Calculate Raft Buoyancy Depth | Density, Volume & Pressure Formula

[Jbreezy]

Homework Statement

A raft is constructed of wood having a density of 625 kg/m^3. It's surface area is 5.5 m^2, and it's volume is 1.5 m^3. When the raft is placed in fresh water (denistiy = 1000 kg/m^3), to what depth, h, is the raft submerged under the water?

Homework Equations

P = ρgh
Where P = pressure, ρ = density

The Attempt at a Solution

P = ρgh
Sub, F /A = P
F/A = ρgh

F = mg (g will cancel when we rearrange to solve for h)
m here is the mass of wood which is the density of wood times it's volume.
So, V x ρ_wood = M_wood.
Putting this all together.
And solving for h

M_wood / ( A(ρ_h20) = h
With values I got.

.1704 meters.

What do you think? Right wrong please confirm my process.
Thanks

 

[rl.bhat]

Check your calculation.
625x5.5x1.5x9.8 = 5.5xhx1000x9.8
Find h.

 

[Jbreezy]

I didn't get the same answer when I substituted h back into 625x5.5x1.5x9.8 = 5.5xhx1000x9.8. The equations were not equivalent. Where did I mess up?Thanks

 

[Jbreezy]

No I didn't . Is it the right height though?

 

[rl.bhat]

Calculate h from my post#2. What is the value of h?

 

[Jbreezy]

625x5.5x1.5x9.8 = 5.5xhx1000x9.8

625 x 5.5 x 1.5 x 9.8/5.5 x 1000 x 9.8 = h
h = I got .9375?

 

[rl.bhat]

Put the unit. That is the correct answer.

 

[Jbreezy]

What? I know what you mean put the unit but what did I do wrong?

 

[rl.bhat]

h = 0.9375 m.

 

[Jbreezy]

I know the unit. I was just asking from my original set up what did I do wrong? I don't understand why my setup is wrong?

 

[rl.bhat]

Show your calculation. How did you get your answer?

 

[Jbreezy]

(1.5 m^3 x 625 kg/ m^3 ) / (5.5m^2 x 1000 kg/m^3) = .1704m

? This is what I'm asking why is this the wrong approach to the problem?
Mass of wood / area times density of water
Thanks

 

[rl.bhat]

Mass of the wood = density of the wood x area of the raft x height of the raft. In your calculation, you have left the area.

 

[Jbreezy]

I think I just used the wrong equation well sort of.
I have F/A = ρgh
Should be m_wg = ρgh
m_w = mass of wood.
Because if I do F/A then I have an extra multiplication by 1/A. In your equation that cancelled.

Yeah thanks

 

[rl.bhat]

You are welcome.