You are in a boat in the middle of a lake. Inside the boat is a box full of very heavy steel marbles. If you throw all the marbles into the water, does the lake level rise, fall, or stay the same?
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The boat and the marbles in the lake
The scene seems physical, but ultimately it is a problem of comparison: the same matter affects the water in one way inside the boat and in another when it is already in the lake. The difference is in looking at what “counts” in each case.
Hints
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- Compare a marble when it is in the boat with that same marble when it is already sunk.
- An object supported by the boat has influence due to its weight; a submerged object, because of the space it occupies.
Solution
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Answer: The water level goes down. Explanation: While the marbles are in the boat, their weight causes the boat to displace water. And a floating object displaces exactly the volume of water whose weight equals its own. That means that, while in the boat, each marble “displaces” an amount of water equivalent to its weight. When you throw it into the lake, however, the marble no longer floats: it sinks. From that moment on it only displaces the water corresponding to its own volume. Since steel is much denser than water, the volume of water whose weight is equivalent to that of the marble is greater than the volume of the marble itself. Therefore, a marble in the boat displaces more water than that same marble sunk in the lake. By throwing them all into the water, the total displacement decreases, and the lake level lowers.
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