Simple common-sense physics problem


Vort
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Here's an example of the sort of problem I've asked my children while they were growing up, attempting to develop their physical intuition. I sort of considered it part of their homeschooling, but more than that, I just liked asking them such questions.

I have a two-liter bottle of soda pop that I want to drink ice cold, if possible, in my favorite Looney Tunes glass.

Amazon.com : Vintage Looney Tunes Glass Set : Everything Else

(We had two or three complete sets of these while I was growing up. All broken long ago, I'm afraid. I bet they'd be worth a small fortune today.)

My strategy is to put ice from my freezer in the glass and then add soda pop. I want the soda pop as cold as reasonably possible, but I'm most seriously concerned about soda pop dilution—I want my pop to remain as undiluted as possible. How much ice should I add before I pour pop over it?

A. As much ice as fits in the glass
B. Equal amounts of ice and pop
C. Exactly the amount of ice needed to bring the pop's temperature down to the freezing point of water
D. Doesn't matter, as long as there is sufficient ice

For the purposes of this problem, let's pretend (if it makes any difference) that we're using plain old water ice made in a typical American freezer (that works correctly), that the soda pop is the same density as the (liquid) water, that the soda pop's freezing point is below that of water ice, and that the glass is insulated. (Just roll with it. Spherical cow and all that.)

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If we are assuming 'perfect insulation' and that C is physically possible, then the best answer would be C because once the soda is at the freezing point of water, the ice will no longer melt.  That said in a real-world scenario I would require additional variables:

-  What is the capacity of the glass?

-  How much soda do you wish to consume?

-  How quickly will you drink the soda after pouring?  (This one being the most important)

If the quantity of soda is unimportant and you intend to drink it quickly, then A and C will achieve the same result, although A will achieve it faster.  If you intend to drink it slowly, A will preserve the coolest temperature longer.  Assuming B does not achieve C, and that C requires a quantity of ice that is between A and B, then B will minimize dilution over a longer period.  C would give you the best of both worlds, but could not individually win either requirement on it's own.

The real question is, why are you not doing one of the following to better fulfill your desires?

-  Put the soda bottle in the freezer for sufficient time to chill it to satisfaction.  (I seriously put my soda in the freezer - I especially like when it get just slightly slushy!)

-  Pour some soda into an ice-cube tray and make 'soda ice' such that dilution does not become a factor.  (I also have done this and it is awesome!)

-  Mix the syrup to a higher concentration such that the initial dilution of the soda by the ice melting during the temperature adjustment brings the mixture to the correct level of consumption?  (Although I haven't done a truly scientific test, I am certain we do this for the fountain machines we have at work)

Okay.  I've had my fun.  😁

ANECDOTE:  I once got into a heated argument with a college professor about a test question that went something like this: "Daily, a manager reviews the production data for all branches from the previous day and uses it in making business decisions; what is this called?"  Supposedly, the answer was 'using real-time data'; no way I was letting that go!  The professor refused to relent because that was the answer given by the creators of the text book 🙄.  She was unwilling to accept the difference between day old data and true real-time or near real-time data, like stock-market updates.  It may come as no surprise that despite her PHD in business management, she had never worked a non-teaching job in her life!

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I remember all of those except the "Cool Cat" glass. Oh to be young and carefree again [wistful sigh].

As one who hates "watered down" more than "a little too warm", my answer is probably something like C, but I'm not too worried about cooling it to 0 C. Just a minimum of ice needed so it is not "warm" (what would that be -- above 25 C?). I would generally prefer 10-20 C soda than watered down soda.

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Assuming moderately cold ice (20°F (-6°C) or so), A is the most likely correct answer. Depending on the temperature of the ice and the soda pop, it is possible that A would result in ice-cold soda pop with no dilution at all. B could possibly have this same result, but it is less likely. C actually results in maximum dilution of the soda pop. D is a mealy-mouthed non-answer; of course it matters how much ice there is. What does "sufficient ice" even mean?

Edited by Vort
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8 minutes ago, Vort said:

Assuming moderately cold ice (20°F (-6°C) or so), A is the most likely correct answer. Depending on the temperature of the ice and the soda pop, it is possible that A would result in ice-cold soda pop with no dilution at all. B could possibly have this same result, but it is less likely. C actually results in maximum dilution of the soda pop. D is a mealy-mouthed non-answer; of course it matters how much ice there is. What does "sufficient ice" even mean?

The answer is non-of-the-above.  Because nobody here knows what a soda pop is.

