Solve Enjoyable Enigmas with Mr.E's Challenge

[drizzle]

The fruit of course!

Edit: Hmm, writing 'THE WATER IS IN THE GLASS' with matchsticks on the table... while eating the fruit.

If this doesn't work I'll go look for a fruit in my refrigerator to eat then go to classes, and see how would other PFers solve it.
Still, the fruit is mine!

 

[collinsmark]

I know this one too. Except for the fruit. The fruit inclusion confuses me.

 

[zoobyshoe]

Don't know if this would work in practice, but I'd try it:

Put a piece of fruit on the plate, push a match into it sticking straight up with the business end at the top. Light it, then invert the glass over it. As the oxygen burns away, some, hopefully all, of the water would be pushed up into the glass by atmospheric pressure. The water would be "back in the glass".

 

[collinsmark]

Don't know if this would work in practice, but I'd try it:

Put a piece of fruit on the plate, push a match into it sticking straight up with the business end at the top. Light it, then invert the glass over it. As the oxygen burns away, some, hopefully all, of the water would be pushed up into the glass by atmospheric pressure. The water would be "back in the glass".

Ah, yes. That would work. That's where the fruit comes into play.

It's the warming of the air inside the glass that does the trick. As the air cools it creates a vacuum "sucking"* the water back into the glass from the bottom. *(or more technically, "pushed" into the glass by atmospheric pressure, as zooby describes. Essentially the waiter/waitress just created a makeshift barometer.)

But you don't really need the fruit for that. All you really need to do is hold the match under the upside-down glass for awhile (you can hold the glass with one hand and the match with the other [you can also use a lighter, a candle, or pretty much any heat source that's hot enough]), and then carefully [albeit immediately] place the glass, still upside-down, on the water, and it will suck the water right in.

[Edit: And that way, Gad can snack on the fruit if she likes. ]

 

[collinsmark]

I just did bit of experimentation. Two scenarios:

• Match in the fruit: where the glass is held above the lit match and then eventually lowered into the water, completely encasing the fruit and match (the match eventually runs out of oxygen and then goes out).
• Glass held upside down in one hand and a lighter in the other, then the glass (still upside down) was carefully, yet immediately, placed on the water: This case allowed me to keep the glass over the flame for a somewhat longer interval, not only heating the air in the glass, but the glass itself to an extent.*

The results were nearly the same. I think the match in the fruit trial brought slightly more water into the glass, but if so, not very much more.

Given the options, and considering the tasty treat possibilities, I'd say snack on the fruit.

[Edit: in both cases, I wasn't able to draw more than about a centimeter height of water back into the glass. So don't pour too much water on the plate, because there seems to be limit on the amount of water one is able to get back into the glass using this process.]

*[Another edit: further experimentation reveals that keeping the glass above the flame for longer periods does not aid in the process, and may even be counterproductive. A couple of seconds over the flame is all it takes.]

[Even one more edit: I hypothesize that one might get the most bang for the buck by using the match in the the fruit method, but ensuring that the glass is placed completely over the match and fruit and into the water before the sulfur head of the match completes its burning. Unfortunately I ran out of matches, so experimentation in this regard will have to be delayed for a bit.]

 

[zoobyshoe]

Nice experiments, Collinsmark!

Alternatively, the waiter could say, "Lemme think about it a minute," then go into the kitchen and find a bus boy and say, "I want you to go out in the dining room and watch for my signal. When you see the signal, rush quickly over to the table where I'm at. You'll see a plate of water and a glass. Pour the water into the glass. Then leave. The signal is: I'll light a match. Do this, and later I'll give you $5.00."

 

[OmCheeto]

I'm starting to understand why you are known as Enigman, as both of these puzzles puzzle me.

In the meniscus experiment, the cork floats to the higher level. But why? At that position, it would have the highest potential energy. I always thought systems tended towards the lowest level of energy.

And now this matchstick problem. The cellulose burning, consumes free oxygen, but emits both CO₂ gas, and H₂O vapor, and obviously is heating up the whole system. It doesn't make sense, if you know as little as I do.

I'm glad it's Friday. I will contemplate, or perhaps google, why these two enigmas baffle me.



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ps. I would play the matchstick problem on my bartender, but he's on "Psychiatrist duty" at the moment.

 

[OmCheeto]

I just did bit of experimentation. ...

Me too!

The bucket* didn't work at all.

The pint glass amazed everyone, including me.

