What does the buoyant force depend on?

[NewSoul]

Homework Statement

What does buoyant force depend on: the mass of the object, its volume, its density, or the material from which it's made?2. Relevant concepts
Archimedes' principle: Buoyant force = weight of displaced liquid

The Attempt at a Solution

I just don't quite understand this concept. I want to say that the buoyant force depends on all of these things. Density (and then the material of the object) determine whether or not the object will float. But then the volume and the mass of the object would also determine how much water is displaced.

I'm confused. Is the answer not all of them?

 

[voko]

Take a ship made of steel. It floats. Then melt the ship into a slab. It sinks.

What is the important difference here?

 

[NewSoul]

Take a ship made of steel. It floats. Then melt the ship into a slab. It sinks.

What is the important difference here?

Hmm. I've never thought of that. It sounds like surface area is the important factor, but that isn't one of my options.

 

[Chestermiller]

The buoyant force is equal to the weight of the water that is displaced by the portion of the object below the surface. This is equal to the volume of the object that is below the surface times the density of water, times g.

 

[NewSoul]

Okay, I did some googling on the boat problem and it makes more sense now.

The buoyant force is equal to the weight of the water that is displaced by the portion of the object below the surface. This is equal to the volume of the object that is below the surface times the density of water, times g.

Thanks, but would it be incorrect for me to write that the buoyant force is also dependent on the density of the object? Some websites say that this is incorrect, but I don't understand why. It's just the "another way" of saying that the buoyant force is dependent on the density of the liquid, isn't it?

 

[nasu]

Yes. It is incorrect. The buoyant force depends on the density of the liquid but not the density of the objects.

If you have two balls of the same diameter, one made of wood and one made of steel and you deep them completely in water, the buoyant forces will be the same. Equal to the weight of a volume of water equal to the volume of either ball.

However, the density of the object determines if the buoyant force can support the weight of the object or not. In other words, if the object can float or not.

 

[NewSoul]

Thanks guys!

 

[Chestermiller]

Okay, I did some googling on the boat problem and it makes more sense now.



Thanks, but would it be incorrect for me to write that the buoyant force is also dependent on the density of the object? Some websites say that this is incorrect, but I don't understand why. It's just the "another way" of saying that the buoyant force is dependent on the density of the liquid, isn't it?

No. The water surrounding the object doesn't know that the object has replaced the water that was originally there. So it continues to provide just enough force to support only the weight of the displaced water.

 

[voko]

However, the density of the object determines if the buoyant force can support the weight of the object or not. In other words, if the object can float or not.

Care should be taken to include voids in the object when calculating the density. See my earlier ship/slab example.

 

[Vrangr]

Take a ship made of steel. It floats. Then melt the ship into a slab. It sinks.

What is the important difference here?

When you build it in a ship, as gravity pulls the ship down the ship displaces water creating a buoyant force that keeps it afloat while for example when a boat leaks the space before filled with air is no longer displacing the water (when the ship gets flooded) so the buoyant force is weaker than gravity and the ship sinks.

 

[CWatters]

The buoyancy force clearly doesn't depend on the volume of the whole ship. A large part of that volume, in fact the majority of a cruise ship, is out of the water.

 

[SteamKing]

The buoyancy force clearly doesn't depend on the volume of the whole ship. A large part of that volume, in fact the majority of a cruise ship, is out of the water.

As long as the weight of the water displaced = the weight of the ship, you're golden.

Vessels like cruise ships are limited by the volume which can be enclosed by the hull and superstructure; the actual carrying capacity of such vessels is quite small in proportion to their size.

Modern cruise vessels, with their large windage areas, can fall to the mercy of sudden storms while at sea, and they become difficult to maneuver once bad weather arrives.

 

[Tom.G]

Buoyant Force Net Weight = <mass of displaced volume> - <mass of displacing volume>

Consider a Helium balloon. At normal atmospheric pressure, attach it un-inflated to a scale. Start inflating it, the scale will show a progressively decreasing weight. As the balloon inflates it gains a small amount of mass from the added Helium, but it displaces a greater mass of air. When the displaced air mass equals the mass of the balloon+Helium, the scale reads zero; this is analogous to the equilibrium point when a ship floats on water.

EDIT: Oops. As @haruspex pointed out, 'Net Weight' is indeed a much better term here!

 

[haruspex]

Buoyant Force = <mass of displaced volume> - <mass of displacing volume>

No, two confusions there.
The buoyant force equals the weight of the displaced volume, period. You may be thinking of the net weight.
Mass is not a force.

 

[haruspex]

I want to say that the buoyant force depends on all of these things.

I can see your difficulty. Since it depends on displaced volume, no single one of the three statistics suffices. You need to know whether it willl float. But since the three are directly related, knowing any two determines the third. So I would say it depends on any two of the three. In any event, you would also need to know the density of the fluid, whether there is enough of it in the vessel, whether it is being held down by another force...

Maybe you should check you have stated the entire question exactly as given to you. No mention of being fully immersed, for example?

