Dimensional AnalysisDate: 10/06/2001 at 15:33:00 From: Katie Subject: Dimensional Analysis The question is... Mr. R wants to give all of his chemistry students enough chocolate to make them goofy for the rest of the day. It's a known fact that it takes 47 chocolate chips to make a student goofy. The average cookie contains 29 chocolate chips. Mr. R has 5 classes and each class has an average of 26 students. How many toll house cookies does Mr. R need to make? I have to use dimensional Analysis while doing figuring this question. How should I go about doing it? Date: 10/08/2001 at 14:27:48 From: Doctor Greenie Subject: Re: Dimensional Analysis Hi, Katie - Cool problem! I'm glad to see that dimensional analysis is being taught somewhere - it seems to be a topic that is unfortunately missing from the curriculum in many schools. I have always found it a very useful tool, and this problem makes the topic fun. Let's work this problem first without using dimensional analysis, so we will be able to confirm later that our solution to the problem using dimensional analysis is correct. (Or perhaps we will use our solution using dimensional analysis to confirm this solution...) Mr R has 5 classes averaging 26 students; so he has 5*26 students. It takes 47 chocolate chips to make the average student goofy, so he needs 5*26*47 chocolate chips. Finally, the average cookie contains 29 chocolate chips, so the number of cookies he needs is 5 * 26 * 47 ----------- 29 Now let's look at the problem using dimensional analysis. We have the following information: (1) number of classes = 5/1 (2) students/class = 26/1 (3) chips/student to make student goofy = 47/1 (4) chips/cookie = 29/1 I have written all these numbers as fractions because, with dimensional analysis, I may find I want to use, for example, classes/student = 1/26 instead of students/class = 26. With dimensional analysis, I start by looking at what I am trying to determine. What I am after in this problem is the number of cookies required. In my given information, "cookies" appears only in (4): chips/cookie = 29/1. Since I want my answer to be "cookies," I need to use the reciprocal of the given information: cookies 1 ------- = -- chips 29 Now I see that I need to multiply this by something with "chips" in the numerator; (3) above tells me that chips/student = 47/1... cookies chips cookies 1 47 ------- * ------- = ------- = -- * -- chips student student 29 1 Now I see that I need to multiply this by something with "students" in the numerator; (2) above tells me that students/class = 26/1... cookies students cookies 1 47 26 ------- * -------- = ------- = -- * -- * -- student class class 29 1 1 I now have "cookies/class"; I need to multiply that by the number of classes to get "cookies" ... cookies 1 47 26 5 ------- * classes = cookies = -- * -- * -- * - class 29 1 1 1 So, using dimensional analysis, we see that the number of cookies required is 47 * 26 * 5 -------------- 29 which agrees with the result we got above. Thanks again for a problem that can be used nicely to demonstrate the use of dimensional analysis. I hope this helps. Write back if you have any questions on this. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/ |
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