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Math in the News: 1/26/12

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Page 1: Math in the News: 1/26/12
Page 2: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaClick on the video link to learn more about the sinking of the Costa Concordia.

https://www.youtube.com/watch?v=MxPJCNv_U84

Page 3: Math in the News: 1/26/12

The following reconstruction of the

sinking of the Costa Concordia is

based on news reports, videos, and

photographic evidence. We apply

logical reasoning to come up with

the scenario.

Page 4: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaBecause the ship was approaching too close to land, it hit a rock jutting out of the water, almost like a car riding over a bump on one side of the car.

Page 5: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaThe rock would have caused the ship to list clockwise, as shown. Because of its high center of gravity, the ship would have listed at a greater angle than a ship with a lower center of gravity.

Page 6: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaThink of a hemispherical piece of styrofoam with a short straw sticking out. Tilting it sideways will have the hemisphere return to its equilibrium position fairly quickly.

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The Sinking of the Costa ConcordiaTry the same thing with a longer straw, which has a much higher center of gravity. In this case, the straw will bend more and return to equilibrium much slower, due to the higher center of gravity.

Page 8: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaA cruise ship has a very high center of gravity, so when it lists, it returns to its equilibrium position slowly.

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The Sinking of the Costa ConcordiaThe collision with the rock created a giant hole in the hull of the ship. And water immediately rushed into the hull.

Hole in the hull.

Page 10: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaBecause of the ship’s tilt, the water rushing into the hull collects on the opposite side, away from the hole.

Water fills one side of the hull.

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The Sinking of the Costa ConcordiaThe slowness of returning to an equilibrium while water is rushing into the hull actually keeps the ship listing. From this point on the ship will continue listing and will not return to its equilibrium position.

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The Sinking of the Costa ConcordiaIt’s possible that the ship reached a new equilibrium point. If so, the ship was listing at such an angle that the hole in the hull was above water, with little additional water was coming in.

20°

At this angle no additional water comes in

Page 13: Math in the News: 1/26/12

The Sinking of the Costa ConcordiaThe ship should probably have been evacuated immediately, but the captain decided to continue sailing, until it was clear the ship could go no further. At this point a hard turn to the port on the island is attempted.

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The Sinking of the Costa ConcordiaThe sharp turn would have reduced the angle of the ship’s listing, due to centripetal acceleration. But reducing the angle of title would have exposed the hole in the hull to more water and the ship would have taken on more water.

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The Sinking of the Costa ConcordiaWith more water coming into the hull, while the ship is turning, the Costa Concordia capsized.

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The Sinking of the Costa ConcordiaBecause the ship was so close to land, in capsizing it hit bottom and remained in the position it now finds itself in.

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The Sinking of the Costa Concordia

• In summary, this chain of events led to the sinking of the Costa Concordia:– The ship hits a rock jutting out of the

water.– The rock causes the ship to list and rips

a hole in the hull.– The ship takes on water on one side,

causing the ship to stay tilted.– The ship continues sailing but then a

sharp turn is attempted.– This sharp turn changes the angle of

tilt of the ship, exposing the hole in the hull to more water.

– After taking in more water, the ship capsizes and runs aground.