ACKKK!! Of all the difficult and complex problem solving questions in physics, s

Question

ACKKK!! Of all the difficult and complex problem solving questions in physics, something as simple as buoyancy force still manages stump me.

Logs of density 600 kg/m^3 are used to build a raft. What is the weight of the maximum load that can be supported by a raft built from 400 kg of logs? Answer to be given as MASS of max load (in kg).

What I thought/tried:

Calculated total volume of raft (0.66666667 m^3) and volume of submerged portion (if density of water is ~1000 kg/m^3, then 60% of raft is submerged, so vol of submerged portion = 0.4 m^3)

Calculated total weight of raft, weight of submerged portion, and weight of unsubmerged portion, knowing that buoyancy force = weight of displaced fluid.

My initial thinking was that if the buoyancy force = total weight of raft (3920 N) in order for it not to accelerate up or down, then the max weight would be equal to the buoyancy force. I realize that's probably an incorrect assumption, since pressure increases with depth. I tried answering with the mass of the unsubmerged portion, the submerged, and the total mass of the raft. All incorrect.

No idea how to proceed. Please help!!!

Explanation / Answer

Total weight lifted by buoyancy = (volume of raft)*(density of water)*g

total weight =weight of raft +additional load =( 400 + x)g

so, using