Napoleonic & ECW wargaming, with a load of old Hooptedoodle on this & that


Sunday, 26 April 2020

Hooptedoodle #361a - Home Physics Puzzle - SOLUTION

Thanks very much to everyone who sent in a comment - I've now published these against the original post - here - and am pleased with the responses.

Yes, this is all about things which float, starring Archimedes - a man who was famous in my schooldays as someone who made his life's greatest discovery when he broke wind in the bath.

The puzzle is set out in yesterday's post.


Solution:

When the stones are in the boat, they are floating - well, technically it is the boat that is floating, but the stones will push the boat down into the pool to displace an extra volume of water equal in weight to the weight of the stones themselves. This is where Archimedes comes in.

When the stones go over the side, they sink, and will now displace their own volume of water, which - since stones are more dense than water - is less than what they displaced when they were in the boat. Thus - yes, that's right - the water level on the side of the pool will go down. The only special case would be if the stones were able to float on their own (because they were pumice, or hollow, or fake stones made of wood, or because the water was polluted to an astonishing degree), in which case, of course, they would continue to displace their own weight of water, and the level would remain the same.

Once again, thanks very much for having a go. Some excellent answers, and some very good explanations of the less correct ones. Just to put an official seal on things, I was going to attempt this experiment today, but the bird bath is too small.


9 comments:

  1. I received an anonymous message this morning, to the effect that Count Goya (international man of mystery) has business associates in the Mount Etna region who have found this to be a practical difficulty when disposing of problems.

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  2. Well I'll be a . . . futtwitt, clearly!

    H

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  3. Actually it doesn't matter whether the stones are i the boat or in the water - they displace the same amount of water either way. The difference is air - the average density of the boat is now less so the boat will ride higher out of the water. As the boat is higher out of the water then yes, the water level on the side of the pool will go down - just for a slightly different reason!

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    1. If the stones displace their volume of water when they are still in the boat then the boat has already sunk, I think.

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    2. Tony, I think so too. If a rock is more dense than water then it displaces its mass when in the boat and displaces its volume when sitting on the bottom of the pool. If mass (rock) > volume (rock) then water level falls when the rock is thrown overboard.

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  4. Actually that's also not strictly true as I haven't factored in the direct water dis[placement caused by the stones... and that is a density issue. The higher the density of the stones, the more it would have 'pushed' the boat down and thus the higher the boat would ride in the water once the stones have been dumped - fact is, without taking unstated factors such as this into the equation a final answer is not possibe to determine!

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  5. Well that was fun. Having sent my immediate response, I then spent a happy half an hour looking it up through Google. Having done that, and reading your comments Tony, I learned that apparently I spent too little time considering Archimedes’ farts when in high school. Lesson for my daughter there, and an enriching and pleasurable time here. Thanks.

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    1. God bless you, Ivan. May your stones float in peace and tranquillity.

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