http://www.straightdope.com/columns/read/423/is-frozen-milk-heavier-than-liquid-milk
Call me nuts, but I don’t think the lady referred to in the question meant literally “it weighs more frozen”. It stands to reason that a frozen block of milk inside a box is going to feel quite different when lifting it into a dispenser than the equivalent liquid quantity of milk. A layman might very well describe that as feeling “heavier”.
Powers &8^]
My thoughts exactly. A carton of frozen milk is going to have a larger “effective” moment of inertia than liquid milk, and for many objects this is an effective proxy for heaviness (or density). It stands to reason that someone may mistake the two physical properties, especially given the traditional shake of the milk carton to determine how full it is (though the letter is presumably talking about somewhat larger containers).
Can you show me the math behind this?
I could, but it would be easier to just describe it. For simplicity, imagine a spherical carton of negligible mass and milk of negligible viscosity (made from a spherical cow?). When you rotate it, the milk inside will remain stationary and thus the system as a whole will have a very small “effective” moment of inertia.
Compare to a system with frozen milk inside. The milk rotates along with the carton and thus adds to the moment.
Of course the real world is not so simple. The milk has viscosity and thus there is some momentum transfer to it, and the container is not spherical (so milk at the extremes must move with the container). And there’s nothing you can do about the “true” moment of inertia–given enough time, the milk inside will stop flowing, and the total angular momentum will end up the same as in the frozen case (sans any difference due to a change in volume).
Nevertheless, the moment of inertia that a person feels by rotating a container of liquid around is going to be less than if it were frozen. A delicate instrument could detect the total angular momentum transfer, but our hands ain’t it.
I don’t get this. You learn in elementary school (practically) that the reason ice floats is because it becomes more dense as it cools but in the last few degrees in cooling it expands until it is lighter than liquid water. That is why it floats.
It would seem to be obvious that the same would be true of frozen milk. He should consult Una before reposting old columns.
Oops. Now that I think about this, my comment was dumb. Sorry.
Some things are easier to demonstrate. Take a fresh egg and a hard-boiled one. Spin both of them on a tabletop at roughly the same speed.
See which one stops sooner. The difference should be fairly dramatic.
It is true, though, that milk, like water, expands when it freezes. When I was a kid in Maine, we had our milk delivered (it was common then), and it would sometimes happen that we would find a bottle with a column of frozen milk standing in the mouth, with the bottlecap proudly sitting at the top.
With respect, a lot of things “make sense” until you try to do the math, and find out they don’t work in real life. Your system requires a significant air gap for this “effective” moment of inertia to work. What if there’s little to no air gap? When I buy a gallon on milk there is almost no air to speak of at the top of the plastic jug, and I don’t seem to detect any movement.
No it doesn’t, it just requires reasonably low viscosity, such that a rotation applied on the outside of the carton doesn’t rotate the fluid inside as a rigid body.
Mr. Moto and zut are entirely correct: no air gap is required, and an egg is an excellent suggestion for a demonstration.
However, the egg may not be an entirely satisfactory experiment, since you cannot see the internal movements. And unfortunately, even when the container is clear, household liquids that are transparent enough to see through typically don’t contain enough particulate matter to observe the flow patterns.
That said, you might try this: find a clear jar with an aspect ratio somewhat close to 1, such as a Mason or peanut butter jar. Fill it most of the way with water, then add a teaspoon or two of ground black pepper. Attach the lid and shake, such that the pepper is dispersed. Add more water to the point of forming a meniscus and reattach lid. Make some quick rotating motions to mix again, and let rest until the internal movements die down.
Assuming the pepper remains in suspension for a useful period of time (a point I’m not sure of, since I haven’t tried the experiment), you should be able to easily see how the water does not immediately rotate with the rest of the container, especially with axial rotations (assuming the jar has a circular cross-section).
I see. Thank you for the suggestions. An experiment or two may be in order.
Just for the record, and so lurkers don’t get the wrong idea, I’m guessing the milk carton in question was an industrial-size multi-gallon box (the kind with a rubber spout), rather than a standard off-the-shelf half-gallon or the like.
Powers &8^]
I made a quick video of my experiment:
It works reasonably well, although only a small fraction of the pepper remains suspended, with the rest either floating or sinking. If I took the time to remove this portion, the effect would be a lot better, especially for non-axial rotations.
I’m going to talk to Cecil about this later this weekend to see if he might like to mention something else as a related topic in the online column.
I’d say it’s worth more than a “guess”. The wording seems quite explicit.
When I was young, they used modified standard 5-gallon (or thereabouts) aluminum milk cans with a rubber hose in the bottom, instead of a plastic bag in a cardboard box. The hoses would be sealed, and after the can was installed in the machine, you’d just whip out a knife and slice the last few inches off the hose to open it.
The distribution of the weight can make a difference in which muscles are engaged during lifting and to which degree.