HH_Sec_8_4 - is 1 2 b a and this is the midpoint of a b...

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(9/30/08) Math 10B. Lecture Examples. Section 8.4. Density and centers of mass Example 1 The density of a two-foot-long rod is δ = 2 + 6x (pounds per foot) at a distance x feet from one end. How much does it weigh? Answer: [Weight] = 16 pounds Example 2 Find the center of mass of the rod from Example 1 with density δ = 2 + 6x (pounds per foot) at x for 0 x 2 . Answer: x = 1 . 25 feet Example 3 Show that if a rod has constant density, then its center of gravity is at its midpoint. Answer: If the rod has constant density δ and extends from x = a to x = b with a < b , then its center of gravity
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Unformatted text preview: is 1 2 ( b + a ) and this is the midpoint of [ a, b ]. Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 7.8: Examples 1 and 2 † Lecture notes to accompany Section 8.4 of Calculus by Hughes-Hallett et al ‡ The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. 1...
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

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