More brain teasers

[cerb]

Teaser #1:

You're sitting in a boat in the middle of a lake. You have a considerably large rock (say, basketball sized) in the boat with you. If you throw the rock in the lake, will the level of water in the lake
a) rise,
b) fall, or
c) stay the same?

Teaser #2:

A balloon (inflated, of course) is tied to a house brick, and dropped in a deep lake. The brick is heavy enough to drag the balloon under water. After some time, the system stabilises itself and floats at some arbitrary depth. If the brick is dragged by hand down some more, will it then
a) continue to sink to the bottom
b) float to the surface, or
c) eventually return to the same depth it was at before being moved?

This second one is a tough one, and I thought I had the answer, but have since had a rethink and I am not sure if I'm right.

Answers must be given with an explanation (ie, no guessing, people! )

Oh, and throw any others you know of up here - I'm always keen for a challenge.

Cerb

[Gurm]

In the first example, it will rise by a minute amount. Weight is immaterial here, we are merely discussing volume of displacement, which you are increasing.

As for the second, my "guess" is that it will in fact rise. That's in a perfect system. However, in real life I think it might be more complicated and there might be factors we haven't considered yet.

- Gurm

P.S. If the northern hemisphere of a planet is 100% water, and the southern hemisphere is 100% land, is the south an island or is the north a lake?

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Listen up, you primitive screwheads! See this? This is my BOOMSTICK! Etc. etc.

[Kruzin]

The water level will stay the same.
When the rock was in the boat it was displacing water by making the boat heavier. When the rock was moved from inside the boat to outside the boat, it still displaced the same amount, so the boat rose a little, but the water level stayed the same.


The balloon will eventually rise back to it's original level of bouyancy, assuming water temperature remains the same.

[Rags]

Technically since balloons aspirate air naturally, it will go to a slightly lower level.

Rags

[cerb]

Just remembered the problem I was having with the second teaser.

The question I had at the end of it when I first heard it, was this: Can the volume of the balloon change as pressure around it increases?

I don't know whether to give my answers yet, or wait until tomorrow. ICQ me on 46044319 if you want the answers before then.

Cerb

[Himself]

I have a 5 year old balloon on a stick here I got on one valentine's day, still fully inflated, most unnatural.

[damage]

all answers are wrong so far, so seeing as there have been 2 different answers for the first teaser and there are only 3 posibilities (goes up, stays put, goes down), the average yogi bear should be able to deduce what really happens
as for the second, again there are the same 3 possibilities and the one guessed at so far was wrong, but once you have the answer, you have to have some reasoning

however my first quesiton would be why did aaron through a perfectly good rock overboard when he could have attached his gf's poodle to it!

[damage]

btw aaron = cerb and i noticed i put through instead of throw that's ok, i'm dumb and never claimed to be anything else

[spoogenet]

Dunno about number 2, but as for number 1, it all depends.

The rock will only displace as much water as the volume of the rock, period. But the mass of the rock (density considered) matters quite a bit, because a basketball rock that weighs 1 gram will not cause the boat to displace a noticeable amount of water over what the boat displaces without the rock. However if the rock is so dense that it has a mass of 2000 kg, the boat (assuming a rather small boat, no ocean liners here) will displace a much more noticeable amount of water than it would without the rock.

So the answer is, if the rock has a small mass, then the lake level will rise, if it has a certain critical mass, the lake level will remain unchanged, and if it has a very high mass, the lake level will fall.

So there's my answer. And a balloon will have a different volume depending on the depth it is, because the pressure will cause the air in the balloon to compress, thus having a smaller volume. Same thing applies to temperature (think hot air balloons), and it's cold and high pressure at deep places. So I would assume that if the brick/balloon are pulled below a critical depth that they will continue to sink, whereas there is a buffer zone where it will keep going back to equilibrium.

Ok, so that's enough thinking for one night, don't ya think?

b

[damage]

your second answer is correct in that it continues on downwards, but your answer to the first is a little off the mark, if the rock is heavy enough to sink, then the water level will fall. If the rock is not heavy enough to sink (fat chance) the water level will remain the same. At no point will the water level increase.
does anyone have some new ones to post?

[cerb]

Yup. The rock is more dense than the water, so the boat would have to displace more water than the volume of the rock in order to float. This means that when the rock is thrown in the water, it will be displacing less water, so the level will fall.

As far as the balloon goes, the balloon will compress as the pressure increases, so its density increases. But so does the density of the water. Would these densities change by the same amount? Not sure. Would have to test that physically I guess. One thing that is for certain is that the density of the brick would not change. Therefore, the further down we go, the more bouyant the brick becomes. But this is dependant on the change in density of the water, which is really the deciding factor as to whether the system sinks or not.

That is, whether the system floats depends on whether or not the bouyancy change from the balloon compressing is offset by the bouyancy change of the brick. Common sense would say that it is not, so the system would sink, but I'd still like to see it tested.

Cerb

[cerb]

I guess at the start I should have clarified the fact that the rock is more dense than the water, but I myself would have made that assumption cause isn't that true for almost all types of rock?

Cerb

[damage]

i'll post it in this thread, although hell i could just icq you
but the balloon definately sinks because air is far more compressible than water
easiest intuitive example i can think of is compare a water bed to an air cushion
also this is the reason they use water in hydrolics, air would compress and induces lag into the system
also it wouldn't really be hydrolics with air would it and airdrolics doesn't have the right ring? i'm not certain, but MAYBE that is why oil is used sometimes too, because it would be even less compressible than water and have even less lag, just an idea

[Vlip]

Cerb, if my remembering are correct there is a rock that has a smaller density as water and actually floats.

I remember having one of those in my hands when I was a kid, this thing was damn light.

I think the rock is so porous it's almost completely filled with air and therefor floats.

Can anybody confirm that? And if possible give the name of that kind of rocks?

P.S: And no it was not made of plastic

[spoogenet]

Damage:

You mean to tell me that if you put a 10,000 kg rock (the size of a basketball) in a small boat, that the boat will not displace any more water than the rock itself would displace?

A heavy rock in a boat can cause the boat to displace much much much more water than the rock itself would displace in the water.

b