hw3 - Muraj, Hamza Homework 3 Due: Jan 27 2006, 4:00 am...

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Muraj, Hamza – Homework 3 – Due: Jan 27 2006, 4:00 am – Inst: Florin 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. The due time is Central time. 001 (part 1 o± 1) 10 points A structural I beam is made o± iron. A view o± its cross-section and its dimensions is shown in the fgure, where d = 3 cm, w = 27 cm, h = 29 cm and the length (not shown) o± the beam is = 1 . 44 m. The density o± iron is 7560 kg / m 3 . The atomic weight o± iron is 55.85 g/mol and Avo- gadro number is N A = 6 . 02214 × 10 23 / mol. 27 cm 29 cm 3 cm 3 cm How many atoms are there in this section? Correct answer: 2 . 71159 × 10 27 atoms. Explanation: Let : d = 3 cm , w = 27 cm , h = 29 cm , and = 1 . 44 m . w h d d The cross-sectional area o± the beam is A = 2 · (27 cm) (3 cm) + (29 cm - 2 · 3 cm) (1 cm) = 231 cm 2 = 0 . 0231 m 2 . The volume o± a piece = 1 . 44 m long is then V = A ‘ = 0 . 033264 m 3 . The mass is then given by m = ρ V = 251 . 476 kg . Let : m = 251 . 476 kg = 251476 g and N A = 6 . 02214 × 10 23 / mol . Presuming that the atoms are iron, we look to the periodic table and fnd the molar mass to be M = 55 . 85 g / mol . The number o± moles is then n = m M = 251476 g 55 . 85 g / mol = 4502 . 7 mol and the number o± atoms is N = n N A = (4502 . 7 mol) (6 . 02214 × 10 23 / mol) = 2 . 71159 × 10 27 atoms . 002 (part 1 o± 1) 10 points Identi±y the equation below which is dimen- sionally incorrect . A, x, y and r have units o± length. k here has units o± inverse length. v 0 and v have units o± velocity. a and g have units o± acceleration. ω has units o± inverse time. t is time, m is mass, V is volume, ρ is density, and F is ±orce. 1. v 0 = p v 2 - 2 a x 2. t = - v 0 + q v 2 0 + 2 a x a + v 2 a 2 t 3. v = p 2 g y + r r F m 4. F = m ω 2 r 5. v = ± ω p A 2 - x 2
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Muraj, Hamza – Homework 3 – Due: Jan 27 2006, 4:00 am – Inst: Florin 2 6. g = F m + ρ m g V 7. y = A cos( kx - ωt ) 8. F = m g 1 + v r g correct Explanation: Check y = A cos( kx - ωt ): Since k is an inverse length, kx is dimension- less, and similarly, ωt is also dimensionless, so kx - ωt is dimensionless, as an argument of a trigonometry function must always be. The value of a trigonometry function (
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hw3 - Muraj, Hamza Homework 3 Due: Jan 27 2006, 4:00 am...

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