Determine the mass of an object given the volume it has displaced

1. Aug 8, 2014

needingtoknow

1. The problem statement, all variables and given/known data

Determine the mass of object A if it is placed in a test liquid that has a specific gravity of 2. The object was placed in the liquid and the recorded submerged volume of the object was found by measuring the displacement of water which is 150 cm^3.

2. Relevant equations

I actually require help in this section, because the only formulas I have to solve this are for floating objects but this is submerged in water and I am unsure of whether or not it is floating or not? Thank you.

2. Aug 8, 2014

Staff: Mentor

I would assume that it is floating, partly submerged. (Without that assumption, you would not have enough information to solve for the mass.)

3. Aug 8, 2014

needingtoknow

I tried to solve this question assuming that it was completely submerged but still floating near the top. So I did

Vsub/Vobj = densityobj/densityfluid

150 /150 = densityobj/2

densityobj = 2

2 = m/v

2 = m / 150

m = 300 g

But how would you do this question if you were assuming it was "partly submerged"?

4. Aug 8, 2014

olivermsun

The displaced water only equals the mass if the object is still able to float "partly submerged." Floating right below the surface with even the barest amount sticking out would count. However, if the object sank to the bottom, you'd only know that it was more massive than the same volume of water—you would have no idea how much more massive.

5. Aug 8, 2014

Orodruin

Staff Emeritus
If it is fully submerged you will only get the volume of the object (and the knowledge that it has a higher specific gravity than the liquid).

Note that the liquid is not water since it has specific gravity 2.

6. Aug 8, 2014

needingtoknow

So olivermsun, what I did would be correct right. I assumed that the object was floating right below the surface and assumed that the "barest amount sticking out" was so small that Volume submerged was equal to Volume of object. Does that mean that the mass is 300 g?

Also can I say that this line, "However, if the object sank to the bottom, you'd only know that it was more massive than the same volume of water—you would have no idea how much more massive." has cleared up a lot! Basically what you're saying in this line is that if an object sinks to the bottom and you asked to find its you won't be able to (b/c you can't use those equations which only work for objects that are floating) but you can find it's volume because Volume submerged would be equal to Volume of object. Is what I just said correct?

Finally Orodruin thank you for the note. I believe I did consider the liquid's specific gravity of 2 in my calculation!

7. Aug 8, 2014

olivermsun

300 g sounds right for 150 cm3 * 2 g / cm3.

Yeah, you would still know the volume of the object even if it were sitting on the bottom. It could be super-heavy though.

8. Aug 8, 2014

needingtoknow

Great thank you very much both of you!