Beaker of water and bouyancy in a sink

[Physics197]

Homework Statement

You place a glass beaker, partially filled with water, in a sink. The
beaker has a mass of 517 g and an interior volume of 280 cm3. You now start to fill the sink with water and find, by experiment, that if the beaker is less than half full, it will float; but
if it is more than half full, it remains at the bottom of the sink as the water rises to its brim. What is the density of the material of which the beaker is made?

Homework Equations

Fb = pVg
P2 = P1 + Pgh

The Attempt at a Solution

 

[Stonebridge]

We know that the beaker just floats when it is half full.
In this case the volume of water in it is half 280 = 140 cm3
Given the density of water you can calculate the mass of water now in the half-full beaker.
If you add the mass of water to the mass of the beaker now, you get the total mass (and hence weight) that is just supported by the upthrust of the water.
The volume of water that is supporting the beaker is equal to the external volume of the beaker. This means you can calculate the external volume.(Archimedes)
The difference between the two volumes is the volume of the glass.
You know the mass of the glass so you can find its density.

 

[Physics197]

Thanks, that's what I needed, just an explanation.

In short, is the weight of an object that is floating always going to equal the weight of the displaced water which equals density of the water * volume displaced * gravity?

It just seemed like we blew through this topic in class.

And if you have worked this out did you get just under 1400 kg/m^3 for the density?