# Buoyancy: solid things position in the water

#### Yoseph

There are three things P, Q, R. The density of P is 2000 kg/m3, Q is 1000 kg/m3, R is 2500 kg/m3. If all of them are put into the water having density 1000 kg/m3, which one is the correct position of the things? Picture A or Picture B (see attachment)?

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#### ChipB

PHF Helper
Well, what do you think? Both P and R have densities greater than water. A rock also has density greater than water - what happens when you drop a rock into a pond?

#### Yoseph

Well, what do you think? Both P and R have densities greater than water. A rock also has density greater than water - what happens when you drop a rock into a pond?
I chose picture B because things P and R are solid, so they will go to the bottom of the container as well as the rock. Whereas, my teacher choose picture A. It's to make sure that the density of R is greater than P so that R position is lower than P position. According to you, does my teacher's reason make sense?

#### ChipB

PHF Helper
I chose picture B because things P and R are solid, so they will go to the bottom of the container as well as the rock.
Correct, although the reason picture B is correct is due to the density of P and R relative to the density of water.

Yoesph said:
Whereas, my teacher choose picture A. It's to make sure that the density of R is greater than P so that R position is lower than P position. According to you, does my teacher's reason make sense?
Your teacher is incorrect. Picture A shows item P in suspension in the water submerged, but not on the bottom. The only way this can occur is if the density of P is equal to the density of water, same as the density of Q. It's not. It doesn't matter how the density of one item compares with the density of another - if both P and R have densities greater then water then both will sink to the bottom. Perhaps what your teacher was trying to say is that R will sink to the bottom faster than P will, due to it's greater density? That would be true, but I interpret the question to be about the steady-state condition of the objects.

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#### Yoseph

Okay ChipB, I see. Thanks a lot for your complete explanation.

#### THERMO Spoken Here

So "Q" floats midway?

Is "floating" of an object at constant depth described as "having neutral buoyancy?"
Some 65 years ago my brother and I spent 4 hours getting in and out of
a lake trying to weight a model sub with bird-shot to "not sink" and "not float."
To craft something to have density identical to water is no small task.

Choice (a) is wrong, how does the block stick to the wall? Choice (b) (a tempting
physics text answer) is wrong also. I suppose a nuclear sub can keep
station at a depth - but not passively, like "Q" must.

What say ye, ChipB?

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#### THERMO Spoken Here

So "Q" floats midway?

Is "floating" of an object at constant depth described as "having neutral buoyancy?"
Some 65 years ago my brother and I spent about 4 hours getting in and
out of a lake trying to weight a model sub with bird-shot to "not sink"
and "not float."

Choice (a) is wrong, how does the block stick to the wall? Choice (B) (a tempting
physics text answer) is wrong also. I suppose a nuclear sub can keep
station at a depth - but not passively, like "Q" must.

What say ye, ChipB?

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#### ChipB

PHF Helper
Choice (a) is wrong, how does the block stick to the wall?
More importantly choice (A) it's wrong because P does not have neutral buoyancy.

Choice (B) (a tempting
physics text answer) is wrong also. I suppose a nuclear sub can keep
station at a depth - but not passively, like "Q" must.

What say ye, ChipB?
I think you are over-thinking it. They give the density of P as being precisely the same as water. Your point about the practical aspects of doing this is good - it's hard to use bird shot in a model sub and get 4 digits of accuracy as described in this problem. But the OP is being asked to give a response based on the data given, not to replicate this in the lab.

#### mattlock

let's overlook the fact that P appears to be stuck to the side and call that an error in graphics.

when some examples offered to us there are givens that we are supposed to accept, that water has a mass of 1000kg/m3. in that case B is correct.

my question would be; what is the vertical height in your example? water at a 1km depth is more massive per m3 that water at the surface, simple fluid dynamics. given enough depth, or height both R and P would 'settle' at different depths, then case A could be correct.

#### ChipB

PHF Helper
my question would be; what is the vertical height in your example? water at a 1km depth is more massive per m3 that water at the surface, simple fluid dynamics. given enough depth, or height both R and P would 'settle' at different depths, then case A could be correct.
No, water has a very high modulus of elasticuty, so it is almost (but not quite) incompressible. At a depth of 4km it's density is only about 1.8% greater tham at the surface. For reference see https://en.m.wikipedia.org/wiki/Properties_of_water. In order for water to become twice as dense, which is necessary for figure A to be correct, you need an ocean about 110 km deep, much deeper than any ocean on Earth.

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