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Because the weight of the ship is distributed across the water enough for the water to be able to support it.

Think about the large volume of water that previously was in the place where the underwater-part of the ship is. That water weighs a huge amount and it doesn't sink because it would only have to be replaced by water from elsewhere and all the sea would be in turmoil. So all a ship designer has to do is make sure that the weight of his ship is no more than the weight of that volume of water it replaces ("displaces") and that has to happen before the ship sinks so low that the water comes over the sides. Although ships are extremely heavy, they are hollow so the average density is low enough so this can be done. In the end, the weight of water displaced by the ship exactly equals the weight of the ship. This was figured out by Archimedes a couple of thousand years ago.

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Q: Why doesn't a big heavy boat sink?
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