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Think outside the can - a challenge for Y-san


Best Answer jhawk, 05 April 2013 - 07:43 PM

Spoiler for let me rethink this
]

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#1 bonanova

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Posted 05 April 2013 - 05:55 PM

Knowing how it is second nature for my friend Y-san to solve extremal problems by equating derivatives of functions to zero, I was delighted to find a problem that can be solved with only a pencil, some drawing paper and a little thought. Here it is.

 

Imagine an empty can that weighs 1.5 ounces. It is a perfect cylinder with weightless top and bottom, so that any asymmetry introduced by punching  holes in the top can be disregarded. The can holds 12 ounces of beer; so its total weight, when filled, is 13.5 ounces. The can is 8 inches high. Without using calculus, determine the level of the beer at which the center of gravity is at its lowest point.

 

Consider that, as beer is removed from a full can, the center of gravity is lowered. But empty and full, the center of gravity is in the same place. So there must be a filling factor where it is lowest.


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#2 jhawk

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Posted 05 April 2013 - 07:43 PM   Best Answer

Spoiler for let me rethink this
]


Edited by jhawk, 05 April 2013 - 07:53 PM.

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#3 bonanova

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Posted 09 April 2013 - 11:39 AM

Spoiler for let me rethink this
]

 

jhawk, sorry for not replying sooner.

 

That is the correct answer. Care to share your method?

I have a clever thought process (it's not mine) that leads to it that I will share if you want to go first.

It involves freezing.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 plasmid

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Posted 10 April 2013 - 05:20 AM

Not sure if this was the same process that jhawk used, but it's what I would have done if it weren't already answered. And it doesn't seem to involve freezing.
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#5 bonanova

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Posted 10 April 2013 - 05:26 PM

Not sure if this was the same process that jhawk used, but it's what I would have done if it weren't already answered. And it doesn't seem to involve freezing.

Spoiler for

Nice.

Freezing would allow balancing the can sideways on a fulcrum at its beer height. Then exactly what you said is obvious. Either adding beer or subtracting beer will make the can fall toward its empty side.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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