Math in the News: 5/9/11

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In this issue of Math in the News we dissect the forces involves in tornadoes and discover why they can cause so much damage. Conservation of angular momentum and centripetal forces are key to understanding the power of tornadoes.

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Math in the News: 5/9/11

  1. 1. 5/9/11
  2. 2. Tornado DamageData Analysis• The Fujita Scale is used Category Wind Speed (mph) to determine the F5 261-318 severity of a tornado. F4 207-260 F3 158-206• The kinds of tornadoes F2 113-157 that can level whole F1 73-112 buildings are in the F4 F0 < 73 and F5 range.
  3. 3. Tornado DamageAngular Momentum• One of the reasons that tornadoes have such high winds is due to the conservation of angular momentum.
  4. 4. Tornado DamageAngular Momentum• The best example of this is when a figure skater brings her arms in and increases her rate of spin.• This video gives a clear example of this: http://youtu.be/AQLtcEAG9v0
  5. 5. Tornado DamageAngular Momentum• The funnel shape of the tornado causes the narrower part of the tornado to have a faster wind speed.
  6. 6. Tornado DamageAngular Momentum• A simple model of a tornado is a cylinder. Both tornadoes shown have the same angular momentum (L) but different radii and angular speeds.
  7. 7. Tornado DamageAngular Momentum• The tornado on the right has four times the angular speed of the tornado on the left, even though it has half the radius of the first tornado.
  8. 8. Tornado DamageCentripetal Force• But how do swirling winds create such damage to buildings?• The swirling winds of a tornado create a strong centripetal force.
  9. 9. Tornado DamageCentripetal Force• In this diagram, the force shown is from the swirling wind. The speed (v) is the speed of the wind. The value of r is the radius of the circular swirl. And m is the mass of the wind against the building.
  10. 10. Tornado DamageCentripetal Force• Calculate the mass (m) by multiplying the air density by the volume of air.• Think of the column of air in the tornado as a hollow cylinder.
  11. 11. Tornado DamageCentripetal Force• In this diagram, the force shown is from the swirling wind. The speed (v) is the speed of the wind. The value of r is the radius of the circular swirl. And m is the mass of the wind against the building.
  12. 12. Tornado DamageCentripetal Force• Use the following data Variable Value to calculate the force 1.2 kg/m3 on a building from an h 10 m F4 tornado. r1 8m r2 10 m v 112 m/s r 9m
  13. 13. Tornado DamageCentripetal Force• This massive force is equivalent to nearly half a million pounds of weight!

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