Calculate Raft Buoyancy Depth | Density, Volume & Pressure Formula

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In summary, when a raft with a surface area of 5.5 m^2 and a volume of 1.5 m^3, made of wood with a density of 625 kg/m^3, is placed in fresh water with a density of 1000 kg/m^3, it will be submerged to a depth of 0.9375 meters. The calculation is found by using the equation m_wg = ρgh, where m_w represents the mass of the wood and h represents the height of the raft submerged under water. It is important to properly substitute and rearrange the equation to ensure accuracy in the calculation.
  • #1
Jbreezy
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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
 
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  • #2
Check your calculation.
625x5.5x1.5x9.8 = 5.5xhx1000x9.8
Find h.
 
  • #3
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
 
  • #4
No I didn't . Is it the right height though?
 
Last edited:
  • #5
Calculate h from my post#2. What is the value of h?
 
  • #6
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?
 
  • #7
Put the unit. That is the correct answer.
 
  • #8
What? I know what you mean put the unit but what did I do wrong?
 
  • #9
h = 0.9375 m.
 
  • #10
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?
 
  • #11
Show your calculation. How did you get your answer?
 
  • #12
(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
 
  • #13
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.
 
  • #14
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
 
  • #15
You are welcome.
 

FAQ: Calculate Raft Buoyancy Depth | Density, Volume & Pressure Formula

1. What is the Raft Buoyancy Problem?

The Raft Buoyancy Problem is a scientific concept that explores the relationship between the weight and volume of a raft and its ability to float on water.

2. How does the density of the raft affect its buoyancy?

The density of the raft, which is determined by its material and construction, affects its buoyancy by determining how much water it displaces. A denser raft will displace more water and have greater buoyancy.

3. What factors affect the buoyancy of a raft?

The main factors that affect the buoyancy of a raft are its weight, volume, and density. Other factors such as the shape and distribution of weight on the raft can also impact its ability to float.

4. How can the Raft Buoyancy Problem be solved?

The Raft Buoyancy Problem can be solved by using the principles of fluid mechanics and Archimedes' principle. By calculating the weight and volume of the raft, the density can be determined and its buoyancy can be predicted.

5. How can the Raft Buoyancy Problem be applied in real life?

The Raft Buoyancy Problem has practical applications in various fields, including shipbuilding, marine engineering, and water sports. It can also be used in disaster management to design and test the buoyancy of life rafts and other emergency floatation devices.

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