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Re: Why does a less dense object rise in a dense fluid surrounding?

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benj <benj.fake@gmail.com> wrote:
> On 1/10/2019 2:14 PM, Odd Bodkin wrote:
>> benj <benj.fake@gmail.com> wrote:
>>> On 1/10/2019 8:00 AM, Odd Bodkin wrote:
>>>> Arindam Banerjee <banerjeeadda1234@gmail.com> wrote:
>>>>> On Earth. Why does a less dense object rise up in a dense fluid surrounding medium?
>>>> 
>>>> Because the weight of the object is less than the buoyant force of the
>>>> fluid, which in turn is due the differential in pressure with depth of the
>>>> surrounding fluid. High school physics.
>>> 
>>> Babbling jargon. Try explaining something in English for a change if you
>>> can understand things well enough. You are one of those WEstern Idiot
>>> dogs that Banjoji is always talking about.
>> 
>> I’m a little surprised you find this jargon. Let’s suppose that everyone
>> here knows what pressure is and what a fluid is. It is common experience
>> that pressure increases linearly with the depth in a fluid, in cases where
>> the density of the fluid is approximately constant. Anyone that has
>> snorkeled knows this. The pressure on any patch is in fact the weight of
>> the fluid sitting on top of that patch.
>> 
>> To make this visually clearer, consider first a pool of water, and imagine
>> an upright cylindrical volume of this water. If it helps, wrap this volume
>> in a thin cylindrical can made of plastic of the same density as the water,
>> so that it has no effect on the following. There is pressure inwards on the
>> outside of this cylinder due to water pressure. From symmetry, the force on
>> the left side of the can balances the force on the right side of the can,
>> at any given depth. But the pressure increases with depth, so the pressure
>> in the flat top surface of the can is different than the pressure on the
>> flat bottom surface of the can. The net force exerted by the fluid outside
>> the can is just then the difference in the forces on top and bottom of the
>> can. This is called the buoyant force of the fluid on the can. Since the
>> pressure on the bottom of the can is greater than in the top, the buoyant
>> force is upward.
>> 
>> This volume of water (with or without the can) is obviously in equilibrium.
>> It moves neither up nor down. Thus the downward force of gravity on that
>> volume of water (namely its weight) is therefore balanced by the upward
>> buoyant force. This is the statement of Archimedes’ Principle, that the
>> buoyant force is equal to the weight of the fluid displaced.
>> 
>> Quantitatively, the weight of the water inside the can is the mass times
>> the acceleration of gravity. The mass of the water is the density times the
>> volume. If our van has ends of area A and the top of the can is at depth d1
>> and the bottom is at depth d2, then the volume of the can is A * (d2-d1),
>> and thus the weight of the water displaced is (density)*A*(d2-d1)*g. We
>> just said this is equal to the buoyant force (Archimedes’ principle), and
>> we said earlier that this was due to the difference in water pressure on
>> the top and bottom of the can. This is obviously satisfied if the pressure
>> (force per area) on the top is (density)*d1*g and the pressure on the
>> bottom is (density)*d2*g. This is the source of our earlier statement that
>> the pressure increases linearly with the depth in the fluid.
>> 
>> As the last step in thinking this through, replace the contents of the can
>> with some substance other than water. The pressure from the fluid OUTSIDE
>> the can doesn’t change — it doesn’t care what’s inside the can. So the
>> buoyant force is still the same, equal to the weight of the water displaced
>> by the can. But the weight of the contents of the can has changed. If the
>> can is filled with styrofoam, the weight of the contents is now smaller,
>> and the buoyant force is relatively bigger, and so there is a net force
>> upward and the can filled with styrofoam rises. If the can is filled with
>> birdshot, the weight of the can contents is now larger than the buoyant
>> force, and thus can will sink.
>> 
>> This is high school physics.
> 
> then why are you having so much trouble explaining it in words?
> 
>>>>> So exactly why does a cork bounce up when submerged in water?
>>>>> If the top of a hot air balloon was pointy instead of flat would it rise?
> 
> Fact is I looked in the index in a number of College Freshman physics 
> texts and none of them had the term "buoyant force" listed. 

Well, I’m not sure what ones you looked at. First three I pulled from my
shelf sampled different vintages: 

Halliday & Resnick (1977) pg 376

Giancoli (2000) pg 340-343

Mazur (2015) pg 469-471

Buoyant force called out (and carefully defined) there.


> Mostly they 
> only mentioned in passing that under Archimedes principle, objects in 
> fluid are "bouyed up". It's interesting that while you try to explain 
> what is going on with words, you can't. You lapse into equations and 
> jargon and end up chasing your own tail over and over.

Physics is a quantitative science. I added a paragraph about how to do
things quantitatively because it’s important to do so in physics. It also
served to justify the claim of linear dependence between pressure and depth
in a constant-density fluid. 

> 
> You don't explain any general situation at all 

Nor was that asked for. The question was Why does a less dense object rise
in a dense fluid surrounding? 

Which I answered. 

> and then trying to use a 
> single restricted example of a cylindrical "can" you don't even cover 
> that case reasonably. if the can rises out of the liquid how does it 
> have a force on it's top cover? 

I’m glad you asked! That’s an elaboration that can be easily explained in
much the same way. 

