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Unformatted text preview: October 25, 2011 Name Name.nnn TA & Rec. hour Math. 152 – Quiz 3 – Form A PROBLEM 1. (10 points) A force of 8 lb is required to hold a spring stretched 7 in. beyond its natural length. How much work is done in stretching it from its natural length to 9 in beyond its natural length? (Express your answer in ftlb.) Solution. Let k be the string constant. Then 7 in · k = 8 lb 2 by Hooke’s law. It follows that k = 8 7 lb in = 8 7 lb 1 / 12 ft = 96 7 lb ft ≈ 13 . 714 lb ft . 2 The work required to stretch the string from its natural length to 9 in beyond its natural length is W = Z 9 in kxdx 2 = k 2 x 2 9 in 2 = k 2 · 81 in 2 = 1 2 · 8 lb 7 in · 81 in 2 = 324 7 lbin( ≈ 46 . 2857 lbin) 1 = 27 7 lbft( ≈ 3 . 8571 lbft) 1 1 PROBLEM 2. (10 points) Find the following integral Z q 4 ln ( q 8 ) dq Solution #1. Note that R q 4 ln ( q 8 ) dq = 8 R q 4 ln  q  dq . Letting u = ln  q  1 and v = q 4 1 yields u = 1 q 1 and v = q 5 5 1 , from which, together with integration by parts, follows that...
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This note was uploaded on 11/11/2011 for the course MATH 152.01 taught by Professor Geline during the Fall '09 term at Ohio State.
 Fall '09
 GELINE
 Math, Calculus, Geometry

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