Solving a Raft Submersion Problem - Edge Needs a Second Opinion

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In summary, a man weighing 80 kg jumps on a raft with a surface area of 5.8 m^2 and a volume of .60 m^3. To find the percentage of the raft submerged, the weight of the raft and man must equal the buoyant force. Using the equation (440)g = (1000)(V)(g), the displaced volume of water is found to be .44. However, this is the volume, not the percentage. Dividing the displaced volume by the volume of the raft (.44/.6) gives the correct answer of 73%. Always keeping track of units can help avoid simple errors.
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edge
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Okay, I've worked this problem and have what I think is the correct answer...I just want to get a second opinion because I am a little bit unsure.

A raft is constructed of wood having a density of 600 kg/m^3. It's surface area is 5.8 m^2, and its volume is .60 m^3.

- A 80 kg man jumps on the raft. After a while, the man + raft system becomes stable. What is the % of the raft submerged?

My work:

I assume that at equilibrium the weight of the raft + man must equal the bouyant force.

I use mass = (density)*(volume) to get the mass of the raft (360 kg) then add 80 kg to get the new mass, 440 kg. Now I take that mass times gravity to get the weight. And set that equal to the bouyant force of (density of water)*(volume displaced)*(gravity). It looks like this:

(440)g = (1000)(V)(g)
so 440/1000 = v
that gives me .44 as the displaced volume of water.
This is where my question arises. Is 44% the amount of the raft submerged? Or do I then need to divide the displaced volume by the volume of the raft (.44/.6) to get .73 or 73%?

If I've worked it wrong please let me know but I think I've done it correctly...I'm just unsure which of the 2 answers is the correct one.

Thanks!
-edge
 
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  • #2
It's asking for the percentage of the raft that is submerged, not the volume, so the answer is 73%.

If you keep track of units, you can check because percentages should always be unit-less.
 
  • #3
Awesome, thanks. Silly me, simple errors...they kill me. Thanks for the help!
 

1. How do I know if I have a raft submersion problem?

A raft submersion problem occurs when the edge of the raft dips below the surface of the water. This can be visually observed or by measuring the depth of the edge compared to the rest of the raft.

2. What are the potential causes of a raft submersion problem?

Some potential causes of a raft submersion problem could be uneven weight distribution, overloading the raft, or a leak in the raft's structure. It could also be due to rough waters or strong currents pushing against the raft.

3. How can I solve a raft submersion problem?

The first step is to evenly distribute the weight on the raft and make sure it is not overloaded. If the problem persists, check for any leaks and patch them if necessary. You can also try adjusting the position of the raft in the water to avoid rough waters or currents.

4. Do I need a second opinion when trying to solve a raft submersion problem?

It can be helpful to have a second opinion when trying to solve a raft submersion problem, especially if you are uncertain about the cause or solution. Another person may be able to provide a different perspective or offer additional solutions.

5. How can I prevent a raft submersion problem from occurring in the future?

To prevent a raft submersion problem, make sure to evenly distribute weight on the raft, avoid overloading it, and regularly check for any leaks. It is also important to be aware of the water conditions and avoid rough waters or strong currents that could push the raft's edge below the surface.

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