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If A is correct, it seems like we are assuming that the beverage will be consumed very soon after preparation. The optimum time is long enough for the beverage to cool (and the ice to warm) but no longer so that a minimum of ice actually melts.

Of course, this ideal scenario does not account for Murphy's law. According to Murphy's law, as soon as you have poured the drink but before you have a chance to sip contentedly, some little somewhere in the house will have a "crisis" that demands immediate attention, followed by the dog or cat getting into trouble and requiring discipline, and then you will forget that you poured yourself a drink and, by the time you remember and get back to your drink, there is no ice left and it is nothing but watered down sugar water. But, you're a conservative person who doesn't like to waste things, so you knock down the watered down stuff because "you can do hard things" and explain to the littles that they, too, can do hard things -- like drink watered down soda pop with a smile on their face. But, I am still wrong, because the value of the lesson is such that, even accounting for Murphy's law, A is still the best choice (much to my chagrin).

I think I'll just drink straight from the 2L bottle, then no one else will want some and I'll have the whole 2L to myself and drown my sorrows in carbonated sugar water (since I don't believe in drinking anything stronger).

Edited by MrShorty
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I've been thinking about this problem.  And it appears that if we are to eliminate some less likely conditions and only look at most likely scenarios, utilizing only common sense with general physics principles, then it doesn't really matter how fast you drink the soda.

  • You put as much ice as possible into the glass. 
    • This will have the greatest ratio of cooling effect on the soda.
    • The soda has little to no chance of actually freezing.
    • With sufficient ice-to-soda ratio, the soda will cool to near freezing without melting any of the ice.
  • It cold be that you simply max out the ice and pour only small amounts of soda in at a time.  Drink it.  Then pour more soda in. 
    • This means that what little ice does melt will be drunk up as the last bit of dregs of each fill up.  
    • Then you get a fresh, undiluted quantity of soda to be cooled by the remaining ice which now has a greater specific surface to transfer the heat.
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On 5/13/2020 at 12:42 PM, Vort said:

Assuming moderately cold ice (20°F (-6°C) or so), A is the most likely correct answer. Depending on the temperature of the ice and the soda pop, it is possible that A would result in ice-cold soda pop with no dilution at all. B could possibly have this same result, but it is less likely. C actually results in maximum dilution of the soda pop.

Based on this response from you, I suppose I made one incorrect assumption.  As should be clear from a re-read of my answer, I interpreted, "Exactly the amount of ice needed to bring the pop's temperature down to the freezing point of water", to mean INSTANTANEOUSLY (or nearly), as in, 'as soon as the glass is full, it is ice-cold'.  However, I suppose you might believe that indicating eventuality in your question could make the question too easy.  Oh well 🤷‍♂️

Edited by person0
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6 hours ago, Carborendum said:

With sufficient ice-to-soda ratio, the soda will cool to near freezing without melting any of the ice.

Technically this isn't physically possible with room-temperature soda because the initial contact of ice and soda will necessarily melt, at least partially, the first piece of ice with which the soda comes into contact.  Until the entire glass is filled with liquid to the extent that all ice-cubes can share in the cooling of the soda, the ice on top that is continuously hit with 'freshly room-temperature' soda, will continue to melt.  Test it for yourself, it is pretty much unavoidable.  😞

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16 minutes ago, person0 said:

Technically this isn't physically possible with room-temperature soda because the initial contact of ice and soda will necessarily melt, at least partially, the first piece of ice with which the soda comes into contact.  Until the entire glass is filled with liquid to the extent that all ice-cubes can share in the cooling of the soda, the ice on top that is continuously hit with 'freshly room-temperature' soda, will continue to melt.  Test it for yourself, it is pretty much unavoidable.  😞

If the ice is sufficiently cold and the soda pop poured slowly enough. the ice can warm up yet still remain below freezing while cooling down the pop. So it's possible. (Unlikely, but possible.)

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4 minutes ago, Vort said:

If the ice is sufficiently cold and the soda pop poured slowly enough. the ice can warm up yet still remain below freezing while cooling down the pop. So it's possible. (Unlikely, but possible.)

Once again, assumptions fail me!  This time about the temperature of the ice. Hehehe!

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29 minutes ago, person0 said:

Once again, assumptions fail me!  This time about the temperature of the ice. Hehehe!

The ice will warm at a more or less constant rate of heat intake until it reaches its melting temperature. At that point, it will continue to absorb heat without changing temperature; instead, it will change state, from solid ice to liquid water. This is where the dilution comes into play. If you can keep any (or much) of the ice from melting, you will keep the soda pop from diluting. Therefore, you want as much mass of ice as possible to cool the pop without melting the ice. Ergo, maximum ice.

