Bouyancy: mass and displacement

[KeiaYamada]

This is something I've always wondered and I have never taught about this at school so I leave a thread on this forum.

I know that displacement = the mass of the object, but I don't quite get this concept.
For example, if you have a kilogram of gold and a kilogram of iron and put them in different bowls that are filled with water until they sink to the bottom of the bowls, the chunk of gold will displace a different amount of water but that doesn't mean its mass is different from the iron, or does it?

I am sorry this question is very basic and ridiculous, but an hour of googling didn't yield me a satisfactory answer.

 

[mjc123]

A floating body displaces its own mass of water. A submerged body displaces its own volume of water. If the volume of the body is greater than that of the same mass of water (i.e. it is less dense than water), it will float. If it is denser, it will sink.

 

[A.T.]

displacement = the mass of the object,

No.

For example, if you have a kilogram of gold and a kilogram of iron and put them in different bowls that are filled with water until they sink to the bottom of the bowls, the chunk of gold will displace a different amount of water but that doesn't mean its mass is different from the iron, or does it?

You have just explained why the above is wrong.

 

[KeiaYamada]

! Thank you so much! I was doing my project related to ships, and wondered why displacement = mass. I went through the internet for hours and nothing explained me why. Thank you!

 

[A.T.]

! Thank you so much! I was doing my project related to ships, and wondered why displacement = mass. I went through the internet for hours and nothing explained me why. Thank you!

"Displacement" in the context of ships means the mass of the ship. It assumes that the object floats, so the mass of the displaced water equals the mass of the object. But this doesn't apply in general.

 

[KeiaYamada]

Thank you again for answering my question!

Do you mind if I ask another question? Why do ships sink when they are outpopulated?
Because density of human body is smaller than the density of water or seawater, and because buoyant force = displacement in volume (basically kg to m3) * density of liquid * free-fall acceleration, the buoyant force would also increase as the weight of the ship increases. I am sorry that I keep asking ridiculous questions, but I really have trouble understanding what I haven't been taught in class.

 

[A.T.]

Thank you again for answering my question!

Do you mind if I ask another question? Why do ships sink when they are outpopulated?
Because density of human body is smaller than the density of water or seawater,

The humans on the ship are immersed in air not water, until the ship sinks...

 

[russ_watters]

Also, most ships and boats are not closed objects, so the volume they can displace is not fixed. Think about a simple canoe, which has a potential displacement volume dictated by the height of the side-walls and an actual displacement volume dependent on how low they sit in the water. Normally, that volume is filled with air, people and cargo. But if you put just a little too much cargo in or punch a hole in the bottom, that volume then fills up with water instead.

Many ships/boats though have temporary or permanent water-tight compartments, which make them technically unsinkable unless broken-up. Many canoes have compartments fore and aft that are filled with closed-cell styrofoam, which essentially makes them just permanently sealed containers of air. So if you fill such a canoe with water, it won't sink all the way. I once took a canoeing course where one of the activities was to paddle a fully-submerged canoe.

 

[KeiaYamada]

Also, most ships and boats are not closed objects, so the volume they can displace is not fixed. Think about a simple canoe, which has a potential displacement volume dictated by the height of the side-walls and an actual displacement volume dependent on how low they sit in the water. Normally, that volume is filled with air, people and cargo. But if you put just a little too much cargo in or punch a hole in the bottom, that volume then fills up with water instead.

Many ships/boats though have temporary or permanent water-tight compartments, which make them technically unsinkable unless broken-up. Many canoes have compartments fore and aft that are filled with closed-cell styrofoam, which essentially makes them just permanently sealed containers of air. So if you fill such a canoe with water, it won't sink all the way. I once took a canoeing course where one of the activities was to paddle a fully-submerged canoe.

AHHH that fully makes sense now! I've never thought it would be that reason, thank you so much!