Are My Buoyancy Questions Really That Confusing?

[holly]

I am using Spring Break to try to consolidate the information in the course I am taking. I have only two questions from the chapter on fluid dynamics unanswered:
Q. Gas pressure inside an inflated stretched balloon is actually:
(a) less than air pressure outside the balloon
(b) greater than air pressure outside the balloon
(c) equal to air pressure outside the balloon.

I thought it was (b), greater, until I ran across a site from Harvard talking about common misconceptions regarding fluid pressure. The example given was the idea of a balloon that was further inflated. They said the pressure would be equalized inside and out the balloon because the surface area of the balloon became greater and thus the two pressures equalized. IS THIS CORRECT? It's really answer (c)?

The other question seems to be worded "funny."
Q. The reason that buoyant force acts upward on a submerged object is that:
(a) if it acted downward, nothing would float
(b) Upward pressure against the bottom is greater than downward pressure against the top of the submerged object
(c) the weight of the fluid displaced reacts with an upward force
(d) it acts in a direction to oppose gravity.
I think (b) sounds most reasonable, but then again, if the B.F. is really greater, wouldn't it be floating, not submerged?

These buoyancy problems are getting me very nervous. Last night I dreamt I had to eat a bunch of marshmallows floating on the ocean, and when I awakened, I was chewing on a foam-rubber earplug. I really need to finish this chapter, please take pity & help.
Thanking you in advance,
holly

 

[Doc Al]

Originally posted by holly
Q. Gas pressure inside an inflated stretched balloon is actually:
...
I thought it was (b), greater, until I ran across a site from Harvard talking about common misconceptions regarding fluid pressure. The example given was the idea of a balloon that was further inflated. They said the pressure would be equalized inside and out the balloon because the surface area of the balloon became greater and thus the two pressures equalized. IS THIS CORRECT? It's really answer (c)?

The gas pressure is greater inside the balloon. Here's why. Realize that there are three forces acting: air pressure pushing in, elastic force of the balloon material pulling in, and the gas pressure pushing out. Since it's in equilibrium, the gas pressure must be greater than the outside air pressure.

I'm unclear what the site was trying to say. Post the link and I'll check it out.

The other question seems to be worded "funny."
Q. The reason that buoyant force acts upward on a submerged object is that:
...
I think (b) sounds most reasonable, but then again, if the B.F. is really greater, wouldn't it be floating, not submerged?

Correct choice. The bouyant force is due to the difference in pressure between top and bottom. Since the bottom pressure pushes up harder than the top pressure pushes down, the net force (which is the bouyant force) acts upward.

I don't know what you mean by "if the B.F. is really greater"? Greater than what? Something sinks if the bouyant force is not enough to support the weight of the object.

 

[holly]

Uh-Oh

Doc Al, I am shocked, but some people are disagreeing with you!

The Harvard site is www.pz.harvard.edu/ucp/curriculum/pressure/i_challenge.htm[/URL]

I can't remember if I went to another page within the site, I just stuck it in "Favorites" in case I needed it again. I could hardly make out heads nor tails of it!

Someone else JUST told me that the answer to the other question is that the B.F. acts in a direction to oppose gravity, which is answer (d). I didn't even consider that answer! Don't you picture the B.F. shaking a defiant fist at Gravity, and rudely saying, "I oppose you, evil oppressor!" But that is not what they mean. The answer we like would have the item floating, and they say it is submerged.

I just KNOW these questions will be on the test! In fact, ALL our homework questions are on the tests! Plus our other assignments. That's why I'm frantic to understand them.

Thank you for your help! Much appreciated.

I had to edit the link, it is displaying strangely

 

[cookiemonster]

I'd get involved in this, but I think we all remember what happened last time.

cookiemonster

 

[holly]

Bonhomme Monstre de Cookie, I would love to have your two cents' worth, which I consider very valuable indeed! Can you be blamed that my manner of, er, thinking, I guess we will call it, once affected your fine mind temporarily? I have complete faith in the answers I receive on the Board, and feel that if I sometimes receive a "wrong" answer, that's just fate! What worries me is that I am eventually able to find all the answers correct, after thinking on them awhile. So if you weigh in with your opinion, that's really very helpful!

 

[NateTG]

Regarding the baloon:
The pressure inside an inflated baloon is larger than the pressure outside it. (Otherwise baloons would self-inflate). However, as the balloon becomes more inflated the pressure decreases.

Regarding the second question:
The question is ambiguous, so (b) and (d) are both currect. You might say that the the bouyant force acts upward, as opposed to sideways, because it acts in the opposite direction of gravity. Of course, there are many situations where it does not, the most familiar of them is a centrifuge.

 

[cookiemonster]

I agree with Doc Al on both accounts.

