# Conceptual question on floating

1. Mar 20, 2013

### kevinnn

1. The problem statement, all variables and given/known data
An ice cube with many air bubbles is places in water, does the water level rise, sink, or stay the same when it melts? Does your answer change if the ice cube is filled with many grains of sand?

2. Relevant equations

3. The attempt at a solution
I'm not too positive for the ice cube with the air but i believe it will stay the same. I also believe the volume will stay the same if the ice cube had many grains of sand. What i'm confused about is I don't know if the ice cubes are floating or submerged so it must not be important to the question. But I would think it would be because an object floating will displace a volume of water equal to its weight and a submerged object will displace a volume of water equal to its volume. Can someone point a finger in the right direction. Thanks.

2. Mar 20, 2013

### haruspex

For the sand case, it's not clear whether you're to assume the cubes floated initially. Suppose they did. You agree that when floating the water displaced matched the cubes by weight. You can think of that as an amount displaced by the weight of the ice and another amount by the weight of the sand.
Having melted, the water portion of the cubes is displacing an amount by volume, but that's the same as the amount it would displace by weight, and its weight has not changed. Is the same true for the sand?
How does the answer change if the cubes carried so much sand that they sank right off?

3. Mar 20, 2013

### kevinnn

The sands weight has not changed of course but it was floating so it should be displacing more water. If it sank to the bottom then the water level should not change because then the sand is displacing a volume of water equal to its volume. But in a sense when the sand is in the ice cube it is all ready submerged and thus already displacing water, except the water is in solid form.

4. Mar 20, 2013

### haruspex

I'm not entirely sure what you're saying. When the sand was in the floating ice cubes, the liquid water it effectively displaced corresponded to its weight. Yes, it was in a sense submerged, but it was floating, not resting on the bottom, and that's what matters. And yes, it was displacing by volume within the ice cube, but the volume of the ice cube does not affect the level of the liquid water, so that's irrelevant.
When the ice melts, the liquid water it displaces corresponds to its volume, so it now displaces less, right?

5. Mar 20, 2013

### kevinnn

Right. Now my concern is that the question did not specify whether or not the ice cubes were floating or not. The answer is the water level would go down if they were floating with the sand dissolved in it but would remain unchanged if the ice cubes were to be held down with fork or something correct.

But now what about the air???

6. Mar 20, 2013

### haruspex

If the ice cubes had been held down with a fork then the level would be sure to go down when they melted, sand or no sand. The uncertainty is whether there was so much sand in the cubes that they sank. What do you will happen in that case?
Here's one way to think about this case. Imagine that the ice cube were tightly enclosed in a weightless, infinitely thin box. Now redistribute the air in the cube so that it's all at the top, but still held in by the box. Does that change the level at which the cubes float? Now take away the box. Does anything change?

7. Mar 20, 2013

### kevinnn

If there was so much sand they sank the volume of water would go down because water expands as it freezes so the volume of water would go down as a result of that. But I don't think it will go down as a result of the sand. Because the sand is all ready submerged.
Nothing changes after the box is removed.

8. Mar 20, 2013

### haruspex

Yes and yes.

9. Mar 20, 2013

### kevinnn

So for the air the volume of water does not go down because the air does not carry enough weight? What about a massive block of ice with a lot of air in it. When the cube melted (if the block is floating) the water level would still not change because as the ice melts and the air escaped, more air fills its place right? The water level only changes when the cube is submerged and the air escapes.

10. Mar 20, 2013

### Dick

Warm up with a different question. Suppose the block is pure ice? What happens then?

11. Mar 20, 2013

### kevinnn

Nothing. The water level will stay the same because the volume of water displaced will be equal to the volume of the solid block of ice.

12. Mar 20, 2013

### Dick

No, the volume of water displaced will have a volume whose weight is equal to the weight of the block. Not the volume of the block.

13. Mar 20, 2013

### kevinnn

I'm sorry that is what I meant to put. I understand that concept but it is when you get to the air and the sand. For the sand the water level will not fall until the sand has fallen out of the ice cube and under the surface of the water right?

14. Mar 20, 2013

### Dick

Imagine a block of sand enclosed in a block of ice. As long as the ice is melting the weight lost by the block is exactly compensated by the weight of the displaced volume gained by the water, right? So the level doesn't change. What happens when the ice finally melts?

Last edited: Mar 20, 2013
15. Mar 21, 2013

### kevinnn

When the ice finally melts the sand will fall to the bottom and then no longer displace a volume of water equal to its weight but to its volume. So the water level should go down.

16. Mar 21, 2013

### Dick

That sounds exactly right.

17. Mar 21, 2013

### kevinnn

OK thanks. So now what about the air?

18. Mar 21, 2013

### Dick

Apply the same reasoning to that case.

19. Mar 21, 2013

### kevinnn

So in that case as the ice melts the air will escape and the water volume will go down. The weight of the air makes a noticeable difference?

20. Mar 21, 2013

### Dick

Air is a thousand times less dense than water. Ignore that in a first approximation. Apply your logic from the sand case to this case.