# Buoyant Force

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#### cowboys

##### Full Member

Balls A and B of equal mass are floating in a swimming pool, as in the figure shown. (Ball A is drawn larger than Ball B). Which will produce a greater buoyant force?

A. Ball A
B. Ball B
C. The forces will be equal.
D. It is impossible to know without knowing the volume of each ball.

SOMEONE PLEASE EXPLAIN THIS TO ME

#### cheesier

##### Full Member
Balls A and B of equal mass are floating in a swimming pool, as in the figure shown. (Ball A is drawn larger than Ball B). Which will produce a greater buoyant force?

A. Ball A
B. Ball B
C. The forces will be equal.
D. It is impossible to know without knowing the volume of each ball.

SOMEONE PLEASE EXPLAIN THIS TO ME

If they have different volumes then they are displacing different volumes of water, so rho g V should be different for each.

Is the pic drawn so that the balls are totally floating and not partially submerged? If so then their buoyant force is equal to their normal force, which would be the same since they have equal mass.

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#### cowboys

##### Full Member
If they have different volumes then they are displacing different volumes of water, so rho g V should be different for each.

Is the pic drawn so that the balls are totally floating and not partially submerged? If so then their buoyant force is equal to their normal force, which would be the same since they have equal mass.

I think I understand you. They are both floating. Since they are both floating that means mg=pVg and since they have the same mass...they have the same buoyant force

Now if they were completely submerged then that would be a different story right? Then the ball with the bigger volume would displace more fluid and have a bigger buoyant force. Right?

#### cheesier

##### Full Member
I think I understand you. They are both floating. Since they are both floating that means mg=pVg and since they have the same mass...they have the same buoyant force

Now if they were completely submerged then that would be a different story right? Then the ball with the bigger volume would displace more fluid and have a bigger buoyant force. Right?

Right, except since they're totally floating the equation rho g V doesn't really make sense since V = 0 (it's kind of a sucky question for that reason IMO). Think of it as if they were just sitting on a horizontal surface. Their normal forces would be equal there too.

If they were submerged then the one with a greater volume would displace more water, so it would have a greater buoyant force.

#### cowboys

##### Full Member
Right, except since they're totally floating the equation rho g V doesn't really make sense since V = 0. Think of it as if they were just sitting on a horizontal surface. Their normal forces would be equal there too.

If they were submerged then the one with a greater volume would displace more water, so it would have a greater buoyant force.

How can V be 0 though? It thought it has to displace some water to float.

#### cheesier

##### Full Member
How can V be 0 though? It thought it has to displace some water to float.

It does (edit: not), but they're asking you to ignore that and go off of the picture. Idealized physical models that don't really make sense are a part of the test.

And V is equal to the point in contact with the ball if it is perfectly floating, which is equal in both cases and is infintesimally small

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#### cowboys

##### Full Member
It does, but they're asking you to ignore that and go off of the picture. Idealized physical models that don't really make sense are a part of the test.

I get what you're saying though. Thanks for the help!

#### indianjatt

##### Full Member
10+ Year Member
Right, except since they're totally floating the equation rho g V doesn't really make sense since V = 0 (it's kind of a sucky question for that reason IMO). Think of it as if they were just sitting on a horizontal surface. Their normal forces would be equal there too.

If they were submerged then the one with a greater volume would displace more water, so it would have a greater buoyant force.

Haha. You confused me! How can they be completely floating as in they're only infinitesimely(however you spell it lol) touching the surface? Doesn't the Volume have to equal :
V= m/density in order to have a net force of zero and to be floating?

#### cheesier

##### Full Member
Haha. You confused me! How can they be completely floating as in they're only infinitesimely(however you spell it lol) touching the surface? Doesn't the Volume have to equal :
V= m/density in order to have a net force of zero and to be floating?

edit: Nevermind, was wrong. sorry

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#### Saint Fu

##### Full Member
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5+ Year Member
I think people are way overthinking this. For an object to be considered "floating", it doesn't have to be only touching the water at a single infinitesimal point. More likely, it's just partially, but not entirely, submerged. The portion that is submerged is displacing the (non-zero!) volume of water that is generating the buoyancy force.

At any rate, I'm pretty sure being able to see the figure being referenced would clear things up.

#### cheesier

##### Full Member
I think people are way overthinking this. For an object to be considered "floating", it doesn't have to be only touching the water at a single infinitesimal point. More likely, it's just partially, but not entirely, submerged. The portion that is submerged is displacing the (non-zero!) volume of water that is generating the buoyancy force.

At any rate, I'm pretty sure being able to see the figure being referenced would clear things up.

Yeah you're right. I was confused

#### nashaiy

##### Full Member
I've had some trouble with a similar topic and just wanted to put in what I've learned on it in case it helps anyone else:

For a floating object:

1. The buoyancy force is equal to the weight of the OBJECT which is equal to the weight of the fluid displaced by the fraction of the object submerged. This gets confusing because people automatically assume the volume of the fluid displaced is equal to the volume of the object but this is not true for a floating object since the entire object is not submerged.

