Why Cats Land on Their Feet
And 76 Other Physical Paradoxes and Puzzles
1st Edition
Published on 27. May 2012
208 pages
978-1-4008-4172-1 (ISBN)
Description
How to use physical reasoning to solve surprising paradoxes
Ever wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? Why Cats Land on Their Feet is a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. And the surprising answers to virtually all of these astonishing paradoxes can be arrived at with no formal knowledge of physics.
Mark Levi introduces each physical problem, sometimes gives a hint or two, and then fully explains the solution. Here readers can test their critical-thinking skills against a whole assortment of puzzles and paradoxes involving floating and diving, sailing and gliding, gymnastics, bike riding, outer space, throwing a ball from a moving car, centrifugal force, gyroscopic motion, and, of course, falling cats.
Want to figure out how to open a wine bottle with a book? Or how to compute the square root of a number using a tennis shoe and a watch? Why Cats Land on Their Feet shows you how, and all that's required is a familiarity with basic high-school mathematics. This lively collection also features an appendix that explains all physical concepts used in the book, from Newton's laws to the fundamental theorem of calculus.
Ever wonder why cats land on their feet? Or what holds a spinning top upright? Or whether it is possible to feel the Earth's rotation in an airplane? Why Cats Land on Their Feet is a compendium of paradoxes and puzzles that readers can solve using their own physical intuition. And the surprising answers to virtually all of these astonishing paradoxes can be arrived at with no formal knowledge of physics.
Mark Levi introduces each physical problem, sometimes gives a hint or two, and then fully explains the solution. Here readers can test their critical-thinking skills against a whole assortment of puzzles and paradoxes involving floating and diving, sailing and gliding, gymnastics, bike riding, outer space, throwing a ball from a moving car, centrifugal force, gyroscopic motion, and, of course, falling cats.
Want to figure out how to open a wine bottle with a book? Or how to compute the square root of a number using a tennis shoe and a watch? Why Cats Land on Their Feet shows you how, and all that's required is a familiarity with basic high-school mathematics. This lively collection also features an appendix that explains all physical concepts used in the book, from Newton's laws to the fundamental theorem of calculus.
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05/2012
Princeton University Press
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Mark Levi is professor of mathematics at Pennsylvania State University. He is the author of The Mathematical Mechanic: Using Physical Reasoning to Solve Problems.
Content
Chapter 1 Fun with Physical Paradoxes, Puzzles, and Problems 1
1.1 Introduction 1
1.2 Background 3
1.3 Sources 3
Chapter 2 Outer Space Paradoxes 5
2.1 A Helium Balloon in a Space Shuttle 5
2.2 Space Navigation without Jets 9
2.3 A Paradox with a Comet 13
2.4 Speeding Up Causes a Slowdown 14
Chapter 3 Paradoxes with Spinning Water 17
3.1 A Puzzle with a Floating Cork 17
3.2 Parabolic Mirrors and Two Kitchen Puzzles 19
3.3 A Cold Parabolic Dish 21
3.4 Boating on a Slope 23
3.5 Navigating with No Engine or Sails 24
3.6 The Icebergs 25
Chapter 4 Floating and Diving Paradoxes 28
4.1 A Bathtub on Wheels 28
4.2 The Tub Problem--In More Depth 30
4.3 How to Lose Weight in a Fraction of a Second 32
4.4 An Underwater Balloon 33
4.5 A Scuba Puzzle 35
4.6 A Weight Puzzle 36
