How much of an iceberg is beneath the surface Archimedes principle

[mizzy]

How much of an iceberg is beneath the surface...Archimedes principle

Homework Statement

Calculate how much of an iceberg is beneath the surface of the ocean, given that the density of ice is 917kg/m^3 and salt water has density 1025kg/m^3.

Homework Equations

archimedes principle: buoyancy = to the weight of the displaced fluid

The Attempt at a Solution

How can you do this when you're not given area and mass of the iceberg? Can someone guide me with this question?

 

[Gear.0]

Those quantities you don't need will cancel out. It's often hard to see this right away, the best thing to do is to just start solving it manipulating the unknown quantities as variables and just hope for the best.

In this case, you should write out an equality for what you do know.
A hint... The volume of the water should be some fraction of the volume of the ice. (x*V) for example would be the volume of the water, where x is the fraction, and V is the volume of the ice.

 

[mizzy]

Density ice/density water = volume water/volume ice

is that rite?

 

[Gear.0]

Yes that is exactly right.
The reason I said to look at the volume of water as x*V, because then you can see that (volume of water)/(volume of ice) is equal to the submerged fraction of the ice.
Volume of water = x*V
Volume of ice = V
(volume of water)/(volume of ice) = x
and x is the fraction of the ices volume that when multiplied gives you the waters volume. Therefore x is equal to the submerged portion of the ice.

So (Density of ice)/(Density of water)
is exactly the quantity you were looking for.. Also, if you multiply by 100 then you get the value as a percentage of the total volume that is submerged.

 

[rwisz]

I would approach this problem by first defining the variables and assumptions. The density of ice and salt water are given, so we can use those values in our calculations. We can also assume that the iceberg is a perfect cube for simplicity.

Next, we can use Archimedes principle to determine the volume of the iceberg that is submerged beneath the surface. This principle states that the buoyant force acting on an object is equal to the weight of the fluid it displaces. In this case, the fluid is salt water.

We know that the density of salt water is 1025kg/m^3 and the density of ice is 917kg/m^3. Using the formula for density, which is mass/volume, we can rearrange the equation to solve for volume. This gives us the volume of salt water displaced by the iceberg.

Next, we can calculate the weight of the displaced salt water using its density and volume. This weight is equal to the buoyant force acting on the iceberg.

Finally, we can use the buoyant force and the density of ice to calculate the volume of the iceberg that is submerged. This is because the weight of the displaced salt water is equal to the weight of the submerged portion of the iceberg.

Therefore, using Archimedes principle, we can determine how much of the iceberg is submerged beneath the surface of the ocean. This approach can be applied to any shape and size of iceberg, as long as the density and dimensions are known.