partially-filled rolling can experiment

[mostafalelsan]

Hello, I am writing an extensive research paper with the title of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane? (I am planning to make dynamics more specific if I choose to analyze angular velocity/acceleration/momentum specifically).

So far, I was able to derive equations for the acceleration in cases where the can is fully-filled or hollow, but have been struggling in finding a way to model it when it is partially filled. For instance, I tried to model it in such a way where if the mass is assumed to be distributed equally then the water will be at an angle perpendicular to the inclined plane based on the amount of liquid within the can. This is what I have so far: https://docs.google.com/document/d/1loL ... g=h.gjdgxs

Of course, I am now stuck as I do not know how to model it and I am unsure on if I should use a photogate or motion detector as the main tool in the experiment. I have a 4000 word limit so my theoretical background and experiment should be within those boundaries. Does anyone have any ideas on any sources I could use that help me detail these specific situations? Thank you in advance.

[bfinio]

Hi,

Predicting the shape of the water inside a rolling can is a very advanced fluid dynamics problem. I don't have an easy answer, but off the top of my head I can imagine a few different scenarios:

1. The can rolls slowly enough that the water stays at the bottom of the can (possibly with its surface at an angle, not perfectly horizontal)
2. The can rolls fast enough that the water is flung toward the outside of the can, forming an annulus with an air space in the middle
3. A transition period where the water is pulled up the back wall of the can but then falls down (similar to a marble roller coaster not going fast enough to make it through the loop)

A quick Google search shows that there are some existing publications that address this problem, but again the math is very advanced if you are actually trying to predict the behavior of the water:

https://physics-archive.wooster.edu/JrI ... rticle.pdf

https://www.researchgate.net/publicatio ... ined_plane

If possible, I would suggest doing the experiment with a clear cylinder (e.g. a plastic container with a clear lid) so you can film it and see what the water is actually doing. That will help you decide what mathematical model for the water's behavior is the most appropriate.

[bfinio]

It also looks like other students have asked about this project in the past, you might find the links in this post helpful: viewtopic.php?t=21794