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## Open Water 3

A man is in a rowing boat floating on a lake, in the boat he has a brick. He throws the brick over the side of the boat so that it lands in the water. The brick sinks quickly. The question is, as a result of this does the water level in the lake go up or down?

Down.

When an object is floating be it because it is something less dense than water, say polystyrene, or because it is in a boat, say a brick and the whole boat is less dense than water, then it displaces in the water it’s own mass. For example a 10 Kg lump of lead on a boat will force the boat to sink by a volume equivalent to 10Kg of water. Hence displacing 10Kg of water. Or indeed forcing the water level to raise by an amount equivalent to 10Kg of water. (Like when you get in the bath.)

When an object sinks in water it necessarily displaces it’s own volume.

So when the brick is in the boat it is displacing it’s own mass equivalence in water. When the brick is thrown over the side it is displacing it’s own volume in water.

So which of these is greater?

Well we know the brick to be more dense than water because it sinks. So the volume of water equivalent to the mass of the brick is greater than the volume of the brick. And so less water is displaced after than before. Hence the water level goes down!

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