# Buoyant force--quick fact check

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#### SaintJude

##### Full Member

I'm pretty sure this is true...can someone verify please?

When submerged, all objects with the SAME volume (regardless of mass) will experience the same buoyant force.

For floating objects, objects with objects of DIFFERENT volume experience can experience same buoyant force (if they have the same mass)

5+ Year Member
Correct.

#### MrNeuro

##### Full Member
10+ Year Member
I'm pretty sure this is true...can someone verify please?

When submerged, all objects with the SAME volume (regardless of mass) will experience the same buoyant force.

For floating objects, objects with objects of DIFFERENT volume experience can experience same buoyant force (if they have the same mass)

just want to double check the second part

Fb = pfluid Vdisplaced g

so if the objects have different volumes the only way they can experience the same buyoant force is if they displace the same amount of fluid....right? where does the whole mass thing come into play?

are you referring to the same weight displaced?

#### SaintJude

##### Full Member
Yup. A floating object displaces an amount of fluid equal to its own weight. So objects with the same mass, will have the same weight. Buoyant force will thus be same.

#### MedPR

##### Membership Revoked
Removed
Does "submerged" mean 100% below water, but not necessarily sitting on the bottom of the contanier? Or does it mean sitting on the bottom of the container? Or both?

#### SaintJude

##### Full Member
Submerged means the object is 100% beneath the fluid's surface-it's fully immersed.

#### milski

##### 1K member
5+ Year Member
Does "submerged" mean 100% below water, but not necessarily sitting on the bottom of the contanier? Or does it mean sitting on the bottom of the container? Or both?

It does not matter. The only case where you would care about that is when the bottom of the object has a perfect fit/seal with the bottom of the ocean not allowing any water underneath. That does not happen in real life.

#### MedPR

##### Membership Revoked
Removed
It does not matter. The only case where you would care about that is when the bottom of the object has a perfect fit/seal with the bottom of the ocean not allowing any water underneath. That does not happen in real life.

Thank you. This clears up a lot of issues I've been having with buoyant force.

No matter what, once an object is 100% submerged, whether it be just under the surface, or all the way at the bottom, the amount of water it displaces is equal to its volume. Further, the amount of water it displaces is independent of the object's mass, density, shape, or anything else. In other words, a piece of lead and an bean of the same volume will displace the same amount of fluid so long as they are 100% submerged, even if one is sunken further in the fluid than the other.

Sorry to threadjack, but can someone explain how the calculation works when an object is floating and only partially submerged? Say an object is 50% submerged, does it displace a volume of fluid equal to half of its volume? That seems right to me, but I thought it had something to do with weight and/or density?

#### SaintJude

##### Full Member
A floating object displaces an amount of fluid equal to its own weight. I know this sentence sounds weird, but it just has to be internalized. So if an object is 50% submerged (it's density would be 1/2 of the density of the fluid), then it will displace a volume of fluid equal to its own weight.

#### milski

##### 1K member
5+ Year Member
Thank you. This clears up a lot of issues I've been having with buoyant force.

No matter what, once an object is 100% submerged, whether it be just under the surface, or all the way at the bottom, the amount of water it displaces is equal to its volume. Further, the amount of water it displaces is independent of the object's mass, density, shape, or anything else. In other words, a piece of lead and an bean of the same volume will displace the same amount of fluid so long as they are 100% submerged, even if one is sunken further in the fluid than the other.

Sorry to threadjack, but can someone explain how the calculation works when an object is floating and only partially submerged? Say an object is 50% submerged, does it displace a volume of fluid equal to half of its volume? That seems right to me, but I thought it had something to do with weight and/or density?

Cool, you have it right about the fully submerged objects.

You are also right that a 50% submerged body displaces a volume equal to 50% of its volume. If that body is floating, you can deduce a few things about its weight and density. First, floating means that the buoyant force and the weight are same in magnitude. Then you know the volume of the displaced fluid and its density, so you can calculate the buoyant force. From there, you know how much the body weights. From there you can get its mass. And since you know its volume, you can calculate its density.

Here is an example: A 2 m^3 cube is floating on a water surface and is 50% submerged. What is the density of the cube, if density of the water is 1000 kg/m^3?

Volume of cube: 2 m^3
Volume submerged: 50% * 2 m^3 = 1 m^3
Volume of displaced water: 1 m^3
Mass of displaced water: 1 m^3 * 1000 kg/m^3 = 1000 kg
Weight of displaced water: 1000 kg * g = 10000 N
Buoyant force: 10000 N
Weight of cube: 10000 N
Mass of cube: 10000 N /g = 1000 kg
Density of cube: 1000 kg / 2 m^3 = 500 kg/m^3

Is that helping or more confusing? If we're clear so far, I'll mention a few gotchas with which you need to be careful.

#### milski

##### 1K member
5+ Year Member
A floating object displaces an amount of fluid equal to its own weight. I know this sentence sounds weird, but it just has to be internalized. So if an object is 50% submerged (it's density would be 1/2 of the density of the fluid), then it will displace a volume of fluid with weight equal to its own weight.

It might seem minor but you want to be precise here. You cannot equate volume to weight.