Assignment1_solution - Assignment #1 Solutions ME264...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

Assignment1_solution - Assignment #1 Solutions ME264...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online