Floating and Displacement question

[SaintJude]

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My questions are in blue! ! I'm trying to think about the alternate solutions.

Q: A cube of solid ice is floating in a glass of water. After the ice melts, the height of the water in the glass:

A. is higher (Would this be the case if the cube was of a lower density material relative to water?)

B. is lower (if cube substance = higher density than water? )

C. remains the same. (correct answer)


I understand the correct answer. So no need to post "Well, it's C because...🙂 "

 

[pfaction]

Really, I would have guessed B. Ice is less dense than water, and thus displaces more. It then becomes a higher density material, so the volume, I thought, would decrease.

 

[SaintJude]

Don't want to recreate conversation: If you want a thorough explanation: Check below

http://206.82.221.135/showthread.php?p=12131635

 

[milski]

Not enough information.

You need the density of the material before and after it melts and how both of these compares to density of water. (Not the precise density but at least the relation between the two and density of water).

 

[pfaction]

Wait so I just want to clear something up.

More dense = less volume so it falls
Less dense = more volume so levels rise?

 

[SaintJude]

Not enough information.

You need the density of the material before and after it melts and how both of these compares to density of water. (Not the precise density but at least the relation between the two and density of water).

Milksi, the choices I included were meant to indicate density of cube substance relative to density of water.

 

[MrNeuro]

that question in TBR also says that the cube is FLUSH w/ the level

thats why it remains the same b/c the volume of fluid contained by a cube of ice is the same as the volume it composes when its a liquid and all of this volume is submerged under the level...that help?

 

[milski]

Milksi, the choices I included were meant to indicate density of cube substance relative to density of water.

You also need to say what happens to the density of the substance when it melts.

For substances heavier than water in both phases, the result will depend only on how their density changes when melting.

For substances ligher than water when solid, the result will depend on how density of their liquid state relates to density of water.

 

[deleted103644]

Density doesn't really matter here.

The height of the water has more to do with the volume of water displaced than the volume of the ice cube. The mass of water displaced will be equal to the mass of the ice cube, which will not change as it melts.

If you were dealing with something denser than water, then it would be a different issue.

 

[reburbia]

You also need to say what happens to the density of the substance when it melts.

For substances heavier than water in both phases, the result will depend only on how their density changes when melting.

For substances ligher than water when solid, the result will depend on how density of their liquid state relates to density of water.

Sorry I read these posts and the other thread and I'm still confused about situations where the cube is not water.

If the element that made the cube was more dense (in both solid and liquid form) why would the levels rise or fall?

 

[milski]

Sorry I read these posts and the other thread and I'm still confused about situations where the cube is not water.

If the element that made the cube was more dense (in both solid and liquid form) why would the levels rise or fall?

If the substance is more dense in both cases, it will be at the bottom of the container.
When it melts, its density will change and since its mass won't, its volume will change. If the density decreases, the volume will increase and the level of water will rise.

If the substance is lighter than water, it will be floating on top. The total volume will be Vwater + Vdisp where Vdisp is the volume of water with the same weight as the substance.

When the substance melts, there will be no more Vdisp and it will be liquid either at the top or the bottom of the container. So the interesting question becomes if it will have volume larger or smaller than Vdisp. If it has density lower than water, it's volume will be >Vdisp and the level will rise. Opposite for higher density. For density exactly as water (like the case of ice), the level will stay the same.

 

[deleted103644]

Sorry I read these posts and the other thread and I'm still confused about situations where the cube is not water.

If the element that made the cube was more dense (in both solid and liquid form) why would the levels rise or fall?

Then it's just a matter of the change in volume of the substance itself and the shape if the container.

 

[reburbia]

Dope. Thanks guys...

 

[Class1P]

good thing to remember for life in general is that Ice displaces the same amount of water as it will be when it melts. This is why the melting of ice shelfs won't cause a big increase in ocean hights, but a melting of land-based ice will.