For the buoyancy: Pressure for standing water = mgh. It's not difficult to figure that (b) is correct. However, (d) is also right since gravity (or simulated gravity) determines this equation. I imagine that there are setups that can be made to cause the pressure to be different on the sides as opposed to the top and bottom, so (d) is only conditionally right. On the other hand (b) has the same problem since you can find instances where it doesn't act upward (just flip your coordinate system upside-down), so it is only conditionally right with the condition being that deeper depths have greater pressure.

As for the balloon, I wasn't able to read the link (the intraweb couldn't find the webpage), but I'd guess that they're addressing the misconception that the gas pressure is greater when the balloon is fully inflated as opposed to barely inflated, i.e. that it becomes harder to blow up the balloon as it gets bigger. From experience, you know that this isn't the case. It's most difficult to begin blowing up the balloon and in fact becomes easier as it gets bigger. However, the balloon wall does want to restore itself to its original size and so applies pressure inward. Add this pressure to the environment's pressure, and this is what the internal gas pressure must overcome. Therefore, the internal pressure is greater.

Hope I didn't screw up this time...

cookiemonster

 

[Doc Al]

Originally posted by holly
Doc Al, I am shocked, but some people are disagreeing with you!

Oh, no!

Someone else JUST told me that the answer to the other question is that the B.F. acts in a direction to oppose gravity, which is answer (d). I didn't even consider that answer!

Yeah, on second thought answers b and d are equivalent. (But answer b demonstrates an understanding of how bouyant force comes about.) But if they want to be picky, the reason bouyant force points up is that gravity pulls down. (The question---with those answers---is bogus unless you can pick more than one! If you are concerned about getting such an ambiguous question on the test, ask the instructor about it NOW.)

The answer we like would have the item floating, and they say it is submerged.

What do you mean by this?

 

[ShawnD]

Originally posted by holly
The example given was the idea of a balloon that was further inflated. They said the pressure would be equalized inside and out the balloon because the surface area of the balloon became greater and thus the two pressures equalized.

The guys who said that are idiots. You can easily disprove this theory with a pin or sharp pencil.
Take a balloon and have a friend stretch it out. Now poke it with a pin, does it explode? It obviously won't, that's because the air pressure is the same inside as it is outside.
Now inflate a balloon and poke it with a pin. Does it explode? Does it implode? Does it do anything at all? If it explodes, the air pressure inside was greater than outside. If it implodes, the air pressure outside was greater than inside. If nothing happens, the air pressures are the same.

 

[holly]

Okay, so far, I have too many right answers!

Too much of a good thing, as they say.

Regarding the B.F. acting in a manner to oppose gravity: Supposedly this is the only correct answer. Don't ask me, I'm just an overaged student. Answer "b" says that the upward force is GREATER than the downward force, evidently not so. Or it would be winning, right?

As to the balloon, the pressure is equal inside and out. As above, don't ask me. I'm just repeating things people with PhDs in Physics assure me are correct. "Share the misinformation," I call it. Give something BACK to the web! The key here is I guess the balloon's elastic sides shouldn't be confused with air pressure. The energy of the sides pushing in/pushing out/pushing about because of the elastic energy make it seem that air pressure is doing it? Something like that. Anyway, that elastic dog ain't in this fight. The Surface Area increasing to increase the volume, having something to do with Somebody Dead's Law, like Boyle's law or someone, is why the inside and outside are the same. Right? Like why a lunchbag doesn't pop when you blow it up until you change the volume drastically when you pop it by your poor mom's ear? Something like that?

I know why I'm getting good grades now. I just wear the poor professor down. Four pages of my musings and you'd give me an "A" too. ha ha

Thanks to all who answered, did we learn something? ha ha Good news, I'm on Chapter Seven now and I don't understand a thing. (can't spell neither)

 

[Doc Al]

Originally posted by holly
Regarding the B.F. acting in a manner to oppose gravity: Supposedly this is the only correct answer. Don't ask me, I'm just an overaged student. Answer "b" says that the upward force is GREATER than the downward force, evidently not so. Or it would be winning, right?

What?? Of course the upward force of water pressure (on bottom of object) is "winning" compared to the downward force of water pressure (on top of object)! That's why there's a bouyant force. If it was a tie: No bouyant force.

As to the balloon, the pressure is equal inside and out. As above, don't ask me. I'm just repeating things people with PhDs in Physics assure me are correct.

Nonsense! Hey, I've got a Ph.D. too, you know.

Here's a quote I pulled off of that Harvard site:

"Similarly, with a balloon, the pressure in the balloon is pushing out AND the pressure outside the balloon is pushing inward to give a balloon its shape. The balloon remains inflated because the air pressure inside it is equal to, or balanced with, the air pressure outside of it."

This is nonsense! Very sloppy thinking.

 

[turin]

I just wanted to jump in and affirm Doc Al's affirmation.

