory motion: when discharging capacitors, 23–24; of shoe in shoestring , 140–42; of train in Earth tunnel, 25–29 overhang, 2–3, 14–17, 29–30 Ovid (poet), 116 painting showing mirror, 138, 145 paradox in physics, 6, 23–25 Pascal’s experiment, 69 pendulum, period of, 140–42 perturbation theory, 100 Platonic bodies formed by resistors, 18–19 pole vaulting, 109, 113–14 pool, water level in, 1, 5–6, 29 power line over compass, 33, 46–47 powers of ten, names of, 116–17 prefix for powers of ten, 56, 62–63 pressure: in bike tire, 32, 41–42, 54; effect on window pane, 74; in Mariotte’s bottle, 50–53; in sauna, 73–76; SI unit for, 121; in tube with sand, 68–72; variation in atmosphere , 39–40 pulse beats, 132, 140–42 quantum mechanics: and molecular energy, 75; and thought experiment , 6 quark, charge of, 62 radiation: electromagnetic during discharge, 23; thermal from water, snow, and paint, 117–18 railway: shortest to harbor, 32–33, 160 index 43–45; in tunnel through Earth, 4, 25–29 raindrop, 11–13, 102 rain, running in, 2, 9–14 reflection: as analogy for harbor location , 43–45; shown in painting, 138, 145; in water, 130, 138 resistivity, temperature dependence of, 93–94 resistor, color code on, 21 resistors. See network, electric Reynolds number, 102 right hand rule, 47–48 Rokeby Venus, The (painting), 138 safety factor in elevator, 77 sand, 58, 68, 109, 115–16, 126 satellite: measuring ocean level by, 50; orbiting time of, 27–28 sauna, 58, 73–76 Schrödinger’s cat, 6 screw rule, 47 second law of thermodynamics, 124 shot (sports implement), 57, 66 shot putting, 109, 113–14 Sibyl (poem character), 116 significant digits, 142–44 silo, 71 SI unit: for capacitance (farad), 56; for charge (coulomb), 62; comparison with American and British unit, 111; for density, 5; for length (meter), 27; for mass (kg), 111; for pressure (pascal), 121; symbol for liter, 66; used in dimensional reasoning , 27, 71 Slapstick (novel), 58–59, 76 Snell’s refraction law, 45 snow, as black in infrared, 118 Socrates, 110, 123–24, 126 sound propagation in solid, 120–21 specific heat of water, 37, 118 stability: of book pile and bricks, 2– 3, 14–17, 29–30; of floating bar and iceberg, 63–66; of hammer (sport implement), 138–39; of pushed sugar box, 136 stadium, for sports records, 109, 114 statistics, fake, 132–33, 142–43 Stefan-Boltzmann’s radiation law, 117–18 sugar box, friction from table, 128, 136–37 suspension bridge, shape of, 137 switches in unknown network, 131, 139–40, 141 table tennis ball, 102 tank: emptying of, 24, 57–58, 67–68; for gasoline, 32, 45–46 temperature: of coffee, 117–20; in sauna, 58, 73–76 tennis ball, 83, 100–102 terminal speed, 12, 102–3 tetrahedron of resistors, 19, 30 thermal conductivity of gas, 24 thermal expansion, 5, 7, 45–46 thermodynamics, second law of, 124 thought experiment, 6, 122 thumb rule, 47–48 Time (magazine), 28 tire: of bicycle, 32, 41–42, 54; worn, on car, 42 Torricelli’s principle, 52 track from bicycle, 131, 139 train, in Earth tunnel, 4, 25–29 transformer, humming from, 56, 60–61 tungsten, resistivity of, 93–94 tunnel, for train through Earth, 4, 25–29 turbine, power from, 31, 37–39 twin paradox, 6 index 161 underwater mountain, 33, 48–50 unit. See SI unit Velásquez, Diego (painter), 138 Verne, Jules, 64–65 volume: of human body, 108, 110– 11; of oceans, 124 Vonnegut, Kurt, 58, 77 walkway, in airport, 108 warming, global and ocean level, 7 water: density of, 46, 65; emissivity of, 118; heat capacity of, 37, 118; radiation properties of, 118; thermal expansion of, 5, 7, 46 waterfall, 31, 37–40 water mill, efficiency of, 38–39 water tank, emptying of, 24, 57–58, 67–68 wave: elastic in collision, 120–21; electromagnetic during discharge, 23 weighing, using balance, 127, 134, 144–45 Wheatstone bridge, 41, 53 windmill, power of, 38 window glass, bending under pressure , 74 yin and yang symbol, 82, 95, 96 162 index ...