Law of Floatation: Stone on Ice Melts, Water Level?

[starwars32]

Hi.. I understand that if the ice is floating in water, if it melts, the volume of the water will not change as we can apply the law of floatation. But if there is a stone now on top of the ice.. why is it that the water level will decreases when the ice melts. can we like visualise in this way: when the ice melts the stone falls into the water? then the water level increases or decreases? Can anyone explain? Thanks

 

[AC130Nav]

Hi.. I understand that if the ice is floating in water, if it melts, the volume of the water will not change as we can apply the law of floatation. But if there is a stone now on top of the ice.. why is it that the water level will decreases when the ice melts. can we like visualise in this way: when the ice melts the stone falls into the water? then the water level increases or decreases? Can anyone explain? Thanks

While the ice is floating on the water a part of it is submerged displacing an amount of water equal to its weight (it's less dense so larger than the same weight of water, so some of it is above water level. When it melts the level is unchanged.

Now weight it down with a rock or push it down with your finger and the water level rises because more of the less-dense ice is pushed below the surface. If the rock then slips off the ice or the ice melts, the rock only displaces its own volume as it sinks to the bottom and the water level--does what? This is a homework problem.

 

[starwars32]

what do u mean by the statement displaces its own volume and displacing its own mass? i have been reading books on it but i still can't grasp the terms. Ok so can i say that when the rock slips off the ice or the ice melts, the rock displaces its own volume as it sinks to the bottom of the water it will decrease because of the heavier density of the rock? talking about density..can u explain how density can affect the level of the water

 

[Gyro]

In terms of density, the ice floats because it is less dense than water.
The rock would sink because its density is more than water.
When the ice floats, part of it is still above water, but the part below displaces an amount of water equal to the weight of the ice. This volume of water displaced will be less than that of the ice, since water is denser than ice.
If you put the rock on the ice, the combined mass of rock and ice divided by the combined volume of rock and ice has a density still less than water, so it floats.
But it floats lower into the water because the rock is pushing down on the ice. As it pushes down, the weight of the rock displaces an amount of water equal to its weight, and since the density of the water is less than rock, it will take more volume of water to make up the weight of the rock, which is why the level of the water rises when the rock is on the ice.
When the ice melts, the rock falls into the water, but this time only displaces a volume of water equal to its actual volume, which is much less than what was displaced when it was on the ice. Since it now displaces less volume than when on the rock, the water level falls.

Hope this helps.

 

[starwars32]

This volume of water displaced will be less than that of the ice, since water is denser than ice.

I dun really understand this statement. Can u explain it in terms of layman terms

 

[Gyro]

When anything floats, it pushes aside (displaces) an amount of liquid equal to its weight.
The ice moves aside water, the amount of water it moves weighs the same as the ice.
But ice has lower density, so for same mass, it takes more space than the water.
Which is why part of the ice is still above the water.
When the ice floats, if you measured the exact amount of liquid it pushes aside (like by filling a beaker to the brim, dropping in the ice, and capturing the liquid that drips over, and weighing it), you'd see the overflow water weighs the same mass as the ice, but takes up less volume.
Not sure how better to describe what I'm saying in layman terms. I thought I was using layman terms. If I'm not being clear, read about Archimedes and buoyancy here:
http://en.wikipedia.org/wiki/Archimedes
Read about the Golden Crown. Interesting story.

https://www.physicsforums.com/library.php?do=view_item&itemid=123
Scroll to the bottom of the page and read "Partial immersion ("floating") of a uniform body"

 

[AC130Nav]

what do u mean by the statement displaces its own volume and displacing its own mass? i have been reading books on it but i still can't grasp the terms. Ok so can i say that when the rock slips off the ice or the ice melts, the rock displaces its own volume as it sinks to the bottom of the water it will decrease because of the heavier density of the rock? talking about density..can u explain how density can affect the level of the water

If something has a greater density, it has more weight per unit volume. If you drop a cubic inch rock in water, it displaces a cubic inch of water (which weighs a lot less).

Ice weighs less per unit volume than water (it's odd that way, most liquids weigh more as a solid). It only sinks until it displaces as much water as its weight.

Place a rock on it, in it, or attached to it; and the two sink until they displace an amount of water equal to their combined weight (understand, the rock "wants to be" at the bottom of the water).

Look up Archimedes and why ships float.