# The Riddle

Discussion in 'All Things Boats & Boating' started by PAUL XAVIER, Jan 8, 2016.

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### PAUL XAVIERJunior Member

I think its worth a try!

A man stuck in a small sailboat on a lake throws a stone overboard. It sinks to the bottom of the lake.What will happen to the water level of lake?
PS:Lake is not large enough to neglect the effect of stone.

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### Mr EfficiencySenior Member

OK, well, while the rock is in the boat it displaces more than its volume, through the agency of the boat, when it sinks, it displaces exactly its volume, so I'd say the level of the lake falls.

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### jehardimanSenior Member

Concur. The water level in the lake falls proportional to the water volume density equal to the weight of the rock (i.e. boat displaces less). The water level in the lake rises proportional water volume density of the volume of the rock. Since the rock sinks, the rock volume * the water volume density is less than the rock weight, so the volume increase is less than the volume decrease so the total volume (water +rock) is less than the previous volume (water+boat)

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### TANSLSenior Member

But when the stone is on board the ship moves more water than when the stone is at the bottom of the lake.
The ship, without stone, displaces less volume of water, thus decreasing the level of the lake.

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### BarrySenior Member

I would say the level stays the same
When the rock is in the sailboat, the sailboat displaces the weight of the rock and the boat.
Two conditions
When the rock is in the air before it hits the water, the lake level drops as the boat displaces only the weight of the boat

When the rock is under water, the lake level comes up to its original level

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### hoytedowFly on the Wall - Miss ddt yet?

When the rock is on the bottom of the lake it displaces only its volume. When the rock is in the boat it displaces its weight via the boat hull. The lake level drops, more or less, depending upon the surface area of the lake. The greater the area, the more insignificant the variance.

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### Tiny TurnipSenior Member

when the stone is in the boat it displaces its *weight* of water.

when it is in the air it displaces no water

when it is in the water it displaces its *volume* of water.

the weight of the stone's volume of water is less than the stones weight of water.

(we know that because it sinks)

So, as the stone is tossed out of the boat, the level will go down, then come back up as the stone enters the water, but not as far up as it did when it was in the boat.

You can see this demonstrated in the following video from about 2.35 on.

ok, it doesn't really demonstrate it at all, but hey its related, and if you don't know it, its such a glorious short that its worth watching the whole thing

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### hoytedowFly on the Wall - Miss ddt yet?

Hahahaha.

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### gonzoSenior Member

There is no change. The boat, lake and stone comprise a closed system.

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### TANSLSenior Member

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### Mr EfficiencySenior Member

Don't stake too much money on that proposition.

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### Angéliqueaka Angel (only by name)

Same kind of question was asked before, the lake's water level drops . . :idea:

P.S. - See post #22 & #24 for the explanation there.

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### ImaginaryNumberImaginary Member

As a thought experiment, assume the 'stone' is made of whatever a neutron star is made of (extremely high density), and thus is microscopic in volume. How will throwing it overboard change, or not change, the level of the lake?

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### Mr EfficiencySenior Member

The same result, presumably, if the boat doesn't sink first !

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### hoytedowFly on the Wall - Miss ddt yet?

Why postulate on the ridiculously impossible?

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