fluid density problem

[imnotsmart]

A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.30 g/cm3. If the pod has a radius of 4.00 cm and negligible mass, what is the mass of the frog?

How do you go about finding this?

[slider527]

hhmmm well i'm not really sure..but i guess...ruff guess..is if you take the volume of the pod = 268 cm^3 multiply 0.5 for a hemispherical (i'm thinking a hemispherical pod is just half a bal-shape object ) by you density 1.3 g/cm^3 equals 174.3 grams....and since the frog is lighter then the liquid then it's own density becomes equal to 0.65 gr/cm^3 :uhh: which in a way does make sense...to me atleast...

[imnotsmart]

that answer didn't work...the answer should be in kg...i have no idea how to work this problem at all...anyone else have any suggestions?

[FredGarvin]

You're going to need to use Archimedes' Principle to calculate the buoyancy of the frog in the liquid.

Archimedes showed that the buoyant force on any submerged object is equal to the weight of the water displaced. So first calculate how much water was displaced (the volume of the hemisphere).

Once you know the volume, you can take the density of the liquid and multiply it by the volume to get the mass of the water displaced.

Be careful with your problem. The units are all different. You are going to have to convert the volume into cm^3. That will give you the frog's mass in grams.

[Spectre5]

Are you to assume that the pod is "completely" submerged? I.E. The hemisphere is rounded on the button and flat on the top, where the flat side is even with the fluid level?

With the information given, I assume this is what yuou must do

Then, the Bouancy force is equal the weight of the frog:

mg = (row)*g*V

where:
m = mass of frog
g = gravitational constant (it cancels)
row = density of fluid (change it to kg/m^3, or worry about conversions later, just don't lose track of them
V = volume of displaced fluid, in this case, the volume of the hemisphere

[Spectre5]

Oh, Fred beat me to is :)

[imnotsmart]

So how do you find the volume of the hemisphere?

[Spectre5]

The volume of a hemisphere is (2/3)*Pi*r^3

Notice that is is half of the volume of a sphere, hence hemisphere