Buoyant Force in High vs Low Density Liquids: Homework Statement & Solution

In summary: Buoyant Force for both case are the same... Am I right?Yes, you are correct. The buoyant force is the same in both cases because the weight of the object is the same and the volume of water displaced is the same. This is due to the Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. Therefore, the object will float at the same level in both cases. In summary, when the object is submerged into a higher density liquid compared to a lower density liquid, it will float higher in the liquid due to the same buoy
  • #1
chetzread
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1

Homework Statement


When the object is submerged into higher density liquid compared to the lower density liquid, the object will floats higher in the liquid...

Homework Equations

The Attempt at a Solution


The object will be more stable, right? Can someone explain why it so? Because from buoyant force =(rho) (V) (g), the buoyant force of object in two liquid are the same... [/B]
 
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  • #2
chetzread said:

Homework Statement


When the object is submerged into higher density liquid compared to the lower density liquid, the object will floats higher in the liquid...

Homework Equations

The Attempt at a Solution


The object will be more stable, right?
Short answer: depends ... you didn;t write out the whole question did you?
Can someone explain why it so?
... sure: but you posted in homework so you need to work it out.
What makes you think that an object floating higher in the liquid is more stable? What does "stable" mean?

Because from buoyant force =(rho) (V) (g), the buoyant force of object in two liquid are the same...
That is correct - the buoyant force must be equal to the weight of the floating object (for floating at the surface). But there are other forces happening too - even in perfectly still liquid.

Consider: imagine the floating object is a cylinder that is taller than it is wide ... in liquid A it floats with just 1/10th above the surface, in liquid B it floats with 9/10ths above the surface. In which liquid is the cylinder more stable?
 
  • #3
chetzread said:
When the object is submerged into higher density liquid compared to the lower density liquid, the object will floats higher in the liquid...
Is it submerged or floating? Submerged means completely immersed in the liquid.
chetzread said:
from buoyant force =(rho) (V) (g), the buoyant force of object in two liquid are the same.
If it is floating in both instances then yes, the buoyant force is the same, but not for the reason you give.
 
  • #4
haruspex said:
Is it submerged or floating? Submerged means completely immersed in the liquid.

If it is floating in both instances then yes, the buoyant force is the same, but not for the reason you give.
It's floating, so , is my idea correct?
 
  • #5
chetzread said:
It's floating, so , is my idea correct?
You are correct that the buoyant force is the same if it is floating in both cases, but you have not stated the correct reason.
 
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  • #6
haruspex said:
You are correct that the buoyant force is the same if it is floating in both cases, but you have not stated the correct reason.
Not (rho) (V) (g) = same for both case?
 
  • #7
chetzread said:
Not (rho) (V) (g) = same for both case?
Define what you are using V to mean.
 
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  • #8
haruspex said:
Define what you are using V to mean.
Volume of liquid displaced = volume of the part where the object submerged...
 
  • #9
chetzread said:
Volume of liquid displaced = volume of the part where the object submerged...
Ok, but how do you know that the product Vρ will be the same in both cases? There are two different densities.
 
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  • #10
haruspex said:
Ok, but how do you know that the product Vρ will be the same in both cases? There are two different densities.
No, I assume Buoyat Force for both are same, so, when the density is high, then volume displaced small, then Buoyant Force are same for both cases, so is my idea correct?
 
  • #11
chetzread said:
No, I assume Buoyat Force for both are same, so, when the density is high, then volume displaced small, then Buoyant Force are same for both cases, so is my idea correct?
Yes. You originally wrote that the buoyant force is the same because Vρ is the same for both, but that's backwards. Vρ is the same because the buoyant force is the same. But why is the buoyant force the same?
 
  • #12
haruspex said:
Yes. You originally wrote that the buoyant force is the same because Vρ is the same for both, but that's backwards. Vρ is the same because the buoyant force is the same. But why is the buoyant force the same?
No, I mean when the object is floating in less density water, the volume of water displaced by the object is small, when objects is floating in high density water, volume of water displaced by object is small, so in the first case (rho) is small, v is big, in the second case , rho is big, volume of water displaced by object is small, so Buoyant Force for both case are the same... Am I right?
 
