Calculating Minimum Mass of Ice to Make an Object Float

In summary: The equation is set up so that you can plug in the known values (volume of T, density of water, etc.) and solve for M. It may also be helpful to know that ice has a density of approximately 0.92 g/cm^3, as mentioned earlier.
  • #1
pchalla90
55
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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?
 
  • #6
if the density of ice was 1g/ccm it would wallow, neither sinking nor floating.

ice has a density around 0.92
 
  • #7
i'm sorry. that's what i meant.
 
  • #8
pchalla90 said:
then the equation would be:

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

solve for M?
You got it.
 

Related to Calculating Minimum Mass of Ice to Make an Object Float

1. How do you calculate the minimum mass of ice needed to make an object float?

The minimum mass of ice needed to make an object float can be calculated by dividing the density of the object by the density of ice. This will give you the minimum volume of ice needed. Then, multiply the minimum volume by the density of water to get the minimum mass of ice needed.

2. What is the density of ice?

The density of ice is approximately 0.917 grams per cubic centimeter.

3. How do you determine the density of an object?

The density of an object can be determined by dividing its mass by its volume. The mass can be measured using a scale, while the volume can be calculated by measuring the length, width, and height of the object and multiplying them together.

4. Can the minimum mass of ice needed to make an object float vary?

Yes, the minimum mass of ice needed can vary depending on the density of the object and the temperature of the water. The colder the water is, the more dense it becomes, and therefore less ice will be needed to make the object float.

5. Why does an object float when placed on a block of ice?

An object floats when placed on a block of ice because the ice displaces an equal amount of water, creating an upward buoyant force on the object. This force is greater than the downward force of gravity, causing the object to float. The minimum mass of ice needed ensures that the ice displaces enough water to create this buoyant force.

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