Math & Science Home | Proficiency Tests | Mathematical Thinking in Physics | Aeronauts 2000 |
||||
IntroductionMany of the articles on this Web site are versions of the Fermi Problem described in the first section. Others are essays - some short, some long. Some are merely attempts to come to terms with basic concepts, such as the 'size' of the speed of light or the number 'one trillion'. Others discuss more advanced concepts. The last few essays involve college-level physics, and might be difficult for those who have not taken at least some introductory courses. The essays discussing the gravitational field energy density and the thermodynamic four-vector are speculative and invite comments from you, the reader. The energy density article was written to fill a gap, which I noted in books on Special Relativity. Of the three classical problems of General Relativity, two (the deflection of starlight and the gravitational red shift) are routinely presented as exercises with a discussion of similarities and differences with General Relativity; the third (the rotation of perihelion) seems never to be touched at this level. This article is an attempt to rectify this situation. The four-vector article arises from the observation that components of a four-vector satisfy a continuity equation. Einstein used this idea in his early writing on Special Relativity when introducing the current density four-vector. I have raised the question as to whether similar logic might apply to thermodynamics when the heat conduction equation and the thermal diffusion equation are combined to form a continuity equation. The earlier pieces are nowhere near so involved, and require only a little number skill and, possibly, some high school algebra. Enrico Fermi, the theoretical physicist of Manhattan Project fame, knew only too well that physicists are often confronted by situations in which they are forced to reason from minimal information. He, therefore, taught his students how to think about complicated sounding problems by using everyday knowledge. The 'Piano Tuner' is typical: "If 3,000,000 people live in Chicago, then how many of them are piano tuners?" There are many cases in science, and even in everyday life, when we encounter seemingly insolvable problems such as this. So the problems presented here provide an opportunity to practice with Fermi's approach. Some of the problems are of my own invention. Others came from students or people I met when conducting public lectures. Some are simple, others, complex. Each problem has, of course, a rigorous solution, although the solutions presented here make no pretense at rigor! Consider them 'back-of-the-envelope' calculations - estimates, ballpark solutions. In so doing, you will gain valuable insight into a technique much used by professionals. And most of all, remember to have fun! - Joe Kolecki |
||||
Please send suggestions/corrections to: Web Related: David.Mazza@grc.nasa.gov Technology Related: Joseph.C.Kolecki@grc.nasa.gov Responsible NASA Official: Theresa.M.Scott (Acting) |