Buoyant Force of a ship and water

[dab353]

Homework Statement

Consider a ship that is floating in fresh water. The bottom of the ship is a depth of (df) below the surface. If the same ship is floating in sea water, the bottom of the ship (ds) below the surface. Given that the density of sea water is greater than the density of fresh water, which one of the following statements is correct?

The correct answer is ds<df

Homework Equations

Buyont Force = B=pVg

The Attempt at a Solution

B=(pf)(Vf)g=(ps)(Vs)(g)

Vf>Vs ---> How was this simplified to give the correct answer. I am confused.
df>ds

 

[Doc Al]

Vf>Vs ---> How was this simplified to give the correct answer. I am confused.
df>ds

How does volume of water displaced relate to depth below the surface?

 

[dab353]

Volume relates to depth below the surface in the equation (Pressure under water: P=ρ•g•h ; where ρ is the density of water m/V and h is the depth of water)

 

[Doc Al]

Volume relates to depth below the surface in the equation (Pressure under water: P=ρ•g•h ; where ρ is the density of water m/V and h is the depth of water)

That equation describes the pressure beneath the surface of a fluid. What I asked for was much simpler. If a ship displaces a greater volume (Vf > Vs, say), what can you say about the depth of its bottom beneath the surface? (It's an easy question--don't over think it.)

 

[dab353]

That they are proportional. I am still confused as to how from the Buoyant force equation we were able to come up with the result of Vf being greater then Vs.

 

[Doc Al]

That they are proportional. I am still confused as to how from the Buoyant force equation we were able to come up with the result of Vf being greater then Vs.

Ah, now I understand your question.

I think you understood this:
(pf)(Vf)g=(ps)(Vs)(g)

Now just rearrange as ratios, so that (pf)/(ps) = ?

How? Divide both sides by g, then by Vf, then by ps.

 

[dab353]

So if the density of Ps is greater then Pf, and not knowing by how much; how exactly would I set up the ratio? Also the ratio of Vs and Vf --> Would it be something like this? [(Pf)/(Ps)] [(Vf)/(Vs)]=

 

[Doc Al]

So if the density of Ps is greater then Pf, and not knowing by how much; how exactly would I set up the ratio?

Start with the equation I gave in the last post. (Which was from your first post.)

Then do each of the three steps I outline.

1) Divide both sides by g
... and so on.

 

[dab353]

I am more of a visual learner as to where what goes. Still confused, but i'll ask someone from my department at school. Thanks!