# Bouyancy of Ice in Water

## Homework Statement

Two Identical glasses are filled to the same level. One is filled with fresh water (density=1 gm/cm^3) and the other with salt water (density=1.025g/cm^3) Into each glass a cube of ice (density= 0.92 gm/cm^3) one cm on each side is placed. What is the height of the ice above water level in each glass?

## Homework Equations

Maybe Archimedes' principal? We never really went over this in class

## The Attempt at a Solution

I honestly have no idea... Do we subtract the densities to get the cm of displacement? Like the ice in freshwater is .08 becase 1-.92=.08? I am truly lost.

LowlyPion
Homework Helper

## Homework Statement

Two Identical glasses are filled to the same level. One is filled with fresh water (density=1 gm/cm^3) and the other with salt water (density=1.025g/cm^3) Into each glass a cube of ice (density= 0.92 gm/cm^3) one cm on each side is placed. What is the height of the ice above water level in each glass?

## Homework Equations

Maybe Archimedes' principal? We never really went over this in class

## The Attempt at a Solution

I honestly have no idea... Do we subtract the densities to get the cm of displacement? Like the ice in freshwater is .08 becase 1-.92=.08? I am truly lost.

Welcome to PF.

That's pretty much it ... for plain water.

Now what about the salt water?

Well if that were the case for the freshwater I would assume it to be the same for the salt water. so 1.025-.92=.105? It just seems to simple for the final exam I suppose. But if this is correct can you offer any explanation why we simply subtract the densities?

LowlyPion
Homework Helper
Well if that were the case for the freshwater I would assume it to be the same for the salt water. so 1.025-.92=.105? It just seems to simple for the final exam I suppose. But if this is correct can you offer any explanation why we simply subtract the densities?

Salt water is a little different. Your first result was a consequence of the fact that fresh water was given as a density of unity.

Buoyancy is the amount of weight displaced isn't it? (I'm letting gravity cancel out here.) So all the cube needs to displace is .92g . The mass that the cube could displace and be even would be 1.025 g. So the percentage of the cube that will be poking out will be .92/1.025 subtracted from 1 won't it?

Well that does give me an answer on the exam but I don't have an answer key and I don't really understand why I suppose... Maybe I just don't really understand bouyancy

LowlyPion
Homework Helper
Here is a lecture that covers it in a little more detail: