In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions
Paul Nahin has written sixteen popular math books so far. They deal with different topics: biographies, mathematical history, logic, games, probability, computation, philosophy, etc. About half of them have reviews in the EMS book review database. For the present book he collected a number of cases of physical problems that are 'behind everyday questions' as the subtitle says. Not that this kind of questions are essential to survive from day to day, but they could indeed pop up in a casual conversation or they could be raised by a curious somebody during a socializing discussion. What is meant is that you do not need to be working at CERN or be a particle physicist to wonder about the problems that, usually in a simplified but rigorous form, are discussed by Nahin in this book. They could for example be exercises in a physics course or be illustrations in a mathematics course. The physics required are elementary such as Archimedes' principle, Ohm's law, Newton's laws of motion, conservation laws of energy and momentum, calculating the center of mass and the momentum of a system. But their meaning and definition are recalled when needed. On the mathematical side some algebra, trigonometry, vectors, and calculus are used. With Einstein and Zemansky in mind "the problems are kept as simple as possible, but not so simple that they are simply wrong". The book also wants to illustrate that G.H. Hardy's quote "[Knowledge of] a little... physics... has no value at all in ordinary life" is definitely wrong and that mathematics is not "just a bunch of theorems, proofs and boring multiplication tables".
Nahin starts his book with a chapter that list some short teaser problems. Some are solved other are solved in later chapters. We find also the solution of a problem formulated in note 14 of the preface (which actually should be note 15, small typo). Every chapter ends in a section with endnotes. Such an endnote can give a reference or a short bio of a person, or some history of the problem, or some extra comments about the physics or mathematics. And then there follow 22 more chapters with a bunch of problems that are solved. Some examples: If you see a traffic light switch from green to orange, should you hit the break or hit the accelerator? Is it the Moon or or the Sun that exerts the greatest gravitational force on Earth and hence is responsible for the tides? And while tides come into the discussion, how much energy can be extracted from moving water, and how much from moving air? Pressing ecologically relevant questions! With a small energy input, a sequence of monotonically larger dominos can be tumbled over, how large is the energy amplification for this process? At what altitude should a geosynchronous satellite be brought in order to stay there by gravitation only? Why is the sky dark at night? This is a classic. If you throw some volume out of your boat, floating on a pond, will the water in the pond raise or not? How to hit a target that is uphill from you with a canon ball? How can you travel in a vacuum tube from New York to Melbourne in 44 minutes? What are the physics of a ski jump, a Tarzan swing and a bungee jump? How many different experiments can you perform at home to measure gravity? And there are many more problems like this. I am sure that at least one of these questions, and probably more than one, must have caught your attention or has started you thinking. The full solution (at least in a simplified form) can be found in the book.
The last chapter is slightly different. It analysis a problem formulated by Newton and for which he gave a wrong solution. It is different in the sense that it is not 'practical' but it is rather a thought experiment. The problem is: How long does it take for two spheres, each with the mass of the Earth, that are a quarter of an inch apart, to touch each other when only subject to gravitational force. Newton gave no computations but claimed that it would take more than a month. Nahin gives the computations and finds it would take only 336 seconds.
Each of the chapters do indeed involve only elementary physics and are worked out in all detail. Often the problems have some historical background which is carefully researched and communicated. There are of course a lot of formulas and computations, which leaves relatively little room for storytelling in between, but the introductions have some humor to make it more lively. Nahin gives much attention to the proper units and checking that all quantities do have the proper dimensions (dimensions in a physical sense that is). This is something that mathematicians (or mathematics students) are not so familiar with. So Nahin is right in emphasizing this aspect in all his computations. Unfortunately, the book is written for the reader who is not used to the mks-system but in daily life thinks and reasons in inches, feet, miles, pounds and the likes. Since Nahin's intention is to consider problems from the reader's 'everyday's environment', he uses these English units to give a better feeling of what the results really mean. So there is a lot of unfortunate unit conversion going on. But anyway, like in his other books, he knows how to catch the attention of his reader. You will not regret buying any of his books, and I am sure after reading it, you will pick up this one to check again on one of his models and his solution methods.