Why Cats Land on Their Feet: And 76 Other Physical Paradoxes and Puzzles

164 Pages·2012·2.74 MB·English

by  Mark Levi

WHY CATS LAND ON THEIR FEET
Paradox: a seemingly contradictory statement
that may nonetheless be true.
Online dictionary
Puzzle: verb: to confound; noun: a toy
contrived to test one’s ingenuity.
Online dictionary
Mark Levi
WHY
CATS
LAND
ON
THEIR
FEET
And 76 Other Physical
Paradoxes and Puzzles

PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright © 2012 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press, 6 Oxford Street,
Woodstock, Oxfordshire OX20 1TW
press.princeton.edu
All Rights Reserved
Library of Congress Cataloging-in-Publication Data
Levi, Mark, 1951–
Why cats land on their feet, and 76 other physical paradoxes
and puzzles / Mark Levi.
p. cm.
ISBN 978-0-691-14854-0 (pbk. : alk. paper)
1. Science–Miscellanea. I. Title.
Q173.L545 2012
530–dc23
2011045728
British Library Cataloging-in-Publication Data is available This book has been composed in Times Printed
on acid-free paper ∞
Typeset by S R Nova Pvt Ltd, Bangalore, India
Printed in the United States of America 1 3 5 7 9 10 8 6 4 2
TO
Olga,
Kyra,
Eric,
Max,
Nika,
Vicki,
Jose,
and
Ryan
CONTENTS
1 Fun with Physical Paradoxes, Puzzles, and Problems
1.1 Introduction
1.2 Background
1.3 Sources
2 Outer Space Paradoxes
2.1 A Helium Balloon in a Space Shuttle
2.2 Space Navigation without Jets
2.3 A Paradox with a Comet
2.4 Speeding Up Causes a Slowdown
3 Paradoxes with Spinning Water
3.1 A Puzzle with a Floating Cork
3.2 Parabolic Mirrors and Two Kitchen Puzzles
3.3 A Cold Parabolic Dish
3.4 Boating on a Slope
3.5 Navigating with No Engine or Sails
3.6 The Icebergs
4 Floating and Diving Paradoxes
4.1 A Bathtub on Wheels
4.2 The Tub Problem—In More Depth
4.3 How to Lose Weight in a Fraction of a Second
4.4 An Underwater Balloon
4.5 A Scuba Puzzle
4.6 A Weight Puzzle
5 Flows and Jets
5.1 Bernoulli’s Law and Water Guns
5.2 Sucking on a Straw and the Irreversibility of Time
5.3 Bernoulli’s Law and Moving Around in a Space Shuttle
5.4 A Sprinker Puzzle
5.5 Ejecting Water Fast but with Zero Speed?
5.6 A Pouring Water Puzzle
5.7 A Stirring Paradox
5.8 An Inkjet Printer Question
5.9 A Vorticity Paradox
6 Moving Experiences: Bikes, Gymnastics, Rockets
6.1 How Do Swings Work?
6.2 The Rising Energy Cost
6.3 A Gymnast Doing Giants and a Hamster in a Wheel
6.4 Controlling a Car on Ice
6.5 How Does a Biker Turn?
6.6 Speeding Up by Leaning
6.7 Can One Gain Speed on a Bike by Body Motion Only?
6.8 Gaining Weight on a Motorbike
6.9 Feeling the Square in Through the Bike Pedals
6.10 A Paradox with Rockets
6.11 A Coffee Rocket
6.12 Throwing a Ball from a Moving Car
7 Paradoxes with the Coriolis Force
7.1 What Is the Coriolis Force?
7.2 Feeling Coriolis in a Boeing 747
7.3 Down the Drain with Coriolis
7.4 High Pressure and Good Weather
7.5 What Causes Trade Winds?
8 Centrifugal Paradoxes
8.1 What’s Cheaper: Flying West or East?
8.2 A Coriolis Paradox
8.3 An Amazing Inverted Pendulum: What Holds It Up?
8.4 Antigravity Molasses
8.5 The “Proof” That the Sling Cannot Work
8.6 A David–Goliath Problem
8.7 Water in a Pipe
8.8 Which Tension Is Greater?
8.9 Slithering Ropes in Weightlessness
9 Gyroscopic Paradoxes
9.1 How Does the Spinning Top Defy Gravity?
9.2 Gyroscopes in Bikes
9.3 A Rolling Coin
9.4 Staying on a Slippery Dome
9.5 Finding North with a Gyroscope
10 Some Hot Stuff and Cool Things
10.1 Can Heat Pass from a Colder to a Hotter Object?
10.2 A Bike Pump and Molecular Ping-Pong
10.3 A Bike Pump as a Heat Pump
10.4 Heating a Room in Winter
10.5 Freezing Things with a Bike Tire
11 Two Perpetual Motion Machines
11.1 Perpetual Motion by Capillarity
11.2 An Elliptical Mirror Perpetuum Mobile
12 Sailing and Gliding
12.1 Shooting Cherry Pits and Sailing
12.2 Sailing Straight into the Wind
12.3 Biking against the Wind
12.4 Soaring without Updrafts
12.5 Danger of the Horizontal Shear Wind
13 The Flipping Cat and the Spinning Earth
13.1 How Do Cats Flip to Land on Their Feet?
13.2 Can Trade Winds Slow Earth’s Rotation?
14 Miscellaneous
14.1 How to Open a Wine Bottle with a Book
14.2 “It’s Alive!”
14.3 Falling Faster Than g: A Falling Chain “Sucked in” by the Floor
14.4 A Man in a Boat with Drag
14.5 A “Phantom” Boat: No Wake and No Drag
14.6 A Constant-G Roller Coaster
14.7 Shooting at a Cart
14.8 Computing with a Shoe
Appendix
A.1 Newton’s Laws
A.2 Kinetic Energy, Potential Energy, Work
A.2.1 Work
A.2.2 Kinetic Energy
A.2.3 Potential Energy
A.2.4 Conservation of Energy
A.3 Center of Mass
A.4 Linear Momentum
A.5 The Torque
A.6 Angular Momentum
A.7 Angular Velocity, Centripetal Acceleration
A.8 Centrifugal and Centripetal Forces
A.9 Coriolis, Centrifugal, and Complex Exponentials
A.10 The Fundamental Theorem of Calculus
Bibliography
Index