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81204hw11Sol

# 81204hw11Sol - Zzztayloe Rex Homework 11 Heinz 81204 This...

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Zzztayloe, Rex – Homework 11 – Heinz – 81204 – Nov 04, 2004 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Bone has a Young’s modulus of about 1 . 8 × 10 10 Pa. Under compression, it can withstand a stress of about 1 . 55 × 10 8 Pa before breaking. Assume that a femur (thigh bone) is 0 . 46 m long, and calculate the amount of compression this bone can withstand before breaking. Correct answer: 3 . 96111 mm. Explanation: Given : Stress = 1 . 55 × 10 8 Pa , L 0 = 0 . 46 m , and Y = 1 . 8 × 10 10 Pa . The amount of compression Δ L is given by Y = F A L 0 Δ L = (Stress) L 0 Δ L Δ L = L 0 (Stress) Y = (0 . 46 m) ( 1 . 55 × 10 8 Pa ) 1 . 8 × 10 10 Pa · 1000 mm 1 m = 3 . 96111 mm . 002 (part 1 of 1) 10 points A wooden platform is suspended from a ceil- ing by four steel wires at its four corners. Each wire is 7 . 2 m long and of diameter of 2 . 6 mm. The Young modulus of steel is 2 × 10 11 N / m 2 . Two people stand at the center of the plat- form, and the total weight of the two people and the platform is 1800 N. How much do the wires stretch? Correct answer: 3 . 05125 mm. Explanation: Given the symmetry of the situation, each wire pull with equal force F which is therefore equal to one quarter of the gross weight of the loaded platform, F = W/ 4 . Each wire has cross-section A = π ( d/ 2) 2 (mind the units!) and therefore is stressed by Stress F/A = W/ 4 π ( d/ 2) 2 = W πd 2 . Given the Young modulus of the steel, this stress produces strain Δ L L = F/A Y = W πY d 2 which means that the wires stretch by Δ L = WL πY d 2 = 3 . 05125 mm . (mind the units). 003 (part 1 of 1) 10 points Calculate the density of sea water at a depth of 734 m where the hydraulic pressure is about 7 . 49 × 10 6 N / m 2 . (The density of sea water at the surface is 1030 kg / m 3 and the bulk modulus of the water is 2 . 1 × 10 9 N / m 2 .) Correct answer: 1033 . 69 kg / m 3 .

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