Chapter 5 Flows and Jets 39
5.1 Bernoulli's Law and Water Guns 39
5.2 Sucking on a Straw and the Irreversibility of Time 42
5.3 Bernoulli's Law and Moving Around in a Space Shuttle 44
5.4 A Sprinker Puzzle 45
5.5 Ejecting Water Fast but with Zero Speed? 48
5.6 A Pouring Water Puzzle 49
5.7 A Stirring Paradox 51
5.8 An Inkjet Printer Question 54
5.9 A Vorticity Paradox 55
Chapter 6 Moving Experiences: Bikes, Gymnastics,
Rockets 57
6.1 How Do Swings Work? 57
6.2 The Rising Energy Cost 58
6.3 A Gymnast Doing Giants and a Hamster in a Wheel 60
6.4 Controlling a Car on Ice 63
6.5 How Does a Biker Turn? 64
6.6 Speeding Up by Leaning 65
6.7 Can One Gain Speed on a Bike by Body Motion Only? 66
6.8 Gaining Weight on a Motorbike 68
6.9 Feeling the Square in mv2 2 Through the Bike Pedals 69
6.10 A Paradox with Rockets 70
6.11 A Coffee Rocket 72
6.12 Throwing a Ball from a Moving Car 74
Chapter 7 Paradoxes with the Coriolis Force 77
7.1 What Is the Coriolis Force? 77
7.2 Feeling Coriolis in a Boeing 747 79
7.3 Down the Drain with Coriolis 80
7.4 High Pressure and Good Weather 80
7.5 What Causes Trade Winds? 82
Chapter 8 Centrifugal Paradoxes 84
8.1 What's Cheaper: Flying West or East? 84
8.2 A Coriolis Paradox 85
8.3 An Amazing Inverted Pendulum: What Holds It Up? 87
8.4 Antigravity Molasses 91
8.5 The "Proof" That the Sling Cannot Work 92
8.6 A David-Goliath Problem 93
8.7 Water in a Pipe 97
8.8 Which Tension Is Greater? 98
8.9 Slithering Ropes in Weightlessness 100
Chapter 9 Gyroscopic Paradoxes 104
9.1 How Does the Spinning Top Defy Gravity? 104
9.2 Gyroscopes in Bikes 108
9.3 A Rolling Coin 109
9.4 Staying on a Slippery Dome 111
9.5 Finding North with a Gyroscope 113
Chapter 10 Some Hot Stuff and Cool Things 117
10.1 Can Heat Pass from a Colder to a Hotter Object? 117
10.2 A Bike Pump and Molecular Ping-Pong 121
10.3 A Bike Pump as a Heat Pump 122
10.4 Heating a Room in Winter 124
10.5 Freezing Things with a Bike Tire 125
Chapter 11 Two Perpetual Motion Machines 127
11.1 Perpetual Motion by Capillarity 128
11.2 An Elliptical Mirror Perpetuum Mobile 129
Chapter 12 Sailing and Gliding 132
12.1 Shooting Cherry Pits and Sailing 133
12.2 Sailing Straight into the Wind 135
12.3 Biking against the Wind 136
12.4 Soaring without Updrafts 138
12.5 Danger of the Horizontal Shear Wind 141
Chapter 13 The Flipping Cat and the Spinning Earth 142
13.1 How Do Cats Flip to Land on Their Feet? 142
13.2 Can Trade Winds Slow Earth's Rotation? 144
Chapter 14 Miscellaneous 146
14.1 How to Open a Wine Bottle with a Book 146
14.2:"t's Alive!" 149
14.3 Falling Faster Than g: A Falling Chain "Sucked in" by the Floor 150
14.4 A Man in a Boat with Drag 151
14.5 A "Phantom" Boat: No Wake and No Drag 154
14.6 A Constant-G Roller Coaster 156
14.7 Shooting at a Cart 158
14.8 Computing v2 with a Shoe 159
Appendix 161
A.1 Newton's Laws 161
A.2 Kinetic Energy, Potential Energy, Work 163
A.2.1 Work 163
A.2.2 Kinetic Energy 165
A.2.3 Potential Energy 166
A.2.4 Conservation of Energy 168
A.3 Center of Mass 169
A.4 Linear Momentum 171
A.5 The Torque 174
A.6 Angular Momentum 175
A.7 Angular Velocity, Centripetal Acceleration 178
A.8 Centrifugal and Centripetal Forces 181
A.9 Coriolis, Centrifugal, and Complex Exponentials 181
A.10 The Fundamental Theorem of Calculus 184
Bibliography 187
Index 189
1.1 Introduction 1
1.2 Background 3
1.3 Sources 3
Chapter 2 Outer Space Paradoxes 5
2.1 A Helium Balloon in a Space Shuttle 5
2.2 Space Navigation without Jets 9
2.3 A Paradox with a Comet 13
2.4 Speeding Up Causes a Slowdown 14
Chapter 3 Paradoxes with Spinning Water 17
3.1 A Puzzle with a Floating Cork 17
3.2 Parabolic Mirrors and Two Kitchen Puzzles 19
