Do Buoyant Forces Depend on the Material's Density?

[wondermoose]

Homework Statement

A 20cm^3 block of lead and a 20cm^3 block of copper are completely under water. Each is suspended by a thread so that they both hand at the same height in an aquarium filled with water. Which of the following is true?

a) The buoyant force is greater on the lead than on the copper
b)*** The buoyant force is greater on the copper than on the lead
c) The buoyant force is the same on both blocks
d) More information is needed

Homework Equations

F_b=$$\rho$$vg

The Attempt at a Solution

This problem was on a test and I was pretty sure the correct answer was B, but I was wrong. My revised way of thinking about it is since the volume is the same then the material with the greater density should have the larger buoyant force.

$$\rho$$_lead=11300 kg/m³
and
$$\rho$$_copper=8920kg/m³

Soooo

F_lead = (11300 kg/m³)(.020 m³)(9.8 m/s²)
= 2214.8

F_copper = (8920kg/m³)(.020 m³)(9.8 m/s²)
= 1748.3

F_lead > F_copper

Make sense? Thanks!

 

[Kikora]

I think you have some misconceptions here.

Buoyant Force = Vρg, the V is the volume of liquid displaced, p is the density of the LIQUID displaced.

Hence, the upthrust is the same for both, since in both cases, the liquid and the volume of liquid displaced is the same.

Now, you might ask why is it that both can be at the same height at the water even though the lead block is obviously heavier than the copper block.

This is because Buoyant force + Force exerted by the string = Weight of block.

 

[wondermoose]

So does that mean the buoyant force is the same for both blocks, regardless of the density of the material? I guess that makes sense, since both blocks are the same dimensions under the same circumstances.

Just to make sure I'm getting this (because I obviously didn't before):

The buoyant force is the same on both blocks because buoyant force is independent of the density of the material.

 

[Kikora]

Yes. That's correct.