  • #13
chetzread said:
when the object is floating in less density water, the volume of water displaced by the object is small, when objects is floating in high density water, volume of water displaced by object is small, so in the first case (rho) is small, v is big, in the second case , rho is big, volume of water displaced by object is small
Yes, that is all correct.
chetzread said:
so Buoyant Force for both case are the same
The buoyant force is the same in both cases, but what is wrong is the word "so". What you wrote in the first quote above is not the reason that the buoyant forces are the same. There is another reason the forces are the same, and because the forces must be the same, the two submerged volumes are as they are.
Your individual statements are correct, but the causality is backwards.

So, what is the reason the forces are the same?
 
  • #14
Actually the full question is
1) How would the stability of the object be affected if it were floated on a liquid with a greater density than that water?
so , my ans is the stability of object is higher when it is floated on high denstity liquid ... Is it correct ?
 
  • #15
chetzread said:
Actually the full question is
1) How would the stability of the object be affected if it were floated on a liquid with a greater density than that water?
so , my ans is the stability of object is higher when it is floated on high denstity liquid ... Is it correct ?
If we were to say "yes" or "no" to that question, then we would be "doing your homework for you" - which is not allowed.
Instead we are asking you questions to guide you into a better understanding of your answer so you can determine for yourself if the answer is correct. Therefore:

* If you won't answer questions, nobody can help you.
* If you do not follow suggestions, nobody can help you.

ie. from post #2 (flat ignored):
* What does "stability mean"
* Imagine the floating object is a cylinder that is taller than it is wide ... in liquid A it floats with just 1/10th above the surface, in liquid B it floats with 9/10ths above the surface. In which liquid is the cylinder more stable?

That post (#2) also asked "You did not post the full question did you?" which you waited till post #14 to answer.
Post #14 dos not answer the question asked in post #13: "So, what is the reason the forces are the same?"
Why not?

These questions are important to discovering if your answer is correct.
Do you want to know or not?
 
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  • #16
Simon Bridge said:
If we were to say "yes" or "no" to that question, then we would be "doing your homework for you" - which is not allowed.
Instead we are asking you questions to guide you into a better understanding of your answer so you can determine for yourself if the answer is correct.
If you won't answer questions, nobody can help you. If you do not follow suggestions, nobody can help you.

ie. from post #2 (flat ignored):
* What does "stability mean"
* Imagine the floating object is a cylinder that is taller than it is wide ... in liquid A it floats with just 1/10th above the surface, in liquid B it floats with 9/10ths above the surface. In which liquid is the cylinder more stable?

That post (#2) also asked "You did not post the full question did you?" which you waited till post #14 to answer.
Post #14 dos not answer the question asked in post #13: "So, what is the reason the forces are the same?"
Why not?

These questions are important to discovering if your answer is correct.
Do you want to know or not?
Yes, I want to know. Let's just focus on post #14... Is my idea correct?
 
  • #17
chetzread said:
Yes, I want to know. Let's just focus on post #14... Is my idea correct?
You are not paying attention. I just told you:
*** I cannot answer that question "yes" or "no" without breaking the rules of the forum.

You've been around long enough to know the rules.
 
  • #18
Simon Bridge said:
You are not paying attention. I just told you:
*** I cannot answer that question "yes" or "no" without breaking the rules of the forum.

You've been around long enough to know the rules.
For post #15 intuitively, the object float 9/10 in water would be more stable, am I right?
 
  • #19
chetzread said:
For post #15 intuitively, the object float 9/10 in water would be more stable, am I right?
... I never said "water", but, from your experience of objects floating in water you have an intuition that the object that floats with the most submerged will be the most stable, where everything else is the same. In other words: the worse it floats the more stable it is. This is a reasonable statement to make.

Can you tell me why the the object that floats with the most submerged will be the most stable?
Can you tell me which liquid in post #15 is the most dense? Liquid A or liquid B?
 
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  • #20
Simon Bridge said:
... I never said "water", but, from your experience of objects floating in water you have an intuition that the object that floats with the most submerged will be the most stable, where everything else is the same. In other words: the worse it floats the more stable it is. This is a reasonable statement to make.

Can you tell me why the the object that floats with the most submerged will be the most stable?
Can you tell me which liquid in post #15 is the most dense? Liquid A or liquid B?
The object which submerged more is more stable because if we apply the force in arbitrary direction to the object, the object which submerged more is less likely to turn over...
 
  • #21
chetzread said:
The object which submerged more is more stable because if we apply the force in arbitrary direction to the object, the object which submerged more is less likely to turn over...
Well done - do you know why this is?

