# Finding mass of ice, using densities

1. Jan 6, 2013

### careless25

1. The problem statement, all variables and given/known data
a polar bear weighing 1250 kg is on a slab of ice. The slab of ice is at water level. The density of the ice is 925 kg/m3 and the water is 1030 kg/m3. Find the mass of the slab of ice

2. Relevant equations

Density = Mass/Volume

3. The attempt at a solution
SInce the ice is at water level, this means that the density of the polar bear and the ice togeter is equal to the density of water. Using this, solved for the density of the bear (105 kg/m3). Dont know where to go from here... Cant solve for anything else. Just that the bears density is about 10% of the overall density of water.

2. Jan 6, 2013

### Simon Bridge

You know the density of the ice - to get the mass you need the volume.
The ice+bear is floating ... what does that tell you about the volumes (ice+bear vs water displaced)? Can you write that as an equation?

3. Jan 6, 2013

### SteamKing

Staff Emeritus
105 kg/m^3 is a pretty low density for a polar bear.

You need to write an equation (use Archimedes principle) so that you can determine the mass of the ice slab.

4. Jan 6, 2013

### Simon Bridge

OP took $\rho_{bear}+\rho_{ice}=\rho_{water}$ ...
1. you cannot add densities like that
2. the ice+bear is floating with more than neutral buoyancy (the ice is at water level but the bear part is well above it) so the combined density is not going to be equal to that of water.

The relation missing from the list in post #1 is, indeed, the Principle of Archimedes.