Buoyancy and application of Archimedes' principle in two separate but related systems

1. Oct 6, 2008

mwharrell

1. The problem statement, all variables and given/known data
A solid block is attached to a spring scale. The reading on the scale when the block is completely immersed in water is 25.2 N, and the reading when it is completely immersed in alcohol of density 806 kg/m^3 is 25.9 N.

2. Relevant equations

F buoyancy = (Density of the liquid) x (Volume of the liquid displaced) x g
F Gravity = (Density of the object) x (Volume of the object) x g
F total = F buoyancy - F Gravity
F total = ((Density of the liquid)x(Volume of the liquid displaced)-(Density of the object)x (Volume of the object))g

3. The attempt at a solution
I assumed that Density of water was 998kg/m^3

I discussed this with my physics professor, he told me to "subtract the two F total equations from on another." I did so, and found that the Volume of the displaced water = .80763xVolume of the displaced alcohol. However, i do now see how this helps me determine the volumes of the mass in solution. All of my continued efforts result in me ending up with too many unknowns. Without the mass of the object, or its density, or the volume of liquid displaced (to find the buoyant force), I'm just stuck.

Thanks for your time and effort,

Long time reader, first time poster.

2. Oct 6, 2008

Perillux

Re: Buoyancy and application of Archimedes' principle in two separate but related sys

You did not state what the problem is asking for. From reading further I gather that you are looking for volume of the block. In the future make sure to include all the info, don't assume we know what you want.

But what you need to do, is just write out the equations, don't worry if there are too many unknowns.

(the density of water is 1000kg/m^3)
First you need to think as being in 2 parts. water and alcohol. Solve for the density of the block in each of these situations, the 2 equations should be identical except one will have values for water and the other will have alcohol.
Then because the density of the block does not change, you can set these 2 equations equal to each other and then the only unknown you will have is volume, then just solve for that.

NOTE: the weights you are given are called "apparent weights". which is equal to:
(force of gravity) - (force buoyant)
This is because the buoyant force pushes up on the object so it appears lighter.

3. Oct 6, 2008

mwharrell

Re: Buoyancy and application of Archimedes' principle in two separate but related sys

I apologize for not putting my question in my text! I Guess my Copy and Paste skills are lacking.

You are correct in assuming i need the density and volume of the mass. I'll try what you posted and get back to you in a bit.