Balloon:
In the limit that the balloon becomes infinitely large, the pressures will be equal inside and out. Why? Because the tension in the elastic membrane, while infinitely large itself, contributes only tangential force completely perpendicular to the competing pressures. In other words, this is nonsense. The pressure is greater inside the balloon because it must balance with outside pressure and tension.

Bouyancy:
I think it was NateG that brought up a great counterexample. The bouyant force only opposes gravity if gravity is the only force causing the hydrostatic pressure. If, for instance, there is a bucket full of water being swung around in an almost horizontal circle, then the hydrostatic pressure will be caused mostly by centrifugal force, and bouyancy will have very little to do with gravity.

 

[jamesrc]

Orginally posted by Doc Al
Here's a quote I pulled off of that Harvard site:

"Similarly, with a balloon, the pressure in the balloon is pushing out AND the pressure outside the balloon is pushing inward to give a balloon its shape. The balloon remains inflated because the air pressure inside it is equal to, or balanced with, the air pressure outside of it."

This is nonsense! Very sloppy thinking.

While I normally don't stick my nose in where it's unwanted/unneeded, I just wanted to add a snicker at that comment from the Harvard site. I mean, if that really were the case, why bother tying the balloon off?

 

[holly]

Holy shiitaki mushrooms, I am so confused! When people with PhDs all come up with different right answers, what's a gal to do? I am nonplussed... hmmm, perhaps I will just ignore those nasty questions and simply pray they won't be on the test! THAT sounds good! If they are on the test, I will mark down all the answers you all have given and just fight it out with my prof. So thank you.

 

[cookiemonster]

I think it's time for the real world to step in and resolve this little conflict through experiment!

cookiemonster

 

[holly]

Attaboy, Cookiemonster! That's the spirit! A little experimentation is in order! However, that sounds alarmingly like...W O R K! The four-letter word!

We could also experiment by doing the time-honored "thought experiment" and put the question on the General Physics board...I'm not brave enough, though! I bet you, though, that ALL THREE answers would have their adherents, don't you think?

C'est la vie.

 

[cookiemonster]

It seems that all three answers already have their supporters. That's kind of the problem, isn't it?

cookiemonster

 

[holly]

Well, I was thinking along the lines of sticking with the answer with the MOST people saying it's right...or circle all three and get my prof mad, ha ha...

A thought: Say the uninflated balloon is sitting on a desk with no air added except what I'll call ambient air. It's sitting there with one atmosphere of pressure in it...no knot or anything. Say it has a surface area of 4 cm^2. Then, some air is puffed into it. Now, if it could not expand, indeed it would have greater pressure inside as compared to outside. But, a balloon does expand. It stretches out & thus easily increases its volume. Say the air puffed in brought it up to 2 atmospheres. These are just pretend numbers. The s.a. would increase and the vol would thus increase. Say the balloon was stretchy enough to increase the volume double. That's easy, if it's a round balloon. Twicet as much air inside, but now twicet as much volume...meaning it's equal again, right? That's my thinking. But being a sphere, towards the end there, the s.a. needn't increase much to increase the volume, and maybe it gets even less pressure. I don't know.

 

[turin]

Originally posted by holly
When people with PhDs all come up with different right answers, what's a gal to do?

The only disagreement that I saw was from this Harvard site, but, what do they know? I thought that everyone here who has answered (without reference to a website) has been in agreement.

Originally posted by cookiemonster
I think it's time for the real world to step in and resolve this little conflict through experiment!

That shouldn't be too hard for the balloon. Just slap the open ened around the input to a pressure guage. I'll bet the gauge on a bicycle pump would work just fine.

 

[cookiemonster]

Originally posted by holly
Say the balloon was stretchy enough to increase the volume double.

Most everything is "stretchy" enough to increase the volume double, if you apply enough force (and the material can support it). The whole point is that force must be applied to the balloon's material in order to stretch it.

cookiemonster

 

[holly]

YOU WERE RIGHT ALL ALONG!

Okay, okay...it turns out that Doc Al, Turin, Cookie, jamesrc et al were correct (they KNEW it! they KNEW it!) and I had a bum steer from that Harvard site and some inebriated and cruel lying physicists. So, the balloon does have greater pressure than the air.
THE BLOODY END! Pshew!

 

[cookiemonster]

So what finally resolved it? Did you perform an experiment?

cookiemonster

 

[holly]

No, no experiment, other than to email my ex and ask him! Not that I put him above the other brains on this Board, but in terms of answering questions in physics, chemistry, and math, he is superb and ultra-reliable. I bet he wins the Nobel Prize in Physics and in Chemistry some day. But it's rare that he will answer me...very rare...I depend on the Board much more...

