buoyancy ice

[SaintJude]

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I don't understand the concept behind this supposedly critical buoyancy question.

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
B. is lower
C. remains the same.
D. cannot be determined...

Answer is C.

 

[milski]

The ice is floating. That means that the water displaced by it weights exactly as much as the ice. When the ice melts, it will have exactly the same density as the water. Same weight as water displaced and same density -> the water from the melted ice will have the same volume as the displaced water. -> The answer is C.

 

[SaintJude]

I'm sorry, I still don't get. I didn't follow your last sentence milski.

 

[MedPR]

I'm sorry, I still don't get. I didn't follow your last sentence milski.

Start with a glass of water and an ice cube. When you put the ice cube into the water, the water level will rise initially. Before the ice cube melts, it displaces X amount of water. As the cube melts, it begins to displace less water (since it starts to weigh less and less). But wait, if the ice cube is displacing less water, doesn't that mean the water level will drop? No, because the ice that used to be there has just turned into water. The newly formed water is just filling in where the ice used to be, but isn't anymore because it has melted away.

Take two 100mL aliquots of water and freeze 1 aliquot it into an ice cube. Add 100mL of H2O(l) into beaker 1, and add the ice cube into a beaker 2. The water level will rise (initially) the same level. What happens to the ice cube as it melts? It becomes exactly the same as the 100mL aliquot in the other beaker. If the water level in beaker 2 were to rise as the ice cube melted, that would mean that the water level in beaker 1 would spontaneously rise as well since you added the exact same volume of H2O into both beakers.


Also, I must have this memorized because I just read something in TBR that confused me.

It says:

For objects that float: relative densities = %submerged. Vobject > Vdisplaced; densityobject < densitymedium

In SaintJude's problem, the volume of the ice must be equal to the volume of water displaced, or else the water level would rise when it melted. However, TBR says that the volumes are not equal.. So what's the deal?

 

[milski]

Let's start with the ice floating. It has some weight, W. To float, it needs to displace water which weight exactly that much - W. Now, let's imagine that you took the ice out of the water, melted it and raised its temperature to the same temperature as the water. Let's also imagine that it left a big hole with its shape in the water. We know that the 'hole' in the water has the exact volume to fit weight W of water. But the water from the melted ice also weights W and has the same density as the water in the reservoir. It will have to have the exact same volume as the hole. So if we pour it there, it will fit exactly and there will be no change in the level of the water. Better? Or should I try again?

 

[SaintJude]

Yes, thanks! I exactly needed that type of 5th grade level talk 😀

I think I've come to intuitively understand from this problem that : A floating object displaces its weight in fluid.

So this scenario only works because the density of melted ice = density of water?
Also, why is ice cap melting (in relation to global warming) then always associated with rising sea levels? (it's part of the reason I got this question wrong...)

 

[milski]

It's not just the ice cap. Melting the ice floating in the ocean reduces the reflective surface of Earth, raises the temperatures and also melts ice which is not floating (in the mountains, far North/South).

 

[MrNeuro]

correct me if im wrong here but

if the ice cube is floating meaning in most cases that i've seen some percent of it is above the water meaning that V of the ice cube > V displaced then the water level should rise correct?

 

[chiddler]

What if a salt water ice cube was used? Or a frozen alcohol cube?

More dense means fluid levels rise. Less dense means falls. Right?

 

[milski]

What if a salt water ice cube was used? Or a frozen alcohol cube?

More dense means fluid levels rise. Less dense means falls. Right?

The opposite. More dense means that more volume had to be displaced and now you have a bigger hole to fill.

 

[SaintJude]

You know what, chiddler, you've raised a good question.

I just tried the ice cube experiment at home with a measuring cup. (Yeah, that was dorky...) But the water rose!

1.) This means that impurities must have influenced the composition of my ice cube
2.) The "water-impurities" ice cube material was actually less dense than that of water (once dissolved) ?!

 

[chiddler]

You know what, chiddler, you've raised a good question.

I just tried the ice cube experiment at home with a measuring cup. (Yeah, that was dorky...) But the water rose!

1.) This means that impurities must have influenced the composition of my ice cube
2.) The "water-impurities" ice cube material was actually less dense than that of water (once dissolved) ?!

HAHA nice! But if you used water from the same source as your ice, levels should not change, right? What happened!

So with the salty ice cube: the cube will displace more than regular water and when it melts will occupy about the same volume as regular water. So the net effect is that fluid levels drop. Is this accurate?

 

[milski]

HAHA nice! But if you used water from the same source as your ice, levels should not change, right? What happened!

So with the salty ice cube: the cube will displace more than regular water and when it melts will occupy about the same volume as regular water. So the net effect is that fluid levels drop. Is this accurate?

Yes, that sounds right, assuming the salty cube is denser than clean water. (it probably is denser, I just don't want to think about that now)

We did the experiment in class. The physics prof melted a relatively big chunk of ice floating in a big glass baking pot filled with water to the rim - it would have spilled even with the slightest additional volume but there were no spills during the 50 min class.

 

[chiddler]

Yes, that sounds right, assuming the salty cube is denser than clean water. (it probably is denser, I just don't want to think about that now)

We did the experiment in class. The physics prof melted a relatively big chunk of ice floating in a big glass baking pot filled with water to the rim - it would have spilled even with the slightest additional volume but there were no spills during the 50 min class.

excellent thanks very much.