BR physics chapter 7 passage 6 number 36

[2010premed]

Consider a single ice cube that floats in a glass filled to the brim with water in such a way that the ice cube is exposed above the brim. As the ice cube melts, the water:

level remained the same

Is this true for just water and ice or flor all other liquid as well?

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[TieuBachHo]

Considering diff. densities of various materials, you can figure out what effects it does in diff. physical states. Usually other materials expand as they melt, but the opp. is true for ice. So it's how ice floats while other solid matericals sink in their liquid state. This phenomenon can only be observed in ice that I can naturally think of.

 

[2010premed]

Thanks =)

 

[geeyouknit]

Sorry to bring up the dead, but I needed a point clarified. I'm going to write out my thought process and then highlight where my math seems to conflict with my understanding. Please help me resolve my issues, ya?

Density of liquid = 'pl' ; Density of object = 'po'
Volume of liquid displaced = 'Vl'; Vol of object = 'Vo'
g = gravity
If an Obj floats, the buoyant force (Fb) is equal to Weight;
-> Fb = W
so
-> (pl)*(Vl)*(g) = mass of obj * g
-> (pl)*(Vl)*(g) = (po)*(Vo)*g
Simplify
-> (pl)*(Vl)=(po)*(Vo)
Basically, we're saying here that:
-> mass of displaced liquid = mass of the object

So far so good? Here we go.
In this question, we have ice cube floating in water.
If ice cube melts, the mass of the melted water = mass of the original ice cube
and because mass of the melted water isn't changing:
-> mass of displaced liquid = mass of melted water
-> (pl)*(Vl) = mass of melted water, which is mass of original ice cube

However, since density of ice < density of water. And mass here is constant, regardless of if it's ice or water.
If ice turns to water, doesn't the density of the substance increase, and the volume decrease?
Based on the bolded logic, wouldn't the level of the water decrease?

Please help me.

 

[inasensegone]

Whoa there... You have made this problem way more difficult than it needs to be. To be honest, I didn't read through all of your symbols because it's like decrypting a secret code, so instead I'll just explain it more simply (as I did in this thread):

First off, yes, the mass of the displaced liquid = mass of the object.
And yes, the density of ice < density of water.
And again yes, ice turns to water, so the density increases (that is, the H2O that was in the form of ice has increased density because now it is liquid water)
And yes, the density increases, so the volume (of the ice cube) decreases (because now it is liquid)...

But here is where your logic falters:
When the ice cube is floating, the amount of water that it displaces is only equivalent to the volume of the ice cube that is submerged. Let's say half of the ice cube is submerged (way less than it should be, but just for simplicity). The other half is floating above the water. This means that the ice cube displaces a volume of liquid equal to half of it's own volume. But this volume of water (that is displaced) has the same mass as the entire ice cube. So when the ice melts, it now has increased density (exactly the same density of the water that it was displacing). Since the mass of the liquid displaced, equaled the mass of the entire ice cube, there is no change in the water level.

Here is a basic equation that gives the relationship of the volume and densities of an object that floats in a given fluid (because it is a fluid, it can be liquid or gas). Don't just memorize the equation. Understand the relationship, and try to derive it for yourself to get a better understanding of buoyancy:

 

[geeyouknit]

Whoa there... You have made this problem way more difficult than it needs to be. To be honest, I didn't read through all of your symbols because it's like decrypting a secret code, so instead I'll just explain it more simply (as I did in this thread):

First off, yes, the mass of the displaced liquid = mass of the object.
And yes, the density of ice < density of water.
And again yes, ice turns to water, so the density increases (that is, the H2O that was in the form of ice has increased density because now it is liquid water)
And yes, the density increases, so the volume (of the ice cube) decreases (because now it is liquid)...

But here is where your logic falters:
When the ice cube is floating, the amount of water that it displaces is only equivalent to the volume of the ice cube that is submerged. Let's say half of the ice cube is submerged (way less than it should be, but just for simplicity). The other half is floating above the water. This means that the ice cube displaces a volume of liquid equal to half of it's own volume. But this volume of water (that is displaced) has the same mass as the entire ice cube. So when the ice melts, it now has increased density (exactly the same density of the water that it was displacing). Since the mass of the liquid displaced, equaled the mass of the entire ice cube, there is no change in the water level.

Here is a basic equation that gives the relationship of the volume and densities of an object that floats in a given fluid (because it is a fluid, it can be liquid or gas). Don't just memorize the equation. Understand the relationship, and try to derive it for yourself to get a better understanding of buoyancy:

View attachment 178665

Hey! Thanks for the quick reply. And yes, I realize the equations aren't that easy on the eyes, but I did put a Key there for the cryptographers out there.
And the equation you posted is also derived up there too.

I figured out my misunderstanding. Your comments made sense (especially "But this volume of water (that is displaced) has the same mass as the entire ice cube. ") but I had to play around with the math first.