What sort of can would roll the fastest?

[CanFan]

TL;DR Summary

What sort of canned food would roll the fastest (assuming the ramp remained constant and the can couldn't be altered)?

Hello, I'm new here so apologies if this is in the wrong place! I was wondering, hypothetically, what sort of canned food would roll the fastest (assuming the ramp remained constant and the can couldn't be altered)?

I've been looking this up and I know a solid can would roll faster than an empty one. So does that mean a can with more solid, denser food, like Spam, would roll faster than one with thin soup? But I found this lab about a Soup Can Race that says a soup of chicken broth should beat other, thicker soups. I also saw this YouTube video about viscosity which says soups with things inside, like noodles, would roll slower because of friction caused by all the material swirling around.

I don't really have a good understand of moment of inertia and how the movement of substance inside the can affects the can's rolling speed. Any help would be appreciated!

 

[tnich]

Generally, the less turbulent motion within the can, the faster it will roll. So a can full of cranberry sauce should roll faster than a can full of chicken broth, and the chicken broth should move faster than a can of chicken noodle soup. Things moving inside the can do rub against each other and against the can itself, converting energy into heat. So the kinetic energy of the can, and hence its speed, is reduced. The same goes for liquid swirling in the can, though it probably will not convert as much kinetic energy to heat.

 

[CanFan]

Generally, the less turbulent motion within the can, the faster it will roll. So a can full of cranberry sauce should roll faster than a can full of chicken broth, and the chicken broth should move faster than a can of chicken noodle soup. Things moving inside the can do rub against each other and against the can itself, converting energy into heat. So the kinetic energy of the can, and hence its speed, is reduced. The same goes for liquid swirling in the can, though it probably will not convert as much kinetic energy to heat.

Oh wow, interesting! Thank you, that explains it very clearly. Does the mass factor into the can's speed? I'm assuming cans with solid material, like beans, usually have more mass, but they'd be slower because the material rubs against each other?

 

[tnich]

Oh wow, interesting! Thank you, that explains it very clearly. Does the mass factor into the can's speed? I'm assuming cans with solid material, like beans, usually have more mass, but they'd be slower because the material rubs against each other?

If you use similar cans and fill them with different materials, the moment of inertia of the can itself will be the same. Assuming it has a uniform density, the moment of inertia of the food inside is proportional to its weight. If you put the two together, a denser substance inside the can will result in a higher acceleration going down the ramp, though the effect would be very slight. That is because the denser its center, the less an object resists rotation. Think of a figure skater rotating faster as she pulls her arms in toward her body.

 

[Mister T]

Another way of looking at it is that when you have a can filled with a solid, all of the can's contents start to rotate as soon as the can starts to roll. But if you have a can filled with a liquid, all of the can's contents do not start to rotate as soon as the can starts to roll.

 

[tnich]

Another way of looking at it is that when you have a can filled with a solid, all of the can's contents start to rotate as soon as the can starts to roll. But if you have a can filled with a liquid, all of the can's contents do not start to rotate as soon as the can starts to roll.

That's an interesting point. So if less mass is rolling, the moment of inertia is smaller, and the can of liquid picks up speed more quickly, at least to start. I think that effect would be very brief, though.

 

[DEvens]

Another way of looking at it is that when you have a can filled with a solid, all of the can's contents start to rotate as soon as the can starts to roll. But if you have a can filled with a liquid, all of the can's contents do not start to rotate as soon as the can starts to roll.

Which is part of why it's difficult to spin a fresh still-in-the-shell-not-cooked egg, but if it's hard boiled and still in the shell, it spins like anything.

So which would roll fastest, a raw egg or a hard boiled egg? I'm guessing the raw one. Might be some egg rolling going on at my place tonight.

 

[Mister T]

That's an interesting point. So if less mass is rolling, the moment of inertia is smaller, and the can of liquid picks up speed more quickly, at least to start. I think that effect would be very brief, though.

If you set a cup of liquid on a rotating platform that's speeding up, does the rotation rate of the liquid at the core ever reach the rotation rate of the cup?

 

[mfb]

A low viscosity fluid will start rotating slower, keeping the can faster.

I tried to get a can of superfluid helium in the supermarket but they didn't understand me. You probably want to add some insulation or perform the experiment in a vacuum, otherwise you get condensation (water ice or nitrogen/oxygen).

 

[jbriggs444]

If you set a cup of liquid on a rotating platform that's speeding up, does the rotation rate of the liquid at the core ever reach the rotation rate of the cup?

I have in mind a testbed on a long slope. Like a hypothetical 12 mile highway down from the top of Pikes Peak.

An empty can built of thick metal and an equally massive can built of thin metal filled with congealed grease should reach near-identical terminal velocities. The grease can should hit the bottom a bit early due to its head start from its lower moment of inertia.

A third can with the same mass and dimensions filled with chicken broth (and head space) should reach a slightly lower terminal velocity due to the fluid friction and dissipation of energy into turbulence and internal heat. Despite an even larger head start, it should come in dead last due to the reduced terminal velocity.

Without the head space, the broth should wind up spinning at full speed and I'd expect it come in first.

 

[jim mcnamara]

https://arxiv.org/abs/1408.6654 discusses a liquid filled cylinder rolling down and inclined plane.
The authors make claims about viscosity which do not, to me, seem to agree with what has been mentioned.
Caveat - Fluid dynamics is not my area at all. However, this a great thread, IMO.

 

[mfb]

They study the long-term acceleration. Things can get a long head start even if the long-term acceleration is the same.

If we run this in the atmosphere then the object will attain a finite speed and more mass wins over very long distances, independent of the interior (as long as it doesn't keep dissipating energy).

 

[smith_bryan]

We just played with this idea in my AP Physics class. Turns out that there's a clear and consistent ranking of which cans rolled faster down an inclined ramp (about 5% incline, 15 m ramp).

Inviscid fluids like chicken broth were fastest: the liquid wasn't driven to spin and so could slide down the ramp, meaning less potential energy was converted to rotational kinetic and more to translational kinetic.

Solids (or Bingham plastics) like pumpkin pie filling or cranberry sauce or condensed cream of mushroom soup were next fastest. They rotated like you'd expect solid cylinders to, and were all very nearly the same speed, except for the small can of tomato paste which was slower, so we did see a function of radius that doesn't appear in the simple model of a rolling cylinder. My guess is that the tomato paste can rolling slower has something to do with the slight roughness of the surface being large relative to the radius of the can, since it was slower all the way down, not just at high speeds (which might be explained by the relative importance of drag).

Curiously, the slowest cans were filled with viscous fluids, or mixtures of solids in fluids: tomato soup concentrate, canned fruits, corn. Two possibilities here that we didn't have the gumption to explore: A) the viscosity drags the mass up the back of the can, making the net weight vector less far out from the contact point of the can with the ramp; B) the centrifugal effect pushed more of the mass out toward the walls of the can, giving the system a larger moment of inertia than the can had at rest, requiring more energy to spin up.

Now I want to get a pressure canning system and fill (and partially fill) a bunch of cans with fluids of known viscosity. I read the theoretical paper mentioned above and must admit it's been too long since I had anything close to that grasp of fluid dynamics, but still, there's no substitute for experimentation.