Assignment1_solution - Assignment#1 Solutions ME264...

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1 Assignment #1 Solutions ME264 Materials Science for Mechanical Engineering Spring 2009 Due Date: 18 February 2009 (2 pts) 1. (1 pt) (a) Commodity A is currently consumed at the rate C A tonnes per year, and commodity B at the rate C B tonnes per year ( C A > C B ). If the two consumption rates are increasing exponentially to give growths in consumption after each year of r A % and r B %, respectively ( r A < r B ), derive an equation for the time, measured from the present day, before the annual consumption of B exceeds that of A . (b) The table shows figures for consumption and growth rates of steel, aluminum and plastics. What are the doubling-times (in years) for consumption of these commodities? (c) Calculate the number of years before the consumption of (a) aluminum and (b) polymers would exceed that of steel, if exponential growth continued . Material Current consumptions (tonnes years -1 ) Projected growth rate in consumption (% year -1 ) Iron and Steel 3x10 8 2 Aluminum 4x10 7 3 Polymers 1x10 8 4 Solution: (a) If the consumption rates are increasing exponentially we can write as: 100 dC r C dt = where r is the percentage fractional rate of growth per year. Integrating gives
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This note was uploaded on 11/17/2009 for the course MECHANICAL ME 264 taught by Professor during the Spring '09 term at Yeditepe Üniversitesi.

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Assignment1_solution - Assignment#1 Solutions ME264...

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