# Floating ice

Hi. My physics knowledge is very limited, but I know a decent amount. I would greatly appreciate it if you could explain in as much detail as you can. Thanks.

That said.

Imagine you have a container of water in excess. You have a mass M of ice floating on top of the water. Tied to the ice is a mass T that is more dense than water. Therefore T is submerged and under the surface of the liquid. Assume the string is massless.

What information would you need to be able to figure out the minimum mass of ice (M) you need to make the system (M+T) float? T can be submerged, but it should not pull M down below the surface of the water.

If you have that information, how would you solve it to figure out the mass of M?

Similarly. Is it possible to have a mass of ice (M) such that the system would be in equilibrium, but the ice is completely under the water, but T is not touching the bottom of the container of water? I think this phenomenon is called Natural or Neutral Buoyancy.

Thanks again.

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The ice and your heavy mass have to displace an amount of water that is equal to both its own mass and the mass T.

If objects are completely submerged they will displace their own volume of water.

maybe i read it wrong, but it seems as if your two sentences say the same thing, but with different consequences.

The ice and your heavy mass have to displace an amount of water that is equal to both its own mass and the mass T.

If objects are completely submerged they will displace their own volume of water.
I think the first line is the answer to the situation where it will float. If that is the case, it seems to say that if they displace a volume of water that is equal to the sum of both the ice and the dense object, then it will float.

Then the second line seems to be the answer to the question about neutral buoyancy. This also seems to say that if they displace an amount of water that is equal to the sum of both M and T, then it will be submerged.

I'm confused, but willing to learn.

Can you explain in a little more detail please?

russ_watters
Mentor
The first line is about mass and the second about volume. But really, they are two parts of the same issue: in a displacement problem like this, the total mass displaced (the two volumes times water's density) is equal to the total mass of the two objects. Do do the calculation, set those two things (four terms actually, two on each side) equal and solve for the volume of the ice cube.

okay. so you need to know the volume of the dense object, the volume of ice, the density of water (assumed to be 1 g/cm^3), and the mass of the dense object.

if we don't have the volume of ice, but we know everything else, how do we do it?

do we just assume that the density of the ice is also 1 and therefore M/D(ice) is the volume of ice?

then the equation would be:

( (M/D(ice))+T(volume) )*D(water)=M+T

solve for M?

if the density of ice was 1g/ccm it would wallow, neither sinking nor floating.

ice has a density around 0.92

i'm sorry. that's what i meant.

russ_watters
Mentor
then the equation would be:

( (M/D(ice))+T(volume) )*D(water)=M+T

solve for M?
You got it.