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# Interesting Physics Problem watch

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1. I was thinking about this the other day, and I'm not sure if my reasoning is right, but:

Say you have a cup of water, with an ice cube floating on top. The ice cube then melts. Does the level of water go up, down, or stay the same?

I would have said that an object which floats would displace it's weight in water. But when the ice melts, it would effectively become it's weight in water, so the level would stay the same. Ice is less dense than water, yes, but I don't think that really matters in this explanation.

Alternatively, when I googled it, I found some people saying that because ice is less dense than water, a gram of ice takes up more volume than a gram of water (which is obviously true), the water level would decrease when the ice melted. But doesn't that approach assume the ice was completely submerged in the water (ie not floating on the top with part of it stuck out)?

Thoughts?
2. My initial thoughts were in agreement with the explanation you found in google. I think the problem you are having is that you seem to be using weight wrong. When you put an ice cube into the water, it will displace water equal to its volume, not weight. Also, in physics weight is the force an object's mass exerts towards the planet's centre due to gravity, technically. It's also worth remembering that volume and mass are related to each other via the density.

The problem relies on assuming that all mass is conserved and when the ice cube melts, since the same mass of ice cube has more volume than the same mass of water, there is less volume in the cup hence why the water level goes down.

Just reread the last part of your post. Yes, you're right so therefore to find if this makes the water level increase or decrease, you can use the ratio between the density of the ice cube and density of the water to find the point where the mass of the submerged part of the ice cube equals the mass of the unsubmerged part. That's probably not explained very well but the point at which the water level would not change occurs at the point where the volume of water created due to the top part is equal to the volume "lost" by the bottom part when the submerged part of the ice cube melts. I'd do the maths but I'm feeling a little too lazy right now

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3. So, if it displaces it's mass in water when it floats, surely when it melts, it just effectively becomes it's mass in water, so the level would stay the same. No?
4. (Original post by Tomtech)
I was thinking about this the other day, and I'm not sure if my reasoning is right, but:

Say you have a cup of water, with an ice cube floating on top. The ice cube then melts. Does the level of water go up, down, or stay the same?

I would have said that an object which floats would displace it's weight mass in water. But when the ice melts, it would effectively become it's weight mass in water, so the level would stay the same. Ice is less dense than water, yes, but I don't think that really matters in this explanation.

Alternatively, when I googled it, I found some people saying that because ice is less dense than water, a gram of ice takes up more volume than a gram of water (which is obviously true), the water level would decrease when the ice melted. But doesn't that approach assume the ice was completely submerged in the water (ie not floating on the top with part of it stuck out)?

Thoughts?
in my opinion the water level would stay the same. Using Archimedes principle, the ice cube displaces a volume of water with weight equal to its own, since it is the same substance it displaces a smaller volume than itself due to differing densities, when it melts it occupies this smaller volume. Have another qusetion

a boat is in the middle of a lake with a steel anchor on board, what happens to the water level in the lake when the anchor is thrown overboard. Assume the chain joining it to the boat has negligible volume or mass
5. (Original post by excal9)
a boat is in the middle of a lake with a steel anchor on board, what happens to the water level in the lake when the anchor is thrown overboard. Assume the chain joining it to the boat has negligible volume or mass
If the anchor is weighing down the boat initially then a volume of water with equal weight is already displaced with it contained in the boat, so does the water level remain the same when it's thrown overboard?
Wait no, the anchor must sink, so the weight of the water displaced must be less when it's thrown in, so would the water level go down?
6. The anchor displaces it's weight in water when in the boat, but it's volume when in the water? It is more dense than water, so the water level would go down?
7. (Original post by yepyepyep)
If the anchor is weighing down the boat initially then a volume of water with equal weight is already displaced with it contained in the boat, so does the water level remain the same when it's thrown overboard?
Wait no, the anchor must sink, so the weight of the water displaced must be less when it's thrown in, so would the water level go down?
(Original post by Tomtech)
The anchor displaces it's weight in water when in the boat, but it's volume when in the water? It is more dense than water, so the water level would go down?
yeah ^^
8. (Original post by excal9)
yeah ^^
Nice question, cheers.
9. (Original post by yepyepyep)
Nice question, cheers.
no problem
10. not so much a different problem, but can you show that energy is conserved for an object falling under gravity

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