PHYS310_homework_10_solutions

PHYS310_homework_10_ - Homework set 10 due Wednesday November 9 11:30 am Following problems from Analytical Mechanics by Fowles& Cassiday 1

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Unformatted text preview: Homework set 10, due Wednesday, November 9, 11:30 am Following problems from Analytical Mechanics by Fowles & Cassiday 1. 8.1 (20 points) (a) For each portion of the wire having a mass 3 m and centered at , 2 2 b b - , ( 29 0,0 , and , 2 2 b b … 1 2 3 2 3 cm b m b m x m =- + + = 1 2 3 2 3 3 cm b m b m b y m = + + = (b) ( 29 1 2 2 2 ds xdy b y dy = =- ( 29 1 2 2 2 1 b cm y y b y dy m ρ =- ∫ ( 29 ( 29 1 2 2 2 2 2 2 2 1 4 y b y cm b y d b y y b ρ π ρ = =--- = ∫ 4 3 cm b y π = From symmetry, 4 3 cm b x π = (c) The center of mass is on the y-axis. ( 29 1 2 2 2 ds xdy by dy = = ( 29 ( 29 3 1 2 2 1 1 2 2 2 2 b b cm b b y by dy y dy y by dy y dy ρ ρ = = ∫ ∫ ∫ ∫ 3 5 cm b y = (d) The center of mass is on the z-axis. ( 29 2 2 2 dv r dz x y dz bzdz π π π = = + = 2 b b cm b b z bzdz z dz z bzdz zdz ρ π ρπ = = ∫ ∫ ∫ ∫ 2 3 cm z b = (e) The center of mass is on the z-axis....
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This note was uploaded on 12/07/2011 for the course PHYS 310 taught by Professor Jones,m during the Fall '08 term at Purdue University-West Lafayette.

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PHYS310_homework_10_ - Homework set 10 due Wednesday November 9 11:30 am Following problems from Analytical Mechanics by Fowles& Cassiday 1

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