Online Homework Answers 1 (Sept. 14, 2006)

# Online Homework Answers 1 (Sept. 14, 2006) - Hood Charles...

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Hood, Charles – Homework 1 – Due: Sep 14 2006, 11:00 pm – Inst: Jan Opyrchal 1 This print-out should have 10 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 This problem shows how dimensional analysis helps us check our work and sometimes even help us find a formula. A rope has a cross section A = 9 . 5 m 2 and density ρ = 2150 kg / m 3 . The “linear” density of the rope μ , is defined to be the mass per unit length, in the form μ = ρ x A y . Based on dimensional analysis, find the powers x and y . 1. x = - 2 , y = 2 2. x = - 1 , y = 2 3. x = 1 , y = 2 4. x = 1 , y = 1 correct 5. x = 1 , y = - 1 6. x = - 2 , y = - 1 7. x = - 1 , y = 1 8. x = - 2 , y = 1 9. x = - 1 , y = - 1 Explanation: Kilogram (kg): a unit of mass (M). Meter (m): a unit of length (L). [ x ] means “the units of x ”. The units of both sides of any equation must be the same for the equation to make sense. The units of the left hand side (LHS) are given as [ μ ] = M L = M L - 1 and the right hand side has [ ρ x A y ] = M L 3 x × ( L 2 ) y = M x L - 3 x L 2 y = M x L 2 y - 3 x The powers on the units of mass and length need to be the same as for the LHS above, so x = 1 2 y - 3 x = - 1 2 y = - 1 + 3 = 2 y = 1 Thus the answer is ( x, y ) = (1 , 1). keywords: 002 (part 1 of 1) 10 points A 19 th century British naturalist with a pen- chant for archaic units of measurement de- scribed a species of snail crawling at an average speed of one furlong per fortnight.

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