Buoyancy problem and density of ice

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SUMMARY

The discussion centers on calculating the fraction of an iceberg's volume that is exposed above sea water, given the densities of ice (920 kg/m³) and sea water (1030 kg/m³). Participants clarify that the correct approach involves using Archimedes' principle, which states that the mass of the displaced water equals the mass of the iceberg. The final calculation reveals that approximately 0.931 of the iceberg's volume is exposed above water, derived from the formula: Fraction Exposed = 1 - (density of ice / density of sea water).

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Homework Statement


The density of ice is 920kg/m^3, and the density of sea water is 1030kg/m^3. What is the fraction of the total volume of an iceberg that is exposed?

given:
density sea water = 1030kg/m^3
density ice = 920kg/m^3

Homework Equations



density water/density ice



The Attempt at a Solution


I am really not sure of how to start this problem.

I divided 1030 by 920 and got 1.101kg/m^3

how do I start this problem?
 
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First step in this sort of problem is to estimate (guess) what answer you expect.
You know icebergs float, with most of the ice below the water - if you are a native English speaker you know 'tip of the iceberg'

The next step is that you know your answer can't have any units - it's just a ratio = a number.
So if you have two numbers with units and you want an answer with no units - what do you have to do with the numbers?
 
Last edited:
ash4741 said:
The density of ice is 920kg/m^3, and the density of sea water is 1030kg/m^3. What is the fraction of the total volume of an iceberg that is exposed?

Hi ash4741! :smile:

Do it logically …

how much volume of water is displaced by the ice? :wink:
 
Start with the fundamental concept of buoyancy. The mass of the ice is equal to the mass of the displaced water. The volume of the displaced water is equal to the volume of the submerged iceberg.

This should get you on the right track.
 
So the 1.101 is the mass of the iceberg? and the mass of the water displaced? But I thought that was the volume of the iceberg that is under the water.
 
ash4741 said:
So the 1.101 is the mass of the iceberg? and the mass of the water displaced? But I thought that was the volume of the iceberg that is under the water.

One thing that might help is that 1030/920 is not 1.101. At least calculate it more precisely.
 
I divided 1030 by 920 and got 1.101kg/m^3

What do you think this answer MEANS?
Also write down the units in your calculation inputs...because You have the wrong units in your answer...

So the 1.101 is the mass of the iceberg?

no... to calculate the MASS you would need to know the volume of the iceberg in question...but you don't need to know that...

What fraction of the iceberg will be underwater?...something less than the total iceberg,right,because it floats and some stick up above water but most of it is underwater...
 
I though that the answer to this division (which is actually 1.119) was the volume of the iceberg that is under water. Sorry, I do not quite understand.
 
So the answer is 0.931 for the ratio that is exposed?
I am just guessing because what I thought was the portion under water is 1.119.
 
  • #10
ash4741 said:
So the answer is 0.931 for the ratio that is exposed?
I am just guessing because what I thought was the portion under water is 1.119.

Why do you keep guessing? :rolleyes:

use Archimedes' principle (the one about displacement of water), and work it out!
 
  • #11
ash4741 said:
So the answer is 0.931 for the ratio that is exposed?
I am just guessing because what I thought was the portion under water is 1.119.

Maybe try a less abstract approach? If you have a 1 m3 block of ice how much does that weigh?

What percentage of that volume if filled with the heavier sea water would weigh the same? That's all the sea water that needs to be displaced for it to float.

So ... how much is left over? That's the percentage above the waterline "exposed" isn't it?
 
  • #12
Alright, if you start with the approach that the mass of the iceberg must equal the mass of the water displaced you will get to the answer. Use your densities to help you out here.

You should get

Fraction Exposed = 1 - (density of ice)/(density of sea water)
 
  • #13
So if the mass of water displaced= mass of ice then:
density of water * volume of water displace = density of ice * volume of ice
So
(Volume of water displaced)/(volume of ice) =1 and you would subtract 1 from density of ice/ density of water

Is that right?
 
  • #14
ash4741 said:
So if the mass of water displaced= mass of ice then:
density of water * volume of water displace = density of ice * volume of ice
So
(Volume of water displaced)/(volume of ice) =1 and you would subtract 1 from density of ice/ density of water

Is that right?

The first part is correct. Determine first then the volume of water needed to be displaced. And then it is the ratio of the volumes that is a % that you subtract from 1, not as you expressed.
 
  • #15
Thanks everyone
 

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