# An ice cube floating in water, what is the volume of the part under water?

The Problem

Hi, I just got this question in a physics class that I am taking, I have been looking at it for about 30 minutes and can't seem to crack it, probably doesn't help that I'm learning it in another language but anyways. A Ice cube of temperature 0 degress Celsius is floating on water. The ice cube's volume is 7.5 cm^3

Find the buoyancy of the ice cube. Density of ice at 0 degrees is 9.17 g/cm^3

Calculate the volume of the part of the ice cube that is under water.

Relevant Equations
Obviously I used the buoyancy formula to find the buoyancy of the ice cube, F = density x volume x gravity which I got to equal 73.65 Newtons

And then I would assume that I have to use V of the object = Force of buoyancy / density of water * gravity

Attempt
Using the second formula that I mentioned, I plug in the numbers and get the same volume that I was given, the volume of the ice cube. Which unfortunately actually makes sense because I am using the full force of buoyancy, and the density of water, and gravity. Nothing in there is specific to the part of the ice cube that is under water. With the given information i don't see how it is possible to actually calculate the amount of the ice cube that is under water.

Any help is appreciated,

Dane

## Answers and Replies

Borek
Mentor
What is mass of the ice?

Note that ice density is not 9.17 g/mL, more like 0.917 g/mL.

tiny-tim
Homework Helper
Welcome to PF!

Hi Dane! Welcome to PF!!
Density of ice at 0 degrees is 9.17 g/cm^3

erm … noooo
Obviously I used the buoyancy formula to find the buoyancy of the ice cube, F = density x volume x gravity which I got to equal 73.65 Newtons

And then I would assume that I have to use V of the object = Force of buoyancy / density of water * gravity

Look up your notes on buoyant force again …

The difference of the densities is what matters

(and V is the volume of water displaced, not the volume of the ice)

Sorry if the density is wrong but that is what the problem said....

Are you saying that my buoyant force is wrong or that I should look up the buoyant notes again because the answer lies in there?

Sorry there is no mass given.

diazona
Homework Helper

(and V is the volume of water displaced, not the volume of the ice)
That's a key point. In the buoyancy formula $F=\rho g V$ you shouldn't use the volume of the whole ice cube.

Borek
Mentor
Sorry there is no mass given.

You are given volume and density though...

Aha,

So with the amount of water that is displaced that should give me an idea of the volume of the ice cube that is "displacing", meaning the part that is under water. I just don't have the amount of water that is being displaced though?

So I can't even calculate buoyancy though because I don't have the volume of the part under water?

and wow I can't believe I didn't see that, derrrr..... m = d*v, my bad

Borek
Mentor
Now that you know the mass volume under water should be obvious - buoyancy makes the ice float, doesn't it?

tiny-tim
Homework Helper
Hi exutable!
So I can't even calculate buoyancy though because I don't have the volume of the part under water?

So … standard procedure … give it a name!

Call the volume under water V, write out the equations, and solve for V.