Water in a Pool

Classical Mechanics Level 3

You are in a boat that is floating in a pool containing a fixed volume of water. In the boat is a water tight box.

If you move the box from the boat into the water, what will happen to the level of the water in the pool?

NOTE: The contents of the box are unknown.

The water level will drop. The water level will stay the same. The water level will rise. It depends on what the box does.

Gary Miller by Gary Miller , 68, USA

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2 solutions

Gary Miller
Aug 30, 2020

It depends on what the box does.

While the box is in the boat it displaces water equal to its weight through the boat hull.

If the box floats it continues to displace water equal to its weight which is less than its volume (or else it would sink) and the level of the water will stay the same.

If the box sinks it will displace water equal to its volume which is less than that of its weight (or else it would float) and the level of the water would drop.

5 Helpful 3 Interesting 3 Brilliant 1 Confused

This is also the conclusion I came to. Nice problem! Especially the counterintuitive result that a box that sinks into the water actually lowers the water level.

Comments on previous wording of the solution: It sounds odd to say a weight is more than or less than a volume . Every time you say 'its weight,' it would be better to say something like 'a volume of water equal to its weight.' Clunky sounding, but a better basis of comparison.

Matthew Feig - 9 months, 2 weeks ago

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Thank you! I had the exact same problem when I thought of comparing weight and volume. This helped immensely.

Joshua Lowrance - 9 months, 2 weeks ago

I agree, that is much more accurate. I'll edit my post. Thank you.

Gary Miller - 9 months, 2 weeks ago

Stupid question

Tejas S - 8 months, 3 weeks ago

The water container can be made out of wood, metal or some other material, so it might float or sink, and accordingly, might result in rise in water level by sinking (equal to it's volume) or by floating (equal to the level of water inside), so it really depends on the kind of container it is.

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My wording may have been confusing. The box being water tight means no water will enter the box, not that it contains water. The contents are unknown and may be heavy or light. Remember that the box and its contents also displace water while in the boat.

Gary Miller - 9 months, 2 weeks ago

I think you are right if the box has something light it will float and will not cause much water displacement. But if the object is heavy it may sink, but WILL cause more water displacement. But the odds are 50/50 beacuase like you you said the object is unkown. And also you are right on the box being water tight

Ris Neps - 9 months, 1 week ago

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The key is that the box displaces water both while in the boat and while in the water. In the boat, it displaces a volume equal to it's weight by making the boat sit lower in the water. When in the water, the boats displaces less due to the reduced weight and the amount the box displaces depends on whether it sinks or floats.

Gary Miller - 9 months, 1 week ago

please note that I am not a teacher nor student, just a coder that does not focus on one thing or course

Ris Neps - 9 months, 1 week ago

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