2. The fraction SUBMERGED equals to the ratio of the density of the object to the density of the fluid (in the case of water, this equals the specific gravity of the object). Thus, in water, if you have a ball with a specific gravity of 0.9, 90% of the object will be submerged.

For a submerged object:

1. The buoyancy force equals to the weight of the displaced fluid. In this case, the volume of the displaced fluid does equal the volume of the object since the object is completely submerged.

2. The buoyancy force also equals the apparent loss of mass of the object.

So in the case of 2 balls of equal weight that are floating, the buoyancy force is the same for both of them because the buoyancy force is equal to the weight of the floating object regardless of its size.

Anyone please feel free to correct me if I'm wrong.

#### GomerPyle

##### Full Member
10+ Year Member
7+ Year Member
I've had some trouble with a similar topic and just wanted to put in what I've learned on it in case it helps anyone else:

For a floating object:

1. The buoyancy force is equal to the weight of the OBJECT which is equal to the weight of the fluid displaced by the fraction of the object submerged. This gets confusing because people automatically assume the volume of the fluid displaced is equal to the volume of the object but this is not true for a floating object since the entire object is not submerged.

2. The fraction SUBMERGED equals to the ratio of the density of the object to the density of the fluid (in the case of water, this equals the specific gravity of the object). Thus, in water, if you have a ball with a specific gravity of 0.9, 90% of the object will be submerged.

For a submerged object:

1. The buoyancy force equals to the weight of the displaced fluid. In this case, the volume of the displaced fluid does equal the volume of the object since the object is completely submerged.

2. The buoyancy force also equals the apparent loss of mass of the object.

So in the case of 2 balls of equal weight that are floating, the buoyancy force is the same for both of them because the buoyancy force is equal to the weight of the floating object regardless of its size.

Anyone please feel free to correct me if I'm wrong.

Um, so wait. The buoyancy force of a floating object is equal to the weight of the floating object regardless of size? But what if one is more dense than the other? Than according to the specific gravity equation, the object that is more dense will be submerged more in water, thus displace a greater amount of fluid...doesn't this mean the buoyancy force on this object should be greater?

#### Saint Fu

##### Full Member
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5+ Year Member
Um, so wait. The buoyancy force of a floating object is equal to the weight of the floating object regardless of size? But what if one is more dense than the other? Than according to the specific gravity equation, the object that is more dense will be submerged more in water, thus displace a greater amount of fluid...doesn't this mean the buoyancy force on this object should be greater?

That's correct, and this is completely in line with what he said. A denser object (of the same size) will also have a greater weight. Thus, if it's floating, it will experience a greater buoyancy force to match its weight.

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#### nashaiy

##### Full Member
That's correct, and this is completely in line with what he said. A denser object (of the same size) will also have a greater weight. Thus, if it's floating, it will experience a greater buoyancy force to match its weight.

Exactly. If you have 2 objects of equal size and one is more dense than the other, then the denser object will also weigh more because the volume is the same for both of them. Thus, the buoyancy force will be greater on the denser object because a greater volume of fluid is displaced. On the other hand, if you had 2 objects with the same weight but different volumes, the buoyancy force on both of these would be the same because they would end up displacing the same volume of fluid.

P.S. I'm a she not a he.

#### Saint Fu

##### Full Member
10+ Year Member
5+ Year Member
Exactly. If you have 2 objects of equal size and one is more dense than the other, then the denser object will also weigh more because the volume is the same for both of them. Thus, the buoyancy force will be greater on the denser object because a greater volume of fluid is displaced. On the other hand, if you had 2 objects with the same weight but different volumes, the buoyancy force on both of these would be the same because they would end up displacing the same volume of fluid.

P.S. I'm a she not a he.

#### GomerPyle

##### Full Member
10+ Year Member
7+ Year Member
That's correct, and this is completely in line with what he said. A denser object (of the same size) will also have a greater weight. Thus, if it's floating, it will experience a greater buoyancy force to match its weight.

#### Jwinsler7

##### Full Member
Quick question regarding buoyancy,

Buoyant force for an object that is floating would be density of liquid x g x Vof liquid displaced. V of displaced liquid would be the same as volume of the object that is submerged in liquid, right? For example, if 1/4 of the object is submerged in liquid, we can say buoyant force is equal to density of liquid x g x 1/4 of the object's volume. Please let me know if that is not correct. Thank you!

#### nashaiy

##### Full Member
Quick question regarding buoyancy,

Buoyant force for an object that is floating would be density of liquid x g x Vof liquid displaced. V of displaced liquid would be the same as volume of the object that is submerged in liquid, right? For example, if 1/4 of the object is submerged in liquid, we can say buoyant force is equal to density of liquid x g x 1/4 of the object's volume. Please let me know if that is not correct. Thank you!

Yes. It's much easier to just calculate the weight of the object and equate that to the buoyancy force though.