Is a half submerged object submerged in its own displaced water?

[lost captain]

I feel like this is the dumbest question I've ever asked in my life, and honestly I'm sorry for taking anyone's time that's willing to answer.

So I have a rectagular prism container that has 4ml of water and i submerged a metallic plate that has volume 1ml, just like the picture below.
The plate fits snuggly in there and I'm holding the plate with a string so basically it is neutrally buoyant.

1) If the plate is fully submerged, no mater the depth, the displaced water will be 1ml. So we will see the water level rise from 4ml to 5ml. Right?

2) When I half submerge the plate, half of it's volume will be under water so 0.5 ml gets submerged and also 0,5 ml of water will get displaced on top...so the plate ends up fully submerged ? How can the plate be fully submerged with only 0,5ml of water displaced, it can't...,but then again that displaced water will go on top so...? What am i missing here?

I understand that if the submerged volume is 0.5ml then the water level should rise at 4,5ml, but then it will be like the submerged volume is submerged in the displaced water...

Thank you, and I'm sorry

 

[Baluncore]

Maybe you should be measuring the submergence relative to the bottom of the object, and the surface of the water, not the top of the object and the bottom of the container.

Your last diagram is wrong because you have a tight-fitting piston in a cylinder, the water level should be 5.0.

 

[lost captain]

Maybe you should be measuring the submergence relative to the bottom of the object, and the surface of the water, not the top of the object and the bottom of the container.

When the object is half submerged, i am measuring that from the bottom of the object. And if I'm measuring from the surface of the water, then that surface is at 4.5 ml?

 

[Baluncore]

As you lower the object, the bottom meets the water at 4.0 . An instant later, it has displaced one drop of water, that has half filled the narrow space around the piston. The bottom of the object is only just below 4.0, and the water has risen to 4.5 which makes it 50% submerged.

 

[lost captain]

Your last diagram is wrong because you have a tight-fitting piston in a cylinder, the water level should be 5.0.

I submerge half of the piston and 0.5ml of water gets displaced on top, so where am I making a mistake?

 

[lost captain]

The bottom of the object is only just below 4.0, and the water has risen to 4.5 which makes it 50% submerged.

Okay so the volume of the water that got displaced goes up to the 4.5ml mark even though only a small portion of the volume of the object got submerged

 

[Ibix]

I think the problem here is that water cannot be beside a "tight fitting" piston - it just teleports from below the piston to above it. In other words, it's an idealised model and the idealisation means that you cannot partially submerge it.

If you have a 9.999999 millimetre square piston then you can partially submerge it because the tiny volume between the wall and the piston can partially fill with water.

(Edit: I see a conversation along these lines has happened while I was typing.)

 

[lost captain]

I think the problem here is that water cannot be beside a "tight fitting" piston - it just teleports from below the piston to above it. In other words, it's an idealised model and the idealisation means that you cannot partially submerge it.

If you have a 9.999999 millimetre square piston then you can partially submerge it because the tiny volume between the wall and the piston can partially fill with water.

(Edit: I see a conversation along these lines has happened while I was typing.)

The plate has volume of 1ml, it's length is smaller than the container wall length so it can fit inside. In the picture i drew the length in this way, that why the height of the plate exceeds the 1ml mark a little

 

[lost captain]

If i understand correctly from the answers above, i can't figure out how much water was displaced from the volume markings unless the object is fully submerged below the original water level surface, in my case below 4ml

 

[Baluncore]

When the bottom of the object is at 4.0 , the object is 0% submerged and the top of the object is at 5.0 . As you lower the object into the water, the surface of the water covers the object with the water remaining at 5.0
The object goes from 0% submerged, through 50%, to 100% submerged very rapidly as it begins to be covered by the displaced water.

Part of the confusion comes from calibrating the vertical axis in millilitres, not in centimetres.

 

[A.T.]

I submerge half of the piston and 0.5ml of water gets displaced on top, so where am I making a mistake?

Most likely you are confusing yourself with your own misleading terminology. When you say: "I submerge half of the piston", you apparently actually mean: "I bring half of the piston below the initial water level". This are very different things, unless the area of the water surface is much greater than the cross section of the piston.

If i understand correctly from the answers above, i can't figure out how much water was displaced from the volume markings unless the object is fully submerged below the original water level surface, in my case below 4ml

If you know the cross sectional areas of container and piston, then you can figure that out, regardless of how much of the piston is submerged.

But for arbitrarily shaped and oriented objects, that you don't have the exact geometry of, you have to submerge them fully, in order to get the displaced volume only from the water levels and container geometry.