Hypothetical Water Displacement Puzzle

You should still float, the human body is not as dense as water....To sink you would need something more dense, like lead weights....

I have seen a few people that sink like lead weights.

There is also a couple lead singers that have some weight . . .

Not quite like lead, but I used to be able to stand on the bottom of a pool. Had to prove it to a swimming teacher who declared "Everybody floats."

Not quite like lead, but I used to be able to stand on the bottom of a pool. Had to prove it to a swimming teacher who declared "Everybody floats."

Did they tell you you were denser than most?

I've been told that I am denser than most, but I don't think they were talking about my weight.

I have seen a few people that sink like lead weights.
Thin people, mostly. I would expect that a person with a mass of 120 kg would have a somewhat lower density.
And the answer is that you would float the same whether the bag was there or not, assuming that the weight of the bag submerged in water is negligible.

just for that photo I have to give a GA!

I would say that you and the bag will still weigh 240 KGs, and if the bag is sealed and you have air in your lungs, both you and the bag will be held at the surface. The air in your lungs, combined with any fat cells that you may have, will make the entire package lighter than the surrounding water.

Not "held at the surface." The momentum from the fall will carry the combination under the water; after stopping it will gradually rise to the surface--assuming the body would float on its own which is highly likely.

I don't trust that hypothetical water... gimme the real stuff any day...
Or better still I'll take beer.
Del

maybe the bag of water is heavy water?

I agree with kramarat.

Now I want to see the youtube video of it being played out.

Preposterous. Baseless. Definitely not rare!

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_{(I originally commented in agreement... but then I realized such a comment would suggest we were probably both wrong....this way at least one of us can appear right....which is after all what is important, right? So to recap, 'You are wrong. You're welcome.' )}

Yes the weight of matter inside the bag will still be 240 KG. That doesn't change. The force you are look for is bouyancy. A force caused by weight of the fluid your immersed in. Since most of the matter in the bag is water, you included. Whether you sink or not come down to about 4 lbs of matter. And what that matter forms in your body. High body fat are oils that tend to float. Gases in the body also aid this.

Yeah. All that stuff ↑.

I want to point out that it is maybe because your weight is 120 kg that nobody believes you will sink to the bottom of the pool!

Make the same story with a 40 kg bony something and 80 kg lead belt!

Hi Thanks for all the replies so far, I have been having a bad day workwise, and some of the input has me laughing my socks off.

Units, units, units!!!!

A 120kg mass will weigh (present a downward force) in our nominal 9.8 m/s^2 gravitational field 1176 Newtons. When 120kg mass floats in any liquid an equal buoyancy force upward exists to the 1176 Newtons to keep it floating with a net force of zero. When resting on the bottom of the liquid pool the floor and the buoyancy add to an upward force of 1176 Newtons to again make a net force of zero. When falling at a constant terminal velocity in a fluid the net force is zero from the downward weight and the upward fluid dampening force and buoyancy.

I think it depends on the temperature of the water in the bag, compared to the temperature of the pool water. Fill the bag with colder water if you want to sink

Hmmm, Think about it. What is denser; water at 4 degrees C or water at 20 degrees C?

"Hmmm, Think about it. What is denser; water at 4 degrees C or water at 20 degrees C?"

I am afraid that I am missing your point... I realize ice floats, but water at 4DegC is NOT ice, and is indeed DENSER than water at 20DegC. In fact it is denser than water at 5DegC thru 100DegC----thus it will sink. Ever wonder why the water at the bottom of the pond is colder than the water at the top? (at least during summer)

I was actually thinking of the water (not yet ice) less than 4 degrees C. The density actually becomes less in this zone. A unique feature of water that allows lakes to turn over because of the density being greatest at 4 degrees C and still liquid. It is a trivial point but if the water is introduced into the bag at say 1 degree C and the pool is 4 degrees C, the water in the bag will be lighter.

Technicaltom,

The actual terms have been mentioned already. Your mass is 120kG and the added water's mass is 120kG. The word "weight" has always been a misapplication, because it is mass acted upon by the force of gravity. (Thus on the moon you have the same mass but a much lower weight because the force of gravity is less.) Second term--density, which is mass per unit of volume (the closely related term, specific gravity is a ratio of the material's density divided by the density of water at a standard temperature, so it has no units--it is just a multiplier). If you float when you are in a pool and not moving any part of your body, then your net density is less than that of water; if you sink, then it is greater. Some people always float, others always sink. You can decide what it will be for your character.