------------------------
*I don't know the names of "bar-ware", except for "shot" and "pint".

 

[collinsmark]

I'm starting to understand why you are known as Enigman, as both of these puzzles puzzle me.

In the meniscus experiment, the cork floats to the higher level. But why? At that position, it would have the highest potential energy. I always thought systems tended towards the lowest level of energy.

It's true that when the cork is at a higher elevation, it has a higher potential energy. But that's just the cork. The system as a while has a lower potential energy when the cork is at the highest level.

When the cork is placed in water, the cork displaces its own weight in water. In other words, when the cork sinks into the water a little bit, an equal amount of water -- in terms of weight (not volume) -- rises up a little. The potential energy of the cork decreases slightly as it sinks a little, and the potential energy of the displaced water rises a little. Energy is not conserved though as the oscillations die out (at first the cork will do some "bobbing," but that doesn't last). Eventually an equilibrium is reached.

Since the water is denser than the cork, the potential energy of the whole system is lowest when the water is at its lowest level possible, which means the cork is at the highest level possible.

The water will "cling" upwards slightly at the sides of the glass due to capillary action.
http://en.wikipedia.org/wiki/Capillary_action

That means the cork has the tendency to go to the sides of the glass where the water level is highest.

So the solution to the problem is fill up the glass of water as much as possible, such that the surface of the water fills slightly higher than the rim of the glass, and is held in a convex shape (rather than concave as it was previously) and held together by surface tension. Now the highest point in the water is in the center of the glass, rather than the edges. The cork moves to the center.

And now this matchstick problem. The cellulose burning, consumes free oxygen, but emits both CO₂ gas, and H₂O vapor, and obviously is heating up the whole system. It doesn't make sense, if you know as little as I do.

I'm glad it's Friday. I will contemplate, or perhaps google, why these two enigmas baffle me.
[/SIZE]

The fact that one of the byproducts is water probably adds a significant boost. But even just hot air cooling will draw much of the water into the glass.

If the glass is lowered into the water while the fire is still burning, a net amount of gas is actually being produced. But pressure doesn't build up inside the glass because when the pressure above atmospheric pressure, the gas simply exits the bottom of the glass and bubbles to the surface outside of the glass. There's no mechanism to keep the pressure inside the glass much above atmospheric pressure. In the end, at the point in time that the reaction stops, all that's left in the glass is hot gas, whatever that might be. (The fact that a good part of it is water vapor might play a significant role, but it's not essential.)

Neglecting vapor pressure for the moment, as the gas cools, it simply becomes a PV = nRT system. [Edit: with the pressure times area (force) equal to the weight of the net water in the glass.] The volume and pressure inside the glass decrease, causing the water to get "sucked" into the glass. (Or better worded, the water gets "pushed" into the glass by the pressure differential, the pressure difference between the pressure in the glass and atmospheric.)

Now let's consider that a small but significant fraction of the original gas might be water vapor. A good fraction of it probably is because it is one of the byproducts of the flame oxidation (a.k.a. the "burning" reaction). Vapor pressure is dependent on temperature alone (volume plays no role on the vapor pressure). So as the gas cools, the overall pressure can decrease more dramatically the more of the original gas is water vapor. This water vapor part isn't essential for the experiment to work, but it might play a significant role in bringing more water into the glass. (Instead of using a match, if you could pipe some steam into the upside down glass, all else being the same, you could draw *lots* of water into the glass -- as much as a water barometer would allow.)

 

[drizzle]

Don't know if this would work in practice, but I'd try it:

Put a piece of fruit on the plate, push a match into it sticking straight up with the business end at the top. Light it, then invert the glass over it. As the oxygen burns away, some, hopefully all, of the water would be pushed up into the glass by atmospheric pressure. The water would be "back in the glass".

.. I don't think so, my method is faster and would do it while enjoying the fresh fruit, not a smoked squashy one.

Ah, yes. That would work. That's where the fruit comes into play.

It's the warming of the air inside the glass that does the trick. As the air cools it creates a vacuum "sucking"* the water back into the glass from the bottom. *(or more technically, "pushed" into the glass by atmospheric pressure, as zooby describes. Essentially the waiter/waitress just created a makeshift barometer.)

But you don't really need the fruit for that. All you really need to do is hold the match under the upside-down glass for awhile (you can hold the glass with one hand and the match with the other [you can also use a lighter, a candle, or pretty much any heat source that's hot enough]), and then carefully [albeit immediately] place the glass, still upside-down, on the water, and it will suck the water right in.