 

[Metalbob]

What i interpret from this;my understanding of buoyant force (please correct me if I'm wrong. )
Take for example the sea
The water below will provide some force to support the weight of the water above it. When some object is put in water ( for this case, let's consider it is denser than water) the water below will continue to provide the same force as it did before. only this time the weight of the object will be greater than the force given by water below it . So it will sink. In other words this force/ buoyant force= weight of the water dispaced

 

[haruspex]

What i interpret from this;my understanding of buoyant force (please correct me if I'm wrong. )
Take for example the sea
The water below will provide some force to support the weight of the water above it. When some object is put in water ( for this case, let's consider it is denser than water) the water below will continue to provide the same force as it did before. only this time the weight of the object will be greater than the force given by water below it . So it will sink. In other words this force/ buoyant force= weight of the water dispaced

That's the right idea, but I would try to avoid distinguishing above and below. If you consider the spatial region occupied by the immersed object, the surrounding water exerts a net force on it. The net force is independent of what occupies the region. If what occupies it is more of the surrounding fluid then obviously that is in equilibrium, so the net force must equal the weight displaced.

 

[Metalbob]

That's h

That's the right idea, but I would try to avoid distinguishing above and below. If you consider the spatial region occupied by the immersed object, the surrounding water exerts a net force on it. The net force is independent of what occupies the region. If what occupies it is more of the surrounding fluid then obviously that is in equilibrium, so the net force must equal the weight displaced.

Thank you sir.
That is very helpful

 

[NewtoPhysicsStudent]

So then if I may, the buoyant force would or would not be constant? gravity is a force which is constant and does not change or depend on anything. Hence then the buoyant force is not constant as it changes and is dependent upon the weight of the water displaced? Thanks for clarifying

 

[jbriggs444]

So then if I may, the buoyant force would or would not be constant? gravity is a force which is constant and does not change or depend on anything. Hence then the buoyant force is not constant as it changes and is dependent upon the weight of the water displaced? Thanks for clarifying

If you hold a toy boat in steady in your hand as you first fill the bathtub with water and then empty it, the buoyant force on the boat will certainly change.

I would be hesitant to say that the force of gravity is a constant. The force of gravity on the water currently in the tub will change as you fill and empty the tub. Though that is likely not what you have in mind when you consider gravity to be constant.

 

[haruspex]

So then if I may, the buoyant force would or would not be constant

Constant with respect to what?
It always equals the force of gravity on the displaced fluid. The strength of that force depends on the local acceleration due to gravity and the mass displaced. The mass displaced depends on the volume of the object and local density of the fluid.
Thus, if the fluid is compressed, but the submerged object compresses less, the displaced mass increases, increasing the buoyant force.
If you set up the same experiment at another location, the local g may be different. Since that affects both the fluid and the object, it will not change the float/sink result, but the forces will change.
Note also that Archimedes' principle makes an assumption rarely mentioned: that the fluid can reach all parts of the object below the fluid's surface. A rubber suction cup works because the fluid cannot reach one surface.

 

[NewtoPhysicsStudent]

Constant with respect to what?
It always equals the force of gravity on the displaced fluid. The strength of that force depends on the local acceleration due to gravity and the mass displaced. The mass displaced depends on the volume of the object and local density of the fluid.
Thus, if the fluid is compressed, but the submerged object compresses less, the displaced mass increases, increasing the buoyant force.
If you set up the same experiment at another location, the local g may be different. Since that affects both the fluid and the object, it will not change the float/sink result, but the forces will change.
Note also that Archimedes' principle makes an assumption rarely mentioned: that the fluid can reach all parts of the object below the fluid's surface. A rubber suction cup works because the fluid cannot reach one surface.

My professor offered an open ended question that took me by surprise and I had the same question you just asked, constant with respect to what?...constant I am thinking in terms of calculating the value of the Fb. But frankly, I am not sure it's value is constant because constant means not changing, not affected by any other variables and the buoyant force is very much dependent upon other factors. Its value will be different but its affects will still be the same, as it's ALWAYS equal to the weight of the fluid displaced. But if gravity according to my professor is a constant in calculating things from acceleration to Potential gravitational energy to buoyant force,etc, that it is not dependent upon any value in that equation, would then in that sense Buoyant force also then be constant if it will always be equal to the weight of fluid displaced? ;) I guess I should ask my professor to clarify what he means by constant :D

 

[haruspex]

My professor offered an open ended question that took me by surprise and I had the same question you just asked, constant with respect to what?...constant I am thinking in terms of calculating the value of the Fb. But frankly, I am not sure it's value is constant because constant means not changing, not affected by any other variables and the buoyant force is very much dependent upon other factors. Its value will be different but its affects will still be the same, as it's ALWAYS equal to the weight of the fluid displaced. But if gravity according to my professor is a constant in calculating things from acceleration to Potential gravitational energy to buoyant force,etc, that it is not dependent upon any value in that equation, would then in that sense Buoyant force also then be constant if it will always be equal to the weight of fluid displaced? ;) I guess I should ask my professor to clarify what he means by constant :D

Ok.
One more thought... if the system is undergoing an acceleration then that will effectively change the 'gravity'.