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

Mark Levi
Pages: 184
https://www.jstor.org/stable/j.ctt7rw2b

1. Front Matter
(pp. i-vi)
(pp. vii-xiv)
3. 1 FUN WITH PHYSICAL PARADOXES, PUZZLES, AND PROBLEMS
(pp. 1-4)

A good physical paradox is (1) a surprise, (2) a puzzle, and (3) a lesson, rolled into one fun package. A paradox often involves a very convincing argument leading to a wrong conclusion that seems right, or to a right conclusion that seems wrong or surprising. The challenge to find the mistake—or explain the surprise—may be hard to resist. A joke heard back in the Cold War years claimed that the West could impede Soviet military R&D efforts by scattering leaflets containing puzzlers and brainteasers over the secret Siberian weapons research facilities. Times have changed, and these same...

(pp. 5-16)

Problem. Two astronauts, Al and Bob, are strapped to the opposite ends in a space capsule, as in Figure 2.1. Al is holding a large helium-filled balloon, and everything is at rest. Now Al pushes the balloon, which begins to drift toward Bob. Which way will the capsule drift, as seen by an observer hovering in space outside the capsule? Since the astronauts are strapped to the walls, let’s consider them part of the capsule.

A reasonable guess. When Al pushes right, the balloon pushes him back, according to Newton’s “action equals reaction” third law. And since the balloon pushes...

5. 3 PARADOXES WITH SPINNING WATER
(pp. 17-27)

Archimedes discovered his famous law: the buoyancy force exerted by water upon a submerged body equals the weight of the water displaced by the body.¹

In a rotating world, such as Earth, Archmedes’ buoyancy law acquires a twist (no pun intended), with some surprising manifestations. One such surprise is the paradox of the floating cork described next. Another is the iceberg paradox (p. 25).

The experiment. An amusement park with a spinning swimming pool would be a dream of any child, even one trapped in the body of an adult. With the image of such a pool in the back...

6. 4 FLOATING AND DIVING PARADOXES
(pp. 28-38)

Here is a twist on the “space ball” problem, this time on Earth.

Question. A toy boat bobs at one end of a tub with water. The tub is mounted on perfectly frictionless wheels and stands on a perfectly smooth floor. All is at rest. Using the remote control, you make the boat travel from one end of the tub to the other. Gradually all motion stops. Which way did the tub move from its initial position?

The masses of the boat and of the tub aremandM, respectively; the length of the tub isL.

$distance \, = \, \frac m{m +M}L$...

7. 5 FLOWS AND JETS
(pp. 39-56)

Question. Imagine shooting water from a syringe by pushing the piston. With Newton’s first law in mind (motion is steady if no force is applied), I ask: Does it take any force to move the piston with a constant speed—assuming a perfectly frictionless piston and perfectly nonviscous water? In other words, once I push the piston to give it some speed and let it go, will it continue at the same speed by inertia?

Answer. A forceisrequired to push the piston with constant speed—even in a perfectly frictionless world. Newton’s first law of steady motion by...

8. 6 MOVING EXPERIENCES: BIKES, GYMNASTICS, ROCKETS
(pp. 57-76)

Question. Most things in life are easier said than done. But some are the other way around—easier done than said. Rocking on swings is an example. Exactly how does a child pass the energy of his muscles to swinging? The answer is not that obvious.¹

Answer (the anatomy of a resonance). Imagine yourself rocking back and forth on swings. You feel the greatestg-force when zooming past the bottom of your path. By the same token, the leastg-force is near the highest points of your trajectory.² Imagine now holding a weight in your hand, resting it your lap,...

9. 7 PARADOXES WITH THE CORIOLIS FORCE
(pp. 77-83)

Question. Imagine playing ball on merry-go-round. The merry-go-round is enclosed, so you don’t see outside. Standing at the center, you want to hit a target at the rim. You aim the ball straight at the target, but you miss: the ball curves to the right, as in Figure 7.1. Why does this happen? Let us forget gravity. Assume that the spin is counterclockwise.

Answer. The shortest answer is: “The ball actually flies straight. But the platform turns, the target moves, and the ball misses to the right of the target. In the enclosed rotating room it appears as if the...

(pp. 84-103)

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 pointsAandBon the equator, and ask: In the absence of any winds, would the eastbound tripABconsume the same amount of fuel as the westbound tripBA?

Solution. Going east will take less fuel because of Earth’s rotation. Each...

(pp. 104-116)

What holds the spinning top upright is not some force that actsagainstgravity. Rather, it is a strangedeflectingforce—the force that stays alwaysperpendicularto the direction of the motion of the axis of the top. This diverting force “subverts” the instability: the top begins to fall, but then veers off, thus moving as shown in Figure 9.3. In the next paragraph I will give a feel of how this strange “gyroscopic force” comes about from Newton’s second law.

A gravity-defying bike wheel. Let’s use the bike wheel as our spinning top. Hang the bike wheel on...

12. 10 SOME HOT STUFF AND COOL THINGS
(pp. 117-126)

The answer to the question is, of course, no: in contact between two objects, the heat goes from the hotter object to the colder one.¹ So the following question may sound silly:

Problem. Can a glass of 100° C water heat a glass of 0° C milk to more than 50° C, their common temperature if mixed together? The glasses are of the same size. Let’s also assume that water and milk are completely identical in all their thermal properties.² No heat can be brought in from the outside,but additional containers can be used.

Solution. Such heat transfer is...

13. 11 TWO PERPETUAL MOTION MACHINES
(pp. 127-131)

The perpetual motion machine is a utopian dream. Like other utopias, it attracts its share of cranks. Fortunately, in contrast to many social utopians of the past (and, unfortunately, present), these tend not to be dangerous and do not usually kill for an idea. Common to all utopias is an attempt to break a law—be it the law of conservation of energy, a law of economics, a law of human psychology, or a law of society.

The inventor of a perpetual motion engine must have limitless intelligence to rise to an infinitely difficult task of inventing the impossible. Attempted...

14. 12 SAILING AND GLIDING
(pp. 132-141)

Question. Is it possible to sail on a river on a windless day?

Answer. Yes, sailing with no wind is possible, thanks to the current; Figure 12.1 explains how. The sail in still air acts like a knife in butter: it can only slice through the air, moving along the line of the sail.¹ On the other hand, the keel is being pushed by the current, and thus the boat slides as shown, towards the shore at the right angle. So the keel now acts as the sail and the flowing water acts as the blowing wind. And the sail,...

15. 13 THE FLIPPING CAT AND THE SPINNING EARTH
(pp. 142-145)

A cat released with his feet pointing up needs only a fraction of a second to point his feet down. How does he do it, with nothing to push off of?¹ Some people say that the cat does it by spinning the tail. On closer inspection this turns out to be false. As an experimental fact, tailless cats are just as good as the tailed ones in flipping over. Alternatively, a theoretical argument shows that to accomplish a 180° flip in a fraction of a second, the cat would have to spin its tail so fast that its tip would...

16. 14 MISCELLANEOUS
(pp. 146-160)

This method actually works—I tried it myself, having been stimulated by a combination of scientific curiosity and the lack of a corkscrew, not necessarily in that order.

Begin by pressing a book against a wall. Then strike the bottom of the bottle against the book. I recommend holding the bottle with a towel and wearing protective glasses to prevent injury should the bottle break (anyone doing this with a champagne bottle risks winning Darwin’s award). With repeated strikes, the cork will inch out, bit by bit, so that eventually it can be pulled out by hand.

I did this...

17. APPENDIX
(pp. 161-186)
18. BIBLIOGRAPHY
(pp. 187-188)
19. INDEX
(pp. 189-190)