# Buoyant Force

## 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....

## 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]

Simon Bridge
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## 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....

## 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?

haruspex
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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.
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.

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?

haruspex
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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.

• 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?

haruspex
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Not (rho) (V) (g) = same for both case?
Define what you are using V to mean.

• Define what you are using V to mean.
Volume of liquid displaced = volume of the part where the object submerged....

haruspex
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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.

• 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?

haruspex
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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?

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?

haruspex
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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.
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?

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 ?

Simon Bridge
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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:

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?

Do you want to know or not?

• If we were to say "yes" or "no" to that question, then we would be "doing your homework for you" - which is not allowed.

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?

Do you want to know or not?

Yes, I wanna know. Let's just focus on post #14.... Is my idea correct?

Simon Bridge
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Yes, I wanna 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.

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?

Simon Bridge
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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?

• ... 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.....

Simon Bridge
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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?

• 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...

Simon Bridge
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Liquid A is denser...

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?

• 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