Developing a good sense of how to use your physical intuition for solving problems involves learning the technique of deciding which approach to solving a problem tends to work more "easily" than other possible approaches. In some cases, detailed mathematical analysis is necessary, but, for many questions, an amazing degree of accuracy can be obtained by a series of "educated guesses" for which the correct order of magnitude for each quantity involved and simple calculations are all is all that is necessary to get a surprisingly accurate answer. The great nuclear physics Enrico Fermi is acknowledged as one of the great masters of this technique and used it to find the answers to what would seem to be almost impossible questions to answer. Hence the kind of problems that can be attacked in this way are termed Fermi problems. Here are some examples:
What thickness of rubber tread is worn off of the tire of a typical automobile as it travels one mile?
We could answer this question if we knew the following information:
Although our answer may be off by a factor of 2 or 3, it is almost certainly not off by a factor of 10. For some problems this is more than adequate.
Fans of a college football team are excited after their team wins the game. They rush onto the field. How many people can fit onto the field of 100 yards by 50 yards?
Start by assuming that each person needs an area of about 18 inches by 12 inches if they are packed as closely as possible. Then, we would have
So 30,000 people can fit onto the field itself.
Sometimes you can use the Fermi method to get some amazingly accurate results from your everyday knowledge. For example, suppose you are asked to state the radius of the earth and you do not have that quantity handily available. Think about your (or others) travel experiences:
The actual answer is 6.37 x 106 m so you can see that the Fermi estimate gets remarkably close.
Although the breadth of the Internet and smart search engines have made it possible to quickly find incredible amounts of information, it is still useful to keep in mind some orders of magnitude for how big or small things are for just the kind of quick Fermi problem calculations we might use to decide how to attack particular problems. Here are a few quantities that might prove useful along with the Web links to where the information was derived. You may wish to explore these links at your leisure, but it is not necessary to do so. These links were valid as of Jun 1, 2001. [Editor's note: Links checked Nov 8, 2004.]
|Type||Numerical value||Web link|
|World population (1999):||6.032 x 109 (estimated: 12/20/99)||US Census Bureau|
|US population (1999):||2.74 x 108 (estimated: 12/20/99)||US Census Bureau|
|World Population (1650):||5 x 108||Brockport HS Science Dept.|
|Power of a hurricane||2 x 1013 W||Brockport HS Science Dept.|
|Height of Mount Everest||8,850 m||Infoplease Everest Almanac|
|Length of a typical virus||10-8 m||Tulane University|