As others have said, the additional water simply diverts your attention from the basic issue of whether you float or not, assuming your pool is filled with fresh water. If you are in a salt-water pool (lake, ocean, ...) the density of you and the bag will be less than the pool, so the bag containing you and the water will float (even in you sink below the level of the water within the bag). The presence of air within the bag (assuming that it is at least a few liters) will cause the bag you are in to float.

OK? --JMM

who cares what the answer is.. I feel for the life guard that will have to TRY and fish you out.... numb nuts!!

Well it was a "Hypothetical " question, Even Achimedies toyed with this puzzle according to one reply,"numb nuts "is not something I hear in my daily conversations , so I am not sure if it a derogatory comment or just a ligthhearted comment,so it s really wasted on me .

But all in all it has been an interesting week, reading all the replies and even doing some Googling as a result.Fear not I am not going to the swimming pool !!!!.

And thanks to all who helped to improve my mind ,

AS with all replies, any perceived insult is on the side of the receiver.... as the gender of the question was one of lightheartedness, (is that a word, or have I been spending to much time on here with all these Americans?) so was my reply.

AS the question was way off field... one must expect a way off field answer....

There are enough people out there at can and do insult other at the slightest opportunity, in many cases they don't even need an opportunity, please take my comment as one of a jovial kind, with no insult intended.

However I do like you thinking... not many folk would come up with that kind of question, with a thought for the lifeguard.

'...lightheartedness, (is that a word, or have I been spending to much time on here with all these Americans?)...'

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'Lightheartedness' being a word

and

the amount of time you spend here with all these Americans being judges as excessive

are not mutually exclusive; False dilemma.

'Lightheartedness' can be a word without excusing or making acceptable the amount of time you spend here.

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If 'lightheartedness' were in fact not a word, what would you suggest to use in its place? Perhaps simply 'lightheart', as in 'the question was one of lightheart' or maybe 'the question was lightheart'?

pray tell.. Are you giving me an english lesson? or does one not understand British humour?

Rhetorical question!!

If I weren't already aware that we are merely engaged in a bit of lightheart,I might find it a bit disingenuous to begin a question with 'pray tell' and then claim it as 'rhetorical'.

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Anyway, how effect could any instruction be to someone who capitalizes 'British humour' and not 'english lesson'?

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What better way to respond to a rhetorical question, than with another rhetorical question?

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Rhetorical questions....who needs'm?

It also depends on the density of the plastic involved. In total, you could either float or sink, but the tendency would not be very strong either way.

water in the bag is the same density as water in the pool, density of human is lighter then water = you will still float (provided you did originally and weren't able to stand on the bottom of the pool). weight doesn't really make a difference in this case as it is all based on density. if you were tied to a bag with 120kg of helium you may not even hit the water :)

"if you were tied to a bag with 120kg of helium"... he'd be dead!!

Not if he's "tied to" it. Only if he's tied IN it!

opps my dyslexic eyeballs again!! its the chain of the question....

As noted, momentum will cause you to sink when you are first thrown into the pool but you will slowly rise. At equilibrium you will float to the top of the water in the bag and you and the bag and the water within will float to the top of the pool.

Fill the bag with salt water. Or, for better results, concrete.

-A-

No, upon entry the density of the water will equalize and the amount of buoyancy, or lack thereof depending on the overall density of your body mass relative to that of water, will determine whether you sink or float.

I think that Archimedes wrote an article very similar to the one you propose.

It is possible that your having introduced a kinetic element (dropping the bag) has invited an obfuscation into the various responses.

Imagine that the bag is suspended from a lifting beam by a crane equipped with a scale that measures the total load. You, within the bag, are also suspended from the load beam with your own personal weigh scale.

With the load suspended, the crane scale will read 240 kg. Your personal scale will read zero - because you are bouyed up by the water. (pool floor walkers are very rare and of those extant, some are in jail for inappropriate pool behavior.)

When the bag is immersed in the pool, both scales will read zero.

This analysis ignores minutae such as the density of the bag material and whether, in the excitement, you may have peed in the bag altering the specific gravity of the contained water.