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9 hours ago, person0 said:

Technically this isn't physically possible with room-temperature soda because the initial contact of ice and soda will necessarily melt, at least partially, the first piece of ice with which the soda comes into contact.  Until the entire glass is filled with liquid to the extent that all ice-cubes can share in the cooling of the soda, the ice on top that is continuously hit with 'freshly room-temperature' soda, will continue to melt.  Test it for yourself, it is pretty much unavoidable.  😞

In a real world, you're right to a degree (NPI).  But @Vort was talking about ignoring the minutiae and getting to the big factors.  You remember the mention of spherical cows.

Edited by Carborendum
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  • 4 weeks later...

I just had to explain something to the project manager of a very large project at work.  I thought it would be a great exercise for this thread.  Here is the problem:

  • There is an electrical control panel (3'x3') mounted on a pole in the middle of an industrial plant. 
  • It is set with the top at about 5'-6" for easy use by someone of average height.
  • The panel has two doors -- one opening in each direction (right and left).
  • There is a roof shelter about 4' x 4' above it.
  • Supporting the roof shelter, is a frame around the perimeter of the 4'x4' projected area.

Question1:  Which direction should the panel doors face for the user to minimize the user seeing the sun while using the panel?

Question2: What would you use for the roof material to be placed on a 4' square frame? Flat steel plate 1/4" thk or corrugated steel sheets (26 guage)? NOTE: corrugations are at 9" on center.

Edited by Carborendum
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9 minutes ago, Carborendum said:

I just had to explain something to the project manager of a very large project at work.  I thought it would be a great exercise for this thread.  Here is the problem:

  • There is an electrical control panel (3'x3') mounted on a pole in the middle of an industrial plant. 
  • It is set with the top at about 5'-6" for easy use by someone of average height.
  • The panel has two doors -- one opening in each direction (right and left).
  • There is a roof shelter about 4' x 4' above it.
  • Supporting the roof shelter, is a frame around the perimeter of the 4'x4' projected area.

Question1:  Which direction should the panel doors face for the user to minimize the user seeing the sun while using the panel?

Question2: What would you use for the roof material to be placed on a 4' square frame? Flat steel plate 1/4" thk or corrugated steel sheets (26 guage)? NOTE: corrugations are at 9" on center.

The wording of your question indicates that there are all sorts of variables that I'm not considering because I don't know what they are. Nevertheless, I'll give it a try.

1. North

2. Given the choice, corrugated sheet steel, because who the heck would ever use quarter-inch steel plate for a simple roof for a 4'x4' shed without walls? 48" is not evenly divisible by 9", but so what? I don't need to attach the corrugated material right at the edges, anyway.

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2 hours ago, mordorbund said:

The panel is 3' tall and 3' wide (even wider when the doors are open). Why not have the user face the sun but block out the sun with the box?

If the panel faces north, the user faces south, with the doors blocking out the sides. But given the height of the box off the ground, probably better to have the user facing north instead of the panel.

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12 hours ago, Vort said:

The wording of your question indicates that there are all sorts of variables that I'm not considering because I don't know what they are. Nevertheless, I'll give it a try.

1. North

2. Given the choice, corrugated sheet steel, because who the heck would ever use quarter-inch steel plate for a simple roof for a 4'x4' shed without walls? 48" is not evenly divisible by 9", but so what? I don't need to attach the corrugated material right at the edges, anyway.

Pretty simple.

The questions and comments I got in that meeting were idiotic and didn't consider the realities of the sun or of constructability.

They wanted a 26 gage flat panel (no flutes).  I had to point out that a 26 gage flat sheet is difficult to work with because it would flop around during construction.  And it would likely sag in the middle of the frame.

They also thought (I kid you not) that the sun would be north at noon (because it is summer).

6 hours ago, Vort said:

If the panel faces north, the user faces south, with the doors blocking out the sides. But given the height of the box off the ground, probably better to have the user facing north instead of the panel.

This would be less desirable.  Sometimes it is done for practicality of construction/access, but is is workable.  The reason is that during winter months, the sun being further south would cause "the partial shadow" problem.

If you're wearing sunglasses, then your eyes cannot as easily discern a field of vision with multiple levels of light.  Your eyes adjust to the brighter areas, and cannot see the darker areas.  So if the sun is partially shading the panel, you have to do a lot of shifting your body to cover/uncover the areas of the panel that you're looking at.

If, instead, the shade/light of the panel area is constant, your eyes can adjust more easily.

Edited by Carborendum
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