math in the news: 5/9/11
DESCRIPTION
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.TRANSCRIPT
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5/9/11
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Tornado DamageData Analysis• The Fujita Scale is used
to determine the severity of a tornado.
• The kinds of tornadoes that can level whole buildings are in the F4 and F5 range.
Category Wind Speed (mph)
F5 261-318
F4 207-260
F3 158-206
F2 113-157
F1 73-112
F0 < 73
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Tornado Damage
Angular Momentum• One of the reasons
that tornadoes have such high winds is due to the conservation of angular momentum.
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Tornado Damage
Angular 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
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Tornado Damage
Angular Momentum• The funnel shape of
the tornado causes the narrower part of the tornado to have a faster wind speed.
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Tornado Damage
Angular 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.
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Tornado Damage
Angular 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.
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Tornado Damage
Centripetal Force• But how do swirling
winds create such damage to buildings?
• The swirling winds of a tornado create a strong centripetal force.
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Tornado Damage
Centripetal 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.
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Tornado Damage
Centripetal 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.
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Tornado Damage
Centripetal 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.
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Tornado Damage
Centripetal Force• Use the following data
to calculate the force on a building from an F4 tornado.
Variable Value
p 1.2 kg/m3
h 10 m
r1 8 m
r2 10 m
v 112 m/s
r 9 m
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Tornado Damage
Centripetal Force• This massive force is
equivalent to nearly half a million pounds of weight!