OK. I have tried to explain the problem and solution in my previous post #12. The answer is in the buoyancy of the 120kg person. Someone mentioned density as a consideration. That is correct. Density has everything to do with the solution to the question. First of all, there are two parts to the solution. One answers the question: "Will the total weight still be 240 kg?" Of course it will. Nothing has changed to alter the weight of the bag full of you and the water. However, the next part of the "Puzzle" has a conclusion that is wrong. It states "...when I assume I will be sinking to the bottom of the pool." There is nothing to prove that you will be sinking to the bottom of the pool in the informaiton given. If you perform the steps that I outlined in my post #12, you can determine if you will sink. It is your body's density that will make that determination. Let's say you are a rotund type of person, rather portly and having a large girth. When you are immersed in the pool your density will be diminished by your physical size. If you displace 120 Liters of water, you will have displaced the exact weight that you are (as defined by the puzzle). One Liter of water weighs 1 kg. Therefore, you will have displaced your own weigh exactly and you will be in equillibrium - you will neither sink nor float. You will be suspended at where ever you are in the water. On the other hand, if your density is such that you displace more than 120 Liters of water, the difference in the weight of the displaced water as it relates to your weight is the buoyancy and you will float. Now, if your 120 kg of weight is packed very tightly into a very fit and slender body that will displace only 100 kg of water, you're going to sink - period. Now let's consider the bag. The bag and the 120 Liters of water in it will sink as well because the falling body will drag it along with it. The answer is totally dependent on the displacement of the water. If your body is a cube that is measurable, you could determine your displacement by simple measurements. However, such is not the case. Hence, your density must be determined by displacement from a vessel (the pool) that has definitive and finite dimensions like height, length, width, circumference, etc.

What puzzling to me is, is the pool already filled with water???

I was under the impression that any body(human) will eventually float unless weighted down or snagged on something, or caught in some kind of current.

'....I was under the impression that any body(human) will eventually float....'

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Most living (or recently alive) human bodies (just the body, not any clothes or accoutrements) that have mostly air filling their lungs are, on whole, less dense than water and therefor float. Exceptions to this rule are not rare though. There are many people with sufficient muscle and bone as to more than make up for their fat and certain amounts of air in their lungs.

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When considering cases where there is little or no air in the lungs, more people fall into the category of those who do not float, but most (depending on how well fed the people that make up the sample are) will still float....though not as high in the water.

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There are other factors as well, like salinity that affect buoyancy.

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Decomposition of the body eventually affects buoyancy as well, but as the OP talks about cutting himself out of the bag, decomposition shouldn't really come into play....hopefully.

If you calculate it out, your volume-to-be-floated would enlarge to where your composite density would be more than 64 pounds-per-cubic-feet and trying to float in water about 62.4 or 5 pcf, and therefore, you would be relatively slowly sinking...

However, if you found yourself in a sinking-Titanic kind of situation, and all the life boats are already gone, and there was an abundant supply of bubble-wrap and duct tape, you just might be able to improvise enough of a flotation device to keep you afloat long enough to get yourself rescued, with a LOT of luck, that is...

"If you calculate it out, your volume-to-be-floated..."

Can you explain exactly how one can "calculate it out"? What are the dimensions that you would use to accomplish this? The only way that one can determine the volume occupied by the human body is by the "displacement" method as described in my previous reply to this problem.* There are no height, width, length, depth, circumference nor any other measurements available to allow one to "calculate it out" as you suggest. It is required that the body in question be immersed in a vessel of known dimensions filled with a liquid of known density (such as water at 62.4 pounds per cubic foot) so that the displaceemt can be measured and calculated to determine the weight of the displaced water and then multiplied by the weight (desnity, if you prefer) of the displaced water. Now, the liquid may be something other than water if you prefer because, if, indeed, the density of the body is less than the density of water, then the body would have to be forcibly submerged because the displaced water will cause the body to try to float. If the the body were immersed in, say, gasloine (regular) at about 46 pounds per cubic foot, it would immediately drop to the bottom of the container due to the disparity in the relative density (or specific gravity) of the two liquids. However, the increase in the depth of the liquid would remain the same when the body is immersed in either liquid, so the density or weight of the body could then be determined using the weight of water as the determining factor. Actually, it is rather simple.

* Just as I finished this reply, I realized there is one other way to determine the volume of the body. It would actually be a variance of the displacement method. You could place the body on one side of a balance and a container on the other side. Then, you could add water to the container until both sides are balanced. Then, you simply record the amount of water you have added to the container and that would equal volume of the body. Then, to answer the question posed by the author, if the water in the container is less than 120 liters, the body will sink. If it is more than 120 Liters, the body will float. Of course, as in some other replies, including mine, the plastic bag and the water in it have no bearing on the outcome, unless we get very picky and try to ascertain the displacement of the bag, take into account the water temperature difference between the bag water and the water in the pool, and the atmospheric pressure at the time of the "dipping".

