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# Physics/How do I calculate the buoyancy?

Question
The rectangular block has a length of 30 cm, a width of 20 cm, and a height of 20 cm. The block floats stably when 12 cm of its height is below the water surface. What is the volume of the displaced water and how much is the buoyant force on the block?
How do I figure out the weight of the block and the density?
I have come up with some solutions but I do not think they are right. I would like some reassurance. :-)

Also, how would the amount of the block under the surface be different if the block were floating in Alcohol, Vegetable Oil, Glycerin, and Salt Water?

I have come up with this so far:
It has displaced 12 * 20 * 30 cubic centimeters of water

12 * 20 * 30 =>
7200

Since water has a density of 1 g/cm^3, then it has displaced 7200 grams of water. That means that the block weighs 7.2 kg.

It has a volume of 30 * 20 * 20 => 12000 cubic cm

7200 grams / 12000 cu cm =>
72/120 g/cm^3 =>
0.6 g/cm^3

I don't work problems, but I think I can walk you through it without any problem.

For buoyant force you can consider that the mass of the water displaced minus the mass of the air displaced.  The mass of the air is negligible (m air = 0), so really we are just talking about the mas of the water displaced.  The mass of the water displaced can be found by the volume of the block that is below water times the density of water.  This will then be the buoyant force.

In turn, the mass of the cube must match this buoyant force (since it is not moving, forces must be equal and opposite). As a side note, you can also calculate the total density of the block if you wanted to - you have the mass and total block volume at this point.

As for alcohol, vegetable oil, glycerin and salt water... you will need to look up these fluid densities.  For liquids with higher densities than water the block will displace less fluid, and have less volume below the surface (ie sits higher) - for liquids with lower densities than water, more fluid will be displaced and there will be more volume below the surface (ie sits lower).

As a final note:  One can also conceptually think about the effects of changing the density of the block as well.  Increasing the density of the block will make it sit lower and decreasing it will make it sit higher... and increasing it past the density of the liquid will make it sink (full submersion).

Physics

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