Can you tell me which liquid in post #15 is the most dense? Liquid A or liquid B?
 
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  • #22
Simon Bridge said:
Well done - do you know why this is?

Can you tell me which liquid in post #15 is the most dense? Liquid A or liquid B?
Liquid A is denser...
 
  • #23
chetzread said:
Liquid A is denser...
... because? Show your reasoning?

Recall:
liquid A it floats with just 1/10th above the surface, in liquid B it floats with 9/10ths above the surface.

Recap:
You have said:
The object which submerged more is more stable
... so, just making sure we are on the same page: which liquid is that: liquid A or liquid B?
 
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  • #24
Simon Bridge said:
... because? Show your reasoning?

Recall:

Recap:
You have said: ... so, just making sure we are on the same page: which liquid is that: liquid A or liquid B?
I maybe misunderstood what you said. Do you mean in liquid A, only 1/10 of the object float on surface? If so, then liquid A is less dense
 
  • #25
Simon Bridge said:
... because? Show your reasoning?

Recall:

Recap:
You have said: ... so, just making sure we are on the same page: which liquid is that: liquid A or liquid B?
Can you continue your explanation?
 
  • #26
... only if you answer questions. I got to turn in for the night. See you tomorrow.
 
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  • #27
Simon Bridge said:
... only if you answer questions. I got to turn in for the night. See you tomorrow.
Liquid A is less dense, can you continue?
 
  • #28
chetzread said:
Liquid A is less dense, can you continue?
Right, so based upon your post #20, should it be more stable in the higher density liquid or the lower density one?

(Note: I feel that the question is a bit misleading. Stability of floating objects is rather a tricky subject. A key factor is the second moment of area of the object in the horizontal plane at the surface of the liquid. E.g. consider a rectangular block with a tall narrow pole (mast) going up from the middle. As long as the water line is around the block, the second moment of area is large. With more submerged, only the mast is above the surface, so the second moment of area is much smaller and it heels over.
See https://en.m.wikipedia.org/wiki/Metacentric_height)
 
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  • #29
haruspex said:
Right, so based upon your post #20, should it be more stable in the higher density liquid or the lower density one?

(Note: I feel that the question is a bit misleading. Stability of floating objects is rather a tricky subject. A key factor is the second moment of area of the object in the horizontal plane at the surface of the liquid. E.g. consider a rectangular block with a tall narrow pole (mast) going up from the middle. As long as the water line is around the block, the second moment of area is large. With more submerged, only the mast is above the surface, so the second moment of area is much smaller and it heels over.
See https://en.m.wikipedia.org/wiki/Metacentric_height)
Less density liquid cause the object to become more stable, so the ans for post #14 is the object would be less stable when it's submerged in higher density liquid?
 
  • #30
chetzread said:
Less density liquid cause the object to become more stable, so the ans for post #14 is the object would be less stable when it's submerged in higher density liquid?
Yes, that would generally be true.
 
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  • #31
haruspex said:
Yes, that would generally be true.
So, the reason that the object is less stable in more dense water is because when the object float higher in liquid, it has more tendency to turn over?
 
  • #32
chetzread said:
So, the reason that the object is less stable in more dense water is because when the object float higher in liquid, it has more tendency to turn over?
Yes. But as I posted, that is only the general trend. There may be exceptions according to shape.
 
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  • #33
haruspex said:
Yes. But as I posted, that is only the general trend. There may be exceptions according to shape.
Exception according to shape? Can you explain further?
 
  • #34
The trick is to realize what gives rise to the stability.
To do that, draw the same shape in two different liquids, as per my example to start with, then do another sketch with them a bit tilted over.
Look to see where the forces act (hint: pressure is perpendicular to the surface, and the pressure at the sides is also important.)

Do you understand where the buoyancy force comes from in the first place?

(I know I said "tomorrow but I have insomnia - and I saw post #25 before post #24 for some reason.)
 
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  • #35
Simon Bridge said:
The trick is to realize what gives rise to the stability.
To do that, draw the same shape in two different liquids, as per my example to start with, then do another sketch with them a bit tilted over.

Look to see where the forces act (hint: pressure is perpendicular to the surface, and the pressure at the sides is also important.)

Do you understand where the buoyancy force comes from in the first place?

(I know I said "tomorrow but I have insomnia - and I saw post #25 before post #24 for some reason.)
Here it is, so what are you trying to say?
 

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