[Edit: And that way, Gad can snack on the fruit if she likes. ]

 

[collinsmark]

A quick calculation shows that if you had a very tall, upside-down glass, and you filled it with completely with steam, then put it in a very large plate of water, it would suck up column of water approximately 10 meters high, at standard temperature and pressure.

If the glass is less than 10 meters tall, the column of water that it would suck up would reach nearly, but not quite, the top of the glass. If the glass is greater than 10 meters tall, the column of water would top out at about 10 meters; increasing the height of the glass wouldn't change the height of the water.

 

[Enigman]

Yep, this is correct. I owe this one to a manga 'Detective Conan'. I did solve it though. In the story a man is murdered using this to create a time alibi...
Well, wait till I think of the next one or post your own Enigma.

 

[zoobyshoe]

A quick calculation shows that if you had a very tall, upside-down glass, and you filled it with completely with steam, then put it in a very large plate of water, it would suck up column of water approximately 10 meters high, at standard temperature and pressure.

If the glass is less than 10 meters tall, the column of water that it would suck up would reach nearly, but not quite, the top of the glass. If the glass is greater than 10 meters tall, the column of water would top out at about 10 meters; increasing the height of the glass wouldn't change the height of the water.

Thanks for properly explaining all this. My idea was correct by complete accident because my logic was based on the idea the match would deplete the oxygen, creating a partial vacuum. I was thinking of the common kid's science demonstration where you stuff some steel wool in the bottom of a glass, then invert it over a plate of water. As the steel slowly oxidizes, the water is draw up into the glass. I wasn't even thinking in terms of the heating and cooling of the air.

 

[OmCheeto]

I'm still trying to work out the FBD forces on the cork in a slanted liquid environment.



---------------------
in my head of course. I've 87 other more pressing problems to solve at the moment...

 

[collinsmark]

I'm still trying to work out the FBD forces on the cork in a slanted liquid environment.

It can get tricky. And the trick is to remember Archimedes.
Wasn't he in Random Thoughts just a few days back, destroying ships and stuff?

http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html

 

[OmCheeto]

It can get tricky. And the trick is to remember Archimedes.
Wasn't he in Random Thoughts just a few days back, destroying ships and stuff?

http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html

I don't think it has anything to do with buoyancy. If you draw a free body diagram of a square, placed in a level liquid, the only net liquid force is on the bottom. If you tilt the liquid to 45 degrees, keeping the square level, there will be a net force opposite the direction that the square actually goes!

I think it may have more to do with the capillary action. Looking at the cork-water-glass system, it's obvious that there are curved surfaces, almost like gravitational fields. But describing how the cohesive/adhesive forces pull the cork to the position where the water-cork-glass system is at its lowest energy state, is beyond my abilities.

 

[lisab]

It can get tricky. And the trick is to remember Archimedes.
Wasn't he in Random Thoughts just a few days back, destroying ships and stuff?

http://hyperphysics.phy-astr.gsu.edu/hbase/pbuoy.html

Yeah he shows up now and then, muttering something about disturbing circles.

 

[collinsmark]

I acquired more matches. Lots and lots of matches.

Experimentation shows that encapsulating the fruit and match before the sulfur tip finishes burning does not draw appreciably more water into the glass, compared to simply holding a flame under the glass and placing the glass on the water.

It seems the fruit is superfluous after all, insofar as drawing water into the glass. I recommend that Gad snack on the fruit.

 

[Enigman]

Yeah he shows up now and then, muttering something about disturbing circles.

one more time...

 

[Enigman]

Well here's another one:
Given that you have only two options and you have to take one which one would you take? And why?
-One day in Venus and get 1 million dollars
-One year in Venus and get 1.2 million dollars
Of course you would get all the food, water and all other necessities needed to survive the period of time you choose. (Note that Venus in reference is a planet and not a girl...)

 

[zoobyshoe]

Of course you would get all the food, water and all other necessities needed to survive the period of time you choose.

Not likely:

Probes have been sent to the surface, but can only survive a few hours in the intense heat and sulfuric acid.

http://www.universetoday.com/14306/temperature-of-venus/

 

[Enigman]

Just for the sake of the puzzle then?

 

[zoobyshoe]

Just for the sake of the puzzle then?

A year. Obviously I've already googled.


When do I get my $100.00 for the glass trick?

 

[Enigman]

A few minutes later the waiter/waitress walked off with hundred bucks. What did you do?

