Something with ice cubes

[Scarletblack]

There was a weird question that I found (I don't remember where):

A large ice cube floats in a cup of water. Several coins are embedded in the ice cube. What happens when the ice cube melts?

(a) The water level falls
(b) The water level stays the same
(c) The water level rises
(d) Cannot be determined

Ok so for a regular ice cube, the water level would stay the same because Archimede's principle states that

"A body wholly or participally immersed in a fluid will be buoyed up by a force = weight of the fluid it displaces."

So a smaller volume of water is displaced because the ice cube is less dense. However as it melts, it becomes more dense and has less volume so the water level would be the same.

However, here, I thought the coins are even MORE dense and thus should make the water level rise.

But the actual answer is that (a) it falls. Why is this?

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[seraph524]

This scenario was brought up a couple of days ago by another poster...

The reason the water level falls is that an un-encapsulated coin displaces a volume of water equal to its own volume, while an encapsulated coin in ice displaces a volume of water that represents the mass of the coin in ice. And since it is in ice, it will displace an even higher volume since ice has lower density than water.

In other words, if a coin is 2 grams, and is in ice, it will displace water by a volume of ice that weights 2 grams. However, if the coin is merely at the bottom of the cup, it will only displace a volume of water equal to its own metal volume.

 

[physics junkie]

There is actually no way to tell. If the ice cubes were very, very large or the coins were very small or of equal density to water you would get different answers. Seraph got the principles right but the actual question is bull****.

 

[nfg05]

as referenced by seraph, I brought up this question a few days ago. The thread is here for more info on this topic:

http://forums.studentdoctor.net/showthread.php?t=533548

 

[BerkReviewTeach]

There is actually no way to tell. If the ice cubes were very, very large or the coins were very small or of equal density to water you would get different answers. Seraph got the principles right but the actual question is bull****.

One can assume that metallic coins are more dense than water and therefore more dense than ice. But it's those damn wooden nickels that cause the problem on a question like this. What if they are balsa wood coins?

Once again, it brings up the point, don't take any wooden nickels.

 

[physics junkie]

One can assume that metallic coins are more dense than water and therefore more dense than ice. But it's those damn wooden nickels that cause the problem on a question like this. What if they are balsa wood coins?

Once again, it brings up the point, don't take any wooden nickels.

You know I was totally wrong in my previous post. The size of the ice cube has nothing to do with it. I was thinking that the fact that the ice cube is only partially submerged would compensate for the reduction of density when the ice melted AND for the additional density of the coin...but when I carried out the calculation it came out exactly even. So the only factor would be the density of the coin. Pennies have a density of ~7g/cm^3 and metallic coins can always be assumed of course. Learn something new every day.