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How high does the teeny tiny shell rocket fly?
A hemisphere shell with mass m and radius R rests on a horizontal table. At the top of the shell there is a hole. The shell is filled with a liquid with density=ρ up to height h<R, The air has density ρ_a=constant. How high (h) does the rocket fly?
Solve this problem using spherical coordinates and
the concept of hydrostatic flux density.
Bonus: What percentage of the water's energy
was imparted to the shell?
Non conservative forces are not involved.
This question was inspired a recent
one asked by Frst Grade Rocks!
very interesting ;)
Dr D: By "fly" I mean how high does
a shell mass=m' move above the plane.
This is a different problem as you know.
Experimentally, using a plastic hemisphere
(half Easter egg) with hole in the top:
No hole: no movement (we know this)
larger hole: definite vertical movement
The hydrostatic energy stored in the "water"
is one logical candidate for said movement.
I'll try to come back with more detail. Thank
you for answering.
It would be interesting to know what
FGR's had in mind when he suggested
that a shell "lifts from the table"
due to the energy density of a liquid.
What is "shell"? If the original question
is not a frolic, there is a deeper physical
meaning that explains the difference between
our answers that has little to do with
liquids or "mass shells" I believe.
3 Answers
- Dr DLv 71 decade agoFavorite Answer
Why do you suppose it will fly? As soon as the shells lifts (assuming that it even does that), all the water will begin to flow out under it, and it will quickly sink back down.
Perhaps you might want to clarify. Is the water continuously poured into the shell until it lifts off? Does someone hold it down, then suddenly let go?
***
I have a means of working it out, at least based on how I see it. As soon as it begins to lift, water is going to start flowing out from under it. This can be worked out via Bernoulli's theorem. Then the water level will decrease until the shell falls back down. That's the idea. When I get some time I'll work it out.
- ?Lv 45 years ago
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