Ice Floats: Calculating Water Level Percent

In summary, to find the percentage of ice that shows above the water level, we can use the densities of water and ice to determine the volume of water needed to support the volume of ice. By subtracting this volume from the total volume of ice, we can get the percentage of ice above the water line. This can also be done by considering the forces acting on the ice and using a free body diagram. Ultimately, the percentage of ice above the water line is 8%.
  • #1
Miri
36
0

Homework Statement


If ice floats in water, how many percent of it show above the water level?
density of water=1000kg/m^3
density of ice=920kg/m^3

Homework Equations


I really don't know how to start and what I have to do with those densities...just give me a hint. solution would be 8%
 
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  • #2
Consider a volume of ice. How much does it weigh?

Then how much water needs to be displaced to support that?

Subtract that from 1 to get the % above the water line.
 
  • #3
So I take for example 100m^3 for the volume of ice. So the mass is (920kg/m^3)*100m^3=92000kg. Then I divide 92000kg by the density of water and I get 92m^3. And then??
 
  • #4
No, no, that won't get you anywhere. Try making a free body diagram of a block of ice, mass m, suspended in water.
What are the forces acting on it? What is the sum of these forces, and what does that say about the volume of ice submerged relative to its total volume? (The %)
 
  • #5
Miri said:
So I take for example 100m^3 for the volume of ice. So the mass is (920kg/m^3)*100m^3=92000kg. Then I divide 92000kg by the density of water and I get 92m^3. And then??

So that means that only 92 m3 of water are needed to support 100 m3 of ice. What's the difference? Isn't that what's left over above the water line? What's the percentage since that's the form they want the answer in?
 
  • #6
Ok, thanks, I got it...
 

1. How does the density of ice affect its ability to float in water?

The density of ice is less than that of liquid water, which means that ice is less dense than water. This allows ice to float on top of liquid water.

2. What is the relationship between the percent of an ice cube that is submerged and the density of the ice cube?

The percent of an ice cube that is submerged is directly related to the density of the ice cube. The denser the ice cube, the lower the percent submerged will be. This is because denser ice cubes will displace more water, causing a smaller portion of the cube to be submerged.

3. How is the water level percent calculated when an ice cube is floating in water?

The water level percent is calculated by dividing the volume of the submerged portion of the ice cube by the total volume of the ice cube, and then multiplying by 100. This will give the percentage of the ice cube that is submerged in the water.

4. Why does the water level change when an ice cube melts?

When an ice cube melts, it changes from a solid to a liquid, which means that its density also changes. The density of liquid water is higher than that of ice, so the melted ice cube will take up less space and cause the water level to decrease.

5. How does the shape of an ice cube affect its water level percent?

The shape of an ice cube does not significantly affect its water level percent. As long as the ice cube is the same size and density, the water level percent will be the same regardless of its shape. However, irregularly shaped ice cubes may displace more water and lead to a slightly lower water level percent compared to perfectly shaped cubes of the same size and density.

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