First note that the shape of the can doesn’t matter. The very same
arguments I used for a cylinder would also apply to a rectangular block,
for instance. One can also see that an assemblage of two stacked cylinders
or stacked rectangular blocks yields the same result. By extension, even
the same result can be found for a cone, either point up or point down, by
approximating it with a stack of concentric cylinders of different radii.
This last point also shows that the orientation of the shape doesn’t
matter. Thus we conclude that Archimedes’ principle applies regardless of
the submerged shape or orientation. Indeed, the story of Archimedes’
revelation had to do with a crown, quite a complicated shape. 

If the buoyant force is greater than the weight of the object, then it will
rise to the surface. At this point, neither the buoyant force nor the
weight have changed, so it will continue to rise so that some portion of
the body is above the fluid. When that happens, the amount of the fluid
displaced starts to drop, and so the buoyant force also drops (see
Archimedes’ principle). When the weight equals the buoyant force, then it
will be in equilibrium again. 

There are many applications that could be discussed here, over many many
pages of additional, plain English prose. 

> Does the principle quit working them? Of 
> course it still works. And even worse you don't even mention the problem 
> that the can might flip over. Why? What are the conditions that control 
> this?
> 
> Sylvia did much better than you on this. Maybe you should ahs Sylvia for 
> some science lessons.
> 
> So If I take your mythical "can" and fill it completely with water 
> sealed with it's lid and then toss it into a pond, will it sink or 
> float? And if it floats in which orientation will it float? Explain 
> using words with no math, please. This is high school physics.
> 
> 
> 
> 



-- 
Odd Bodkin — Maker of fine toys, tools, tables

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Thread

Why does a less dense object rise in a dense fluid surrounding? Arindam Banerjee <banerjeeadda1234@gmail.com> - 2019-01-09 21:12 -0800
  Re: Why does a less dense object rise in a dense fluid surrounding? Sylvia Else <sylvia@email.invalid> - 2019-01-10 23:20 +1100
    Re: Why does a less dense object rise in a dense fluid surrounding? Arindam Banerjee <banerjeeadda1234@gmail.com> - 2019-01-10 05:10 -0800
      Re: Why does a less dense object rise in a dense fluid surrounding? Odd Bodkin <bodkinodd@gmail.com> - 2019-01-10 13:32 +0000
        Re: Why does a less dense object rise in a dense fluid surrounding? benj <benj.fake@gmail.com> - 2019-01-10 13:13 -0500
      Re: Why does a less dense object rise in a dense fluid surrounding? Sylvia Else <sylvia@email.invalid> - 2019-01-13 16:31 +1100
    Re: Why does a less dense object rise in a dense fluid surrounding? poraty6@gmail.com - 2019-01-10 16:11 -0800
  Re: Why does a less dense object rise in a dense fluid surrounding? Odd Bodkin <bodkinodd@gmail.com> - 2019-01-10 13:00 +0000
    Re: Why does a less dense object rise in a dense fluid surrounding? Arindam Banerjee <banerjeeadda1234@gmail.com> - 2019-01-10 05:04 -0800
      Re: Why does a less dense object rise in a dense fluid surrounding? benj <benj.fake@gmail.com> - 2019-01-10 13:12 -0500
    Re: Why does a less dense object rise in a dense fluid surrounding? benj <benj.fake@gmail.com> - 2019-01-10 13:11 -0500
      Re: Why does a less dense object rise in a dense fluid surrounding? Odd Bodkin <bodkinodd@gmail.com> - 2019-01-10 19:14 +0000
        Re: Why does a less dense object rise in a dense fluid surrounding? "reber G=emc^2" <herbertglazier0@gmail.com> - 2019-01-10 12:28 -0800
          Re: Why does a less dense object rise in a dense fluid surrounding? benj <benj.fake@gmail.com> - 2019-01-10 19:36 -0500
            Re: Why does a less dense object rise in a dense fluid surrounding? "reber G=emc^2" <herbertglazier0@gmail.com> - 2019-01-11 09:40 -0800
        Re: Why does a less dense object rise in a dense fluid surrounding? mitchrae3323@gmail.com - 2019-01-10 13:21 -0800
        Re: Why does a less dense object rise in a dense fluid surrounding? benj <benj.fake@gmail.com> - 2019-01-10 19:32 -0500
          Re: Why does a less dense object rise in a dense fluid surrounding? Odd Bodkin <bodkinodd@gmail.com> - 2019-01-11 16:20 +0000
            Re: Why does a less dense object rise in a dense fluid surrounding? poraty6@gmail.com - 2019-01-12 23:56 -0800
              Re: Why does a less dense object rise in a dense fluid surrounding? Odd Bodkin <bodkinodd@gmail.com> - 2019-01-13 12:40 +0000
                Re: Why does a less dense object rise in a dense fluid surrounding? poraty6@gmail.com - 2019-01-13 16:01 -0800
    Re: Why does a less dense object rise in a dense fluid surrounding? poraty6@gmail.com - 2019-01-10 16:13 -0800
  Re: Why does a less dense object rise in a dense fluid surrounding? mitchrae3323@gmail.com - 2019-01-10 10:46 -0800
    Re: Why does a less dense object rise in a dense fluid surrounding? Sergio <invalid@invalid.com> - 2019-01-13 15:40 -0600

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