How Does Iceberg Buoyancy Relate to Sea Water Density?

[Agent M27]

Homework Statement

An iceberg is floating on sea water such that only 10% of its volume is above the water level. What is the density of sea water expressed in terms of the density of ice.

Homework Equations

\frac{Vf}{Vi} = \frac{\rho}{\rho}

\rho_f = density of sea water
\rho_i = density of ice

The Attempt at a Solution

I know this is a rather simple problem but where I am getting hung up is the ratio of the visible portion of the iceberg. I hate to admit but the simple maths trip me up. I began by isolating the eq so that:

\rho_f = \rho_i \frac{Vi}{Vf}

from which I get \frac{9}{10} \rho_i


By the way this is an even number problem so I cannot look up the answer, so is this correct?

Thanks in advance.

Joe

 

[Redbelly98]

Homework Equations

\frac{Vf}{Vi} = \frac{\rho}{\rho}

\rho_f = density of sea water
\rho_i = density of ice

You left out the subscipts on the ρ terms in your equation.

The Attempt at a Solution

I know this is a rather simple problem but where I am getting hung up is the ratio of the visible portion of the iceberg. I hate to admit but the simple maths trip me up. I began by isolating the eq so that:

\rho_f = \rho_i \frac{Vi}{Vf}

from which I get \frac{9}{10} \rho_i

Think about your answer. It says that the sea water is (more, less?) dense than the ice, and therefore the iceberg should (float, sink?).

 

[N-Gin]

As you said, It's a very simple problem.

\rho_{0}V_{0}g=\rho g (V_{0}-V)

\rho_{0} and V_{0} are density and volume of the iceberg and \rho is density of water and V is visible volume of the iceberg.

You can easily get the sought ratio.

\frac{\rho_{0}}{\rho}=\frac{V_{0}-V}{V_{0}}=1-\frac{V}{V_{0}}

 

[Agent M27]

From my answer it says that the sea water is less dense than that of ice, which is actually incorrect when I think about a glass of ice water. So then my answer ought to be:

\rho_f = \frac{10}{9} x \rho_i

which correctly shows that the sea water is more dense than ice, is this the correct answer?

Thanks redbelly. Also I didn't put the subscripts in the original EQ because I have issues when I apply subs scripts in a fraction for some silly reason.

Joe

 

[Redbelly98]

Looks good. One way to remember this is that the total mass of the iceberg (or other floating object) equals the mass of the displaced water (or other fluid). Since mass is equal to ρV, you can set up the equation by equating the two masses.