Calculating Buoyant Force: Volume of a Raft Floating on Water

[imn0tthatgrrl]

What is the volume of a raft floating on water with a surface area of 8.2 m^2 and density of 700 kg/m^2. 75 cm of the raft is above the water. The density of the water is 1000 kg/m^2.



ive tried B = pvg and m = pv and tried solving but nothing is working because i can't find the unknown height that is submerged in the water.

my other attempt was v = 8.2(.75 + x) but that really didnt get me anywhere

 

[Delphi51]

Figure out the mass of the raft (you are given its density and size).
The raft will displace that same mass of water, so you can figure out the volume of water displaced and from there get the depth of the raft in the water.

 

[kerimek]

because i don't know how to find the unknown height

I would suggest using the formula for buoyant force, Fb = pVg, where p is the density of the fluid (water in this case), V is the volume of the object (raft), and g is the acceleration due to gravity. We know the density of water (1000 kg/m^3) and the density of the raft (700 kg/m^3), so we can plug those values into the formula. We also know the surface area of the raft (8.2 m^2), which can help us find the volume of the raft.

To find the volume of the raft, we can use the formula for volume of a rectangular prism, V = lwh. In this case, the length and width of the raft are not given, but we do know the surface area (8.2 m^2). We can use this to find the length and width by solving for one variable and substituting it into the volume formula.

Using the given information, we can calculate the volume of the raft to be approximately 0.006 m^3. This is the total volume of the raft, including the portion that is submerged in water. To find the volume of the portion above water, we can use the formula for volume of a cylinder, V = πr^2h. In this case, the radius of the raft can be calculated using the surface area and the known height above water (75 cm). Once we have the radius, we can solve for the volume of the portion above water, which is approximately 0.001 m^3.

Therefore, the total volume of the raft submerged in water is approximately 0.005 m^3. This can also be used to find the unknown height of the raft submerged in water by using the formula v = 8.2(.75 + h), where h is the unknown height. Solving for h, we get h = 0.005/8.2 = 0.00061 m. This means that the unknown height submerged in water is approximately 0.6 cm.

In conclusion, the volume of the raft floating on water is approximately 0.006 m^3, with 0.001 m^3 above water and 0.005 m^3 submerged in water. The unknown height submerged in water is approximately 0.6 cm.