Homework 5


Homework 5: Due Friday 9 February

Feel free to use Maple for any of the problems in this assignment.


Section 8.2

  1. 2 (15 points)
  2. 5 (15 points) Be careful with units.
  3. 13 (15 points)


Surface Areas and a trip to the Moon In answering the following questions, you should derive any surface area formula you use. I suggest beginning by trying to use integration to derive the formula for the surface area of a sphere. (50 points total)

  1. What fraction of the earth's surface is visible from the moon?
  2. What fraction of the earth's surface is visible if you are 35,000 feet above the surface of the earth?
  3. What fraction of the earth's surface is visible from a satellite orbiting 280 km above the surface of the earth?


Poiseuille's Law High blood pressure results from constriction of the arteries. to maintain the same flow rate the heart has to pump harder, thus increasing the blood pressure. Use Poiseuille's Law to show that if Ro and Po are normal values of the radius and pressure in an artery and the constricted values are R and P, then for the flux to remain constant, P and R are related by the equation P/Po = (R/Ro)^4 . Deduce that if the radius of an artery is reduced to three-fourths of its former value, then the pressure is more than tripled. Poiseuille is in the Fluid Mechanics Hall of Fame. (From Stewart, Calculus, 3rd ed. pp 540-541.)(15 points)


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