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

By Mark Levi | Go to book overview

8
CENTRIFUGAL PARADOXES

8.1 What's Cheaper: Flying West or East?

Problem. A flight east from Boston to London consumes less fuel than the return trip. This is because the jet stream blows roughly toward the east. But what if the jet stream were to magically disappear—would this disparity of fuel consumption disappear as well? To focus on the essentials, let's replace Boston and London by two points A and B on the equator, and ask: In the absence of any winds, would the eastbound trip AB consume the same amount of fuel as the westbound trip BA?

Solution. Going east will take less fuel because of Earth's rotation. Each point on the equator orbits the center of Earth. Going east, the plane goes with the rotation of Earth, thus enhancing its orbiting speed around Earth's center. The increased centrifugal force makes the plane a little lighter. And a lighter plane uses less fuel.

How much lighter? For the travel speed of 250 m/sec the weight difference1 is about 2/3 of 1%. A loaded Boeing 747

1 Worked out in the next problem. The ratio of the weight difference to the actual weight turns out to be 4vω/g, where v is the plane's speed, ω is the angular velocity of Earth, and g is the gravitational acceleration.

-84-

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

Table of contents

  • Title Page iii
  • Contents vii
  • Acknowledgments xi
  • 1 - Fun with Physical Paradoxes, Puzzles, and Problems 1
  • 2 - Outer Space Paradoxes 5
  • 3 - Paradoxes with Spinning Water 17
  • 4 - Floating and Diving Paradoxes 28
  • 5 - Flows and Jets 39
  • 6 - Moving Experiences- Bikes, Gymnastics, Rockets 57
  • 7 - Paradoxes with the Coriolis Force 77
  • 8 - Centrifugal Paradoxes 84
  • 9 - Gyroscopic Paradoxes 104
  • 10 - Some Hot Stuff and Cool Things 117
  • 11 - Two Perpetual Motion Machines 127
  • 12 - Sailing and Gliding 132
  • 13 - The Flipping Cat and the Spinning Earth 142
  • 14 - Miscellaneous 146
  • Appendix 161
  • Bibliography 187
  • Index 189
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