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Materials Science for Mechanical Engineering

Materials Science for Mechanical Engineering - polymers...

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1 Assignment #1 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)
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Unformatted text preview: 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 2. (1 pt) (a) Explain what is meant by exponential growth in the consumption of a material. (b) A material is consumed at C tonne year-1 in 2005. Consumption in 2005 is increasing at r % year-1 . If the resource base of the material is Q tones, and consumption continues to increase at r % year-1 , show that the resource will be half exhausted after a time 2 1 t , given by       + = 1 200 ln 100 2 / 1 C rQ r t...
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