Una lattina di birra in treno
Consider a can of beer.
Assuming the can is a right circular cylinder, it is known that the center of gravity ($CG$) is at its lowest when it coincides with the top of the liquid in the can.
However, riding on British Rail made me wonder what level of fluid in the can would make the can maximally stable.
We can measure the stability as the energy required to raise the $CG$. from its position when the can is vertical, to its position when the $CG$ is just above the point of support of a tilted can.
When is this position maximized?
For standardization, let the can have radius $R$, height $H$, mass $M$, and let it contain mass $m$ of liquid when full.
DAVID SINGMASTER
Nella soluzione si assume che "the thickness of the walls of the can to be negligible"
Cordialmente, Alex
Assuming the can is a right circular cylinder, it is known that the center of gravity ($CG$) is at its lowest when it coincides with the top of the liquid in the can.
However, riding on British Rail made me wonder what level of fluid in the can would make the can maximally stable.
We can measure the stability as the energy required to raise the $CG$. from its position when the can is vertical, to its position when the $CG$ is just above the point of support of a tilted can.
When is this position maximized?
For standardization, let the can have radius $R$, height $H$, mass $M$, and let it contain mass $m$ of liquid when full.
DAVID SINGMASTER
Nella soluzione si assume che "the thickness of the walls of the can to be negligible"
Cordialmente, Alex
Risposte
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Caspiterina! 
Ma quanto ti ci è voluto?
Perché non lo pubblichi fa qualche parte, che ne so, tipo arXiv? Anche se, a dir la verità, pure questo Forum ha una sua qual certa visibilità ...
Cordialmente, Alex
Ma quanto ti ci è voluto?
Perché non lo pubblichi fa qualche parte, che ne so, tipo arXiv? Anche se, a dir la verità, pure questo Forum ha una sua qual certa visibilità ...
Cordialmente, Alex
.
Dal sito di arXiv:
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Registered users may submit articles to be announced by arXiv.
There are no fees or costs for article submission.
Submissions to arXiv are subject to a moderation process ..."
"arXiv® is a curated research-sharing platform open to anyone ...
Registered users may submit articles to be announced by arXiv.
There are no fees or costs for article submission.
Submissions to arXiv are subject to a moderation process ..."
.
[ot]"Material is not peer-reviewed by arXiv"[/ot]
.
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