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# apr25b - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . 6.055 / Art of approximation 70 The volume of the pyramid is V ∼ hb 2 , and the missing constant must make volume 4 / 3 . Since hb 2 = 4 for these pyramids, the missing constant is 1 / 3 . Voilà: V = 1 hb 2 = 4 . 3 3 8.2 Mechanics 8.2.1 Atwood machine The next problem illustrates dimensional analysis and special cases in a physical problem. Many of the ideas and methods from the geometry example transfer to this problem, and it introduces more methods and ways of reasoning. The problem is a staple of first-year physics: Two masses, m 1 and m 2 , are connected and, m 1 m 2 thanks to a pulley, are free to move up and down. What is the acceleration of the masses and the tension in the string? You can solve this problem with standard methods from first-year physics, which means that you can can check the solution that we derive using dimensional analysis, educated guessing, and a feel for functions. dimensional analysis, educated guessing, and a feel for functions....
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apr25b - MIT OpenCourseWare http/ocw.mit.edu 6.055J 2.038J...

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