Simplistically, I view the ''system'' as a 120kg person with a weightless tank completely filled with 120 kg of pure water, completely submerged in a swimming pool, under ''Standard Temperature and Pressure'', etc., wanting to see if he rises higher, or sinks lower, in said pool.

The weight of the system (W$) will thusly equal the weight of the person (Wp) plus the weight of the tank (Wp, essentially nil) plus the weight of the pure-water-as-ballast ( Wb). Similarly, the mass of the system and the volume are found as below:

assume (1 kg weighs 2.20462 lbf) and that water weighs 62.4 lbf/ft4 = 1000 kg/m3

From ''Orders of Magnitude (density)'' in Wikipedia, obtain that the average human body density'' equals 1062 kg/m3, which is identified herein as ''Dp''

Vp = ((Mp = 120 kg/prsn)/(Dp = 1062 kg/m3 =0.112994 m3) =>3.99003 ft3/prsn)

Vt = ((Mb = 120 kg-of-ballast)/(Db = 1000kg/m3) =.120 m3) =>4.23773 ft3/ballast

so, V$ = (Vp =3.990 ft3 + (Vb = 4.237 ft3) + (Vt = 0, nearly) = 8.228 ft3, at least

and, M$ =(Mp = 120 kg) + (Mb = 120 Kg) + (Mt = 0, nearly) = 240 kg, at least

Wp = (Mp = 120 kg) x ( 2.20462 lbf/kg ) = 264.555 lbf/prsn

Wb = (Mb = 120 kg) x ( 2.20462 lbf/kg ) also = 264.555 lbf/blst

Wt = ( Mt = 0, nearly) = 0 lbf/tank

So, W$ is at least = 529.11 lbf/system

D$ = (W$ = 529.11lbf)/(V$ = 8.228 ft3) = 64.3 lbf/ft3 > 62.4 lbf/ft3

Therefore, the person, if perfectly still, would tend to slowy sink...

Hopefully, this was helpful

The value for average human body density in the Wikipedia entry "Orders of Magnitude" comes from a study that estimated and backed out the lung capacity in order to calculate density of the body sans air filled cavities (though they neglected removing gas in the gut from the calculation).

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Typical Functional Reserve Volume in an adult is around 2 liters (usually a little higher for males, lower for females). 2 liters of air is going push the calculation firmly into the realm of positive buoyancy.

Even if they exhaled as much as they could, the extra liter of air still in their lungs will be enough to change the outcome otherwise using the calculations above.

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There is a possibility of negative buoyancy with a combination of some of the following:

-all bubbles were definitely removed from the bag,

-the bag material itself was more dense than water,

-the person inside was of very low body fat and/or comprised in part by large dense bones (not big boned though)

- the person inside (or the facilitator of this 'demonstration') has taste in shoes that runs to the cementitious.

- The water filling the bag is of high salinity or perhaps heavy water, while that in the pool is low salinity and pure protium oxide

- The person in the bag has had extensive dental work with amalgam or gold fillings.

- The person in the bag makes the effort to exchange all the air in their lungs with something far more dense before the bag is sealed.

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The person in the bag carries some of my jokes and puns with them....which is pretty much a guarantee they will sink/bomb/go under like a lead balloon.

I think the problem is that we are not answering the question as it was posed. The question was "...will the total weight still be 240 KG?" Of course it will! But only if it is "weighed" in the same or equal conditions as it was when it was standing on the end of the diving board. The only thing that is not indicated in the "puzzle" is the definition of weight. Weight, as I see it, would be relative. If, for instance, this activity were to be happening on the moon, the "weight" would be quite different. Similarly, since the activity is taking place in a pool of water, the "weight", again, would be subject to a different set of conditions that would render a different answer. As some others, as well as I, have said, it is the "density" that would remain the same. The volume of the bag of water would be very close to the same since water is not compressible at STP. But the same can not be said for the human body. The substance and composition of the human body is very much compressible since there are many voids in the boy's structure that are filled with differing substances, some compressible (gases, tissue, blood, etc) and others that are not (mainly water). This renders the question unanswerable without further input from the author. In its simplest form, the quesiton has been answered several times over, in several different ways. However, depending on the level of detail the the author is seeking, the question is, as I said, unanswerable without further input.