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# Math in the News: 1/26/12

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In this issue of Math in the News we analyze how the Costa Concordia sank.

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### Math in the News: 1/26/12

2. 2. 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.
3. 3. The Sinking of the Costa Concordia Because 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.
4. 4. The Sinking of the Costa Concordia The 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.
5. 5. The Sinking of the Costa Concordia Think 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.
6. 6. The Sinking of the Costa Concordia Try 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.
7. 7. The Sinking of the Costa Concordia A cruise ship has a very high center of gravity, so when it lists, it returns to its equilibrium position slowly.
8. 8. The Sinking of the Costa Concordia The 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.
9. 9. The Sinking of the Costa Concordia Because 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.
10. 10. The Sinking of the Costa Concordia The 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.
11. 11. The Sinking of the Costa Concordia It’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
12. 12. The Sinking of the Costa Concordia The 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.
13. 13. The Sinking of the Costa Concordia The 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.
14. 14. The Sinking of the Costa Concordia With more water coming into the hull, while the ship is turning, the Costa Concordia capsized.
15. 15. The Sinking of the Costa Concordia Because the ship was so close to land, in capsizing it hit bottom and remained in the position it now finds itself in.
16. 16. 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.