You've already got it...
And you get the other prize money after you spend the year there...send me some photos...

 

[collinsmark]

Okay, I'll bite.

Suffice it to say though that Venus is a very inhospitable place.

Venus is a bit unusual compared to other planets that its rotation is retrograde. If we take the sun's North pole as "up" (using the right hand rule -- this is how astronomers define a celestial body's North and South, by using the right hand rule on the body's rotation) the planets/other bodies orbit around the sun in an anticlockwise motion ("counterclockwise," for all you American yahoos). Most planets also rotate anticlockwise, more or less (albeit on a somewhat tilted axis). Venus on the other hand rotates clockwise -- opposite that of its orbit, and the orbit of the other planets. This is called "retrograde" rotation.

And retrograde or not, it doesn't rotate very quickly. Venus has a sidereal day of approximately 243 Earth days. That's the time it takes to rotate once, using the fixed background stars as a reference.

It's orbital period around the sun is about 225 Earth days.

That make a solar day on Venus to be approximately 117 Earth days -- significantly less than its sidereal day.

So, one Venusian year is about 1.92 Venusian (solar) days long. So I suppose I would take the one solar day on Venus, and skip on the extra $200,000.

On the other hand, if "day" is defined as a sidereal day, it makes much more sense to only stay for a Venusian year and take the whole $1.2 M.

("Earth days" in the above are taken to be Earth's solar days, not sidereal days, although the distinction doesn't make a huge difference here.)

 

[zoobyshoe]

You've already got it...
And you get the other prize money after you spend the year there...send me some photos...

I'm not going to Venus. And I haven't gotten my $100.00. You should also probably PayPal Collinsmark about $10.00 for all the fruit and matches for his experiments.

 

[Enigman]

The question clearly states that the waiter (you) has walked off with the money and the question was what did you do, ergo you have got it. As for Collinsmark since you owe him for the correct answer you should recompense him from your prize money. $90 for a tip is quite generous (considering your attitude inasmuch you refuse to go to Venus.) now, don't be a scrooge, zoobie.

 

[zoobyshoe]

The question clearly states that the waiter (you) has walked off with the money and the question was what did you do, ergo you have got it.

You may say I walked away with it all you want, but I haven't walked away yet. I'm standing here waiting.

As for Collinsmark since you owe him for the correct answer...

Whoah! I owe him for the correct explanation, that's all. I published the correct answer before him, and that's all that counts.

 

[Enigman]

You may say I walked away with it all you want, but I haven't walked away yet. I'm standing here waiting.

You PF while standing? Zoobie Brush Shelter sure has got some queer ways...well, wait ON! (preferably on me...)

Whoah! I owe him for the correct explanation, that's all. I published the correct answer before him, and that's all that counts.

Sir Newt would say the same thing about his corpuscular theory and Einstein's photons...
Doesn't change the fact that both of you were wrong.


Now let me think/google up the next one...

 

[zoobyshoe]

Doesn't change the fact that both of you were wrong.

Oh, now we're wrong?!?

What's the right answer, then? Collinsmark is eager to test it experimentally.

 

[collinsmark]

I need to make a clarification. In a previous post I claimed:

If we take the sun's North pole as "up" (using the right hand rule -- this is how astronomers define a celestial body's North and South, by using the right hand rule on the body's rotation)

It turns out it's not quite so simple, at least as defined by the IAU anyway. For a more detailed definition, this might be a good place to start.
http://en.wikipedia.org/wiki/Poles_of_astronomical_bodies

 

[Enigman]

Oh, now we're wrong?!?

What's the right answer, then? Collinsmark is eager to test it experimentally.

You and Newt (on), mes enfants...Collinsmark was right.
BTW Collinsmark, I did not know about the poles...Thanks for the information and the really detailed explanations and saving me the pains...

 

[Enigman]

Well the next one then, you've been given a barrel of beer and I've removed some quantity from it (Hic!).
You are to determine whether the quantity removed was more than half, half or less than it...without using any instruments whatsoever except your 'selves'. Be advised that you are not to drink it, or dunk your hand, legs, head or anything else in it. After solving the puzzle you may drink this hypothetical beer up or dump it on my head. (preferably the later)
Good Luck!
And no googling ZBS (or anyone else)...
Use those (P)Fing brains of yours.

 

[drizzle]

... Look inside the barrel?

 

[Enigman]

You are allowed to do that -however you have to be accurate; there has to be absolute certainty and even a small amount would make a difference.