Finding mass of ice, using densities

[careless25]

Homework Statement

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

Homework Equations

Density = Mass/Volume

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.

 

[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?

 

[SteamKing]

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.

 

[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.

 

[Nickie]

Great job starting off by using the density equation! To find the mass of the slab of ice, we can use the same equation but rearrange it to solve for mass.

Density = Mass/Volume

Mass = Density x Volume

Since we know the density of the ice and the volume of the slab of ice (which is the same as the volume of the polar bear), we can plug those values into the equation to find the mass of the slab of ice.

Mass = 925 kg/m3 x Volume

To find the volume, we can use the same equation but rearrange it to solve for volume.

Volume = Mass/Density

Since we know the mass of the polar bear (1250 kg) and its density (105 kg/m3), we can plug those values into the equation to find the volume of the polar bear.

Volume = 1250 kg / 105 kg/m3 = 11.9 m3

Now, we can plug the volume into the first equation to find the mass of the slab of ice.

Mass = 925 kg/m3 x 11.9 m3 = 10,977.5 kg

Therefore, the mass of the slab of ice is 10,977.5 kg.