This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 firstyear 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 firstyear 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....
View
Full Document
 Spring '08
 SanjoyMahajan
 2 m, special cases

Click to edit the document details