# Homework Help: Two buoyancy questions

1. Mar 10, 2004

### 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.
holly

2. Mar 10, 2004

### Staff: Mentor

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.
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.

3. Mar 10, 2004

### 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.

Last edited by a moderator: Apr 20, 2017
4. Mar 10, 2004

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

5. Mar 10, 2004

### 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!

6. Mar 10, 2004

### 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.

7. Mar 10, 2004

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...

8. Mar 11, 2004

### Staff: Mentor

Re: Uh-Oh

Oh, no!
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.)
What do you mean by this?

9. Mar 11, 2004

### ShawnD

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.

10. Mar 11, 2004

### 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)

11. Mar 11, 2004

### Staff: Mentor

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

Here's a quote I pulled off of that Harvard site:
This is nonsense! Very sloppy thinking.

12. Mar 11, 2004

### 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.

13. Mar 11, 2004

### jamesrc

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?

14. Mar 11, 2004

### 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.

15. Mar 11, 2004

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

16. Mar 11, 2004

### 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.

17. Mar 11, 2004

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

18. Mar 11, 2004

### 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.

19. Mar 11, 2004

### turin

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.

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 guage on a bicycle pump would work just fine.

20. Mar 11, 2004