 

[cookiemonster]

Heh, I'm not sure how I would feel if I had Doc Al's PhD and my opinions on physics were less valuable than somebody's ex. ;)

I guess knowledge doesn't depend on its source, though.

cookiemonster

 

[holly]

I hope no one takes my slowness to absorb correct answers as any reflection upon themselves.

I thought Doc Al was a biologist...that's why I held out for a physicist to settle the matter. I meant no offense and certainly I have depended upon and benefitted from Doc's knowledge many times in the past. My ex taught physics at universities before & I thought he would best know the answer they were looking for...

Amd as for knowledge being knowledge, that's so true. Sometimes you have to give the devil his due, even if the person's personality is not to your taste. And that's one good thing about my ex, very rare among the physicists: he felt if you had brains, you had brains, and didn't need a PhD tagging along behind your name for your thoughts to be valid. I see that on this board, too. Some people lack formal credentials, but their thoughts are sound and every bit as valuable and insightful as if they had the PhD.

I think people ought to reconsider their avatars, while I'm blathering...Doc Al's looks like a peach to me. I thought it was a peach with a moustache. That's why I thought he was a biologist. And some of you don't have any avatar at all! Going bare on the forums, how tacky.

 

[Doc Al]

Originally posted by cookiemonster
Heh, I'm not sure how I would feel if I had Doc Al's PhD and my opinions on physics were less valuable than somebody's ex. ;)

I feel like Rodney Dangerfield... I don't get no respect, no respect at all.

I guess knowledge doesn't depend on its source, though.

Absolutely right!

 

[NateTG]

Originally posted by holly

I think people ought to reconsider their avatars, while I'm blathering...Doc Al's looks like a peach to me. I thought it was a peach with a moustache. That's why I thought he was a biologist. And some of you don't have any avatar at all! Going bare on the forums, how tacky.

Well, I've got an avatar. It's a fully transparent image that represents the clarity of my reason, or the profound nature of my thought, whichever you prefer.

 

[cookiemonster]

Honestly, I don't even know how to use an avatar.

cookiemonster

 

[Doc Al]

Originally posted by holly
I thought Doc Al was a biologist...that's why I held out for a physicist to settle the matter.

Biologist?? That's a good one.

Amd as for knowledge being knowledge, that's so true. ... and didn't need a PhD tagging along behind your name for your thoughts to be valid. I see that on this board, too. Some people lack formal credentials, but their thoughts are sound and every bit as valuable and insightful as if they had the PhD.

This is absolutely true. Some of the most helpful and knowledgeable folks on this board have no advanced degree. Yet they kick ass when it comes to explaining physics. I'll go even further: I know physics Ph.D.s who are clueless and who couldn't figure out the simplest problems discussed here.

I think people ought to reconsider their avatars, while I'm blathering...Doc Al's looks like a peach to me. I thought it was a peach with a moustache.

Yikes! So far no one has figured out the deep meaning of my avatar. Who will accept the challenge?

 

[cookiemonster]

It's obviously a circle.

cookiemonster

 

[holly]

I am going to go over to the general discussion area and post a poll. The poll is going to concern what Doc Al's avatar really is. And I'm also going to ask for suggestions for an avatar for Cookiemonster. He can't use NateTG's hilarious excuse of having an invisible avatar. I'll only buy that once!

 

[ShawnD]

Originally posted by holly
He can't use NateTG's hilarious excuse of having an invisible avatar. I'll only buy that once!

Nate might be serious. You can make transparent layers in Photoshop you know .

 

[marcus]

Originally posted by Doc Al
So far no one has figured out the deep meaning of my avatar. Who will accept the challenge?

It is upside down.
It is recognizable if rotated 180 degrees. IMHO

 

[NateTG]

It's pretty vauge. How about the impact of Shoemaker-levy 9 on Jupiter? Particle decay in a cloud chamber. A stylized face - eyebrows nose and cheekbone on a circular head. A palmtree blowing in the wind in front of a rising moon. The initails T.O. A rocket taking off of surface of the moon.

 

[holly]

Well Folks, it may just remain a mystery. I tried to look at the so-called avatar upside down, as marcus suggested. Thanks for getting me to put a crick in my neck, marcus! ha ha It looks upside down from upside down...

Over in the General Discussion area, we are saddled with a bunch of slugs too lazy to get into the discussion. Hmmph. I put up two questions, one asking what Doc Al's avatar is, and one asking for an avatar for cookiemonster. I guess everyone is too busy thinking lofty physics thoughts to join in. In the meantime, people are going about sans avatar and Doc Al continues to use a poorly-drawn peach as an avatar!

So I am going to post on my website a few avatars I think would be good for cookiemonster and marcus and turin. Doc Al can get himself a nice, happy, colorful one, too. NateTG can keep his ol' invisible one. It's probably a mean-looking smiley saying a bad word, ha ha!