3.3 A Cold Parabolic Dish 21
3.4 Boating on a Slope 23
3.5 Navigating with No Engine or Sails 24
3.6 The Icebergs 25
Chapter 4 Floating and Diving Paradoxes 28
4.1 A Bathtub on Wheels 28
4.2 The Tub Problem--In More Depth 30
4.3 How to Lose Weight in a Fraction of a Second 32
4.4 An Underwater Balloon 33
4.5 A Scuba Puzzle 35
4.6 A Weight Puzzle 36
Chapter 5 Flows and Jets 39
5.1 Bernoulli's Law and Water Guns 39
5.2 Sucking on a Straw and the Irreversibility of Time 42
5.3 Bernoulli's Law and Moving Around in a Space Shuttle 44
5.4 A Sprinker Puzzle 45
5.5 Ejecting Water Fast but with Zero Speed? 48
5.6 A Pouring Water Puzzle 49
5.7 A Stirring Paradox 51
5.8 An Inkjet Printer Question 54
5.9 A Vorticity Paradox 55
Chapter 6 Moving Experiences: Bikes, Gymnastics,
Rockets 57
6.1 How Do Swings Work? 57
6.2 The Rising Energy Cost 58
6.3 A Gymnast Doing Giants and a Hamster in a Wheel 60
6.4 Controlling a Car on Ice 63
6.5 How Does a Biker Turn? 64
6.6 Speeding Up by Leaning 65
6.7 Can One Gain Speed on a Bike by Body Motion Only? 66
6.8 Gaining Weight on a Motorbike 68
6.9 Feeling the Square in mv2 2 Through the Bike Pedals 69
6.10 A Paradox with Rockets 70
6.11 A Coffee Rocket 72
6.12 Throwing a Ball from a Moving Car 74
Chapter 7 Paradoxes with the Coriolis Force 77
7.1 What Is the Coriolis Force? 77
7.2 Feeling Coriolis in a Boeing 747 79
7.3 Down the Drain with Coriolis 80
7.4 High Pressure and Good Weather 80
7.5 What Causes Trade Winds? 82
Chapter 8 Centrifugal Paradoxes 84
8.1 What's Cheaper: Flying West or East? 84
8.2 A Coriolis Paradox 85
8.3 An Amazing Inverted Pendulum: What Holds It Up? 87
8.4 Antigravity Molasses 91
8.5 The "Proof" That the Sling Cannot Work 92
8.6 A David-Goliath Problem 93
8.7 Water in a Pipe 97
8.8 Which Tension Is Greater? 98
8.9 Slithering Ropes in Weightlessness 100
Chapter 9 Gyroscopic Paradoxes 104
9.1 How Does the Spinning Top Defy Gravity? 104
9.2 Gyroscopes in Bikes 108
9.3 A Rolling Coin 109
9.4 Staying on a Slippery Dome 111
9.5 Finding North with a Gyroscope 113
Chapter 10 Some Hot Stuff and Cool Things 117
10.1 Can Heat Pass from a Colder to a Hotter Object? 117
10.2 A Bike Pump and Molecular Ping-Pong 121
10.3 A Bike Pump as a Heat Pump 122
10.4 Heating a Room in Winter 124
10.5 Freezing Things with a Bike Tire 125
Chapter 11 Two Perpetual Motion Machines 127
11.1 Perpetual Motion by Capillarity 128
11.2 An Elliptical Mirror Perpetuum Mobile 129
Chapter 12 Sailing and Gliding 132
12.1 Shooting Cherry Pits and Sailing 133
12.2 Sailing Straight into the Wind 135
12.3 Biking against the Wind 136
12.4 Soaring without Updrafts 138
12.5 Danger of the Horizontal Shear Wind 141
Chapter 13 The Flipping Cat and the Spinning Earth 142
13.1 How Do Cats Flip to Land on Their Feet? 142
13.2 Can Trade Winds Slow Earth's Rotation? 144
Chapter 14 Miscellaneous 146
14.1 How to Open a Wine Bottle with a Book 146
14.2:"t's Alive!" 149
14.3 Falling Faster Than g: A Falling Chain "Sucked in" by the Floor 150
14.4 A Man in a Boat with Drag 151
14.5 A "Phantom" Boat: No Wake and No Drag 154
14.6 A Constant-G Roller Coaster 156
14.7 Shooting at a Cart 158
14.8 Computing v2 with a Shoe 159
Appendix 161
A.1 Newton's Laws 161
A.2 Kinetic Energy, Potential Energy, Work 163
A.2.1 Work 163
A.2.2 Kinetic Energy 165
A.2.3 Potential Energy 166
A.2.4 Conservation of Energy 168
A.3 Center of Mass 169
A.4 Linear Momentum 171
A.5 The Torque 174
A.6 Angular Momentum 175
A.7 Angular Velocity, Centripetal Acceleration 178
A.8 Centrifugal and Centripetal Forces 181
A.9 Coriolis, Centrifugal, and Complex Exponentials 181
A.10 The Fundamental Theorem of Calculus 184
Bibliography 187
Index 189
