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[Mindmaker]

I need more music with this kind of female voice.
Any suggestions?

[ToonyMan]

Hey is it okay if I do what Cthulhu does and post a bad gaming webcomic?

[G-Flex]

That comic is more true if you replace "geeks and gamers" in the first panel with "insufferable tools".

[Urist Imiknorris]

The answer is C.

The ice doesn't matter. All that matters is that the stone begins the exercise floating, and ends the first phase sinking. It's no longer displacing its weight, it's displacing its volume.

If the density of the stone is less than that of the water, the stone would float of its own accord, which we know doesn't happen. Therefore, it is displacing more water when floating than it does when sinking, so the water level will fall. As it sinks, there is no change.

[/very similar Car Talk Puzzler]

I did it because I could, not because I had to.

EDIT: How the hell did I misspell water?

[G-Flex]

If the density of the stone is less than that of the water, the stone would float of its own accord, which we know doesn't happen. Therefore, it is displacing more whater when floating than it does when sinking, so the water level will fall. As it sinks, there is no change.

I already showed why this isn't true. Archimedes' Principle! It doesn't matter if the stone increases the density of the ice block, as long as the block's density is less than that of water as a whole. I even posted some sample math.

[Urist Imiknorris]

I am ignoring the ice block, thank you, as it has no effect on the problem itself beyond its use as a tool to keep the rock from sinking.

[G-Flex]

I am ignoring the ice block, thank you, as it has no effect on the problem itself beyond its use as a tool to keep the rock from sinking.

Wait. How is it that you're ignoring the ice block despite the fact that the first part of the question is explicitly asking what happens as the ice block melts? It's also pretty relevant in the second part, as I explained.

For the second part of the problem: An easier way to demonstrate the answer is to imagine that the ice block has such a large stone attached to it that the entire thing has already sunk and is sitting at the bottom of the fluid. If the stone detaches, the ice starts to float instead, some of it popping above the water. Ergo, less water is displaced by the ice, therefore the water level drops. It's the same thing in the problem itself even though the ice is already floating: more of the ice appears over the water, so the water level goes down.

[Il Palazzo]

If the density of the stone is less than that of the water, the stone would float of its own accord, which we know doesn't happen. Therefore, it is displacing more whater when floating than it does when sinking, so the water level will fall. As it sinks, there is no change.

I already showed why this isn't true. Archimedes' Principle! It doesn't matter if the stone increases the density of the ice block, as long as the block's density is less than that of water as a whole. I even posted some sample math.

Ok. Look, we know you know what Archimedes' Principle is about, but this problem is tricky.
What you've got here is a cube that starts floating, and then changes density as it melts. The more ice melts away, the higher percentage of the ice cube's volume is taken up by the stone, which causes the total density of the cube to rise, and consequently causes it to sink. At some point it gets submerged fully, and loses buoyance. As it sinks to the bottom, and melts, it loses more volume than it adds = the water level is lowered.

I admit that I haven't properly read the problem(how could I do such a thing?), as it turns out that the stone sinks only after ALL of the ice has melted, meaning that no ice ever resurfaces after the stone is released(there is no ice left). But then, you did the same mistake in your analysis.
Nevertheless, this doesn't change the outcome, as it's still C.
As the cube melts, it's density rises, passess that of water, cube sinks, keeps on melting(lowering the water level), and finally leaves just the stone, which doesn't change anything, as it's already sunk.

[Gunner-Chan]

Hey guys. This is interesting but it's getting really off topic. Why not make a new one? Looks good enough for one if it's lasted 3 pages of discussion here.

And now a picture of a melting gecko.

[Il Palazzo]

Because that makes us happy?

[Urist Imiknorris]

I spent most of the afternoon playing Cave Story. I haven't played it in a while.

Also, physics problems make me happy.

EDIT: My current save is just after Monster X and Balrog, with 1 HP left. So far, I've been killed six times in the next area.

[G-Flex]

If the density of the stone is less than that of the water, the stone would float of its own accord, which we know doesn't happen. Therefore, it is displacing more whater when floating than it does when sinking, so the water level will fall. As it sinks, there is no change.

I already showed why this isn't true. Archimedes' Principle! It doesn't matter if the stone increases the density of the ice block, as long as the block's density is less than that of water as a whole. I even posted some sample math.

Ok. Look, we know you know what Archimedes' Principle is about, but this problem is tricky.
What you've got here is a cube that starts floating, and then changes density as it melts. The more ice melts away, the higher percentage of the ice cube's volume is taken up by the stone, which causes the total density of the cube to rise, and consequently causes it to sink.

Honestly? That doesn't matter. My math still holds no matter how the density of the object changes. This is incontrovertible. The math works for as long as the object floats, and I dare you to disprove me on that by showing me exactly where my math is wrong.

I admit that I haven't properly read the problem(how could I do such a thing?), as it turns out that the stone sinks only after ALL of the ice has melted

Why do you assume this? This isn't stated anywhere in the problem, and it is implied that some ice is left when the stone is released from it.

[Earthquake Damage]

as it turns out that the stone sinks only after ALL of the ice has melted

Wait, what?  That implies the stone is the density of water.

[Darvi]

I spent most of the afternoon playing Cave Story. I haven't played it in a while.

Also, physics problems make me happy.

Same here. Last cave makes me almost weep. But only almost.

I admit that I haven't properly read the problem(how could I do such a   thing?), as it turns out that the stone sinks only after ALL of the ice   has melted, meaning that no ice ever resurfaces after the stone is   released(there is no ice left).

Wut? Where does it say that? It wouldn't sink if that were the case.

[Leafsnail]

May be an appeal to authority, but a guy in his 3rd year of physical sciences at Cambridge told us it was D, with a pretty good explanation .

And yeah, it's not a trick or a riddle.  It's just a question based on the physics laid out in front of you.

If the piece of ice+stone is floating, as the question states, then the weight of the ice+stone is equivalent to the weight of the displaced water. As the ice melts, there isn't a change in water level. For every gram of ice that melts, you're displacing one less gram of water, but another gram of water is added from the melting ice. In other words, no change. When the stone slips out of the ice and sinks, however, the ice becomes more buoyant, more of it being exposed to the air, causing the water level to fall to some extent.

In other words, D.

Yeah, that's basically correct.

The only thing is that we required a bit more explanation to see what exactly the stone was doing (your's is basically right, but kindof hard to follow if you don't already know how it works).

Basically, you first need to know that to float, something needs to displace its own weight in water.

So while the stone is in the ice, it is displacing an amount of water equivalent to its own weight.

However, once it's out of the ice, it's only displacing an amount of water equivalent to its own volume.

Since the stone must be more dense than water (because it sank) this means that its weight in water is greater than its volume in water.  So the water level would lower when the stone is released.

It might be easier to think of it in some other form (we had "throwing gold bars out of a boat").

(hey, I know we're meant to be "back on topic", but it seems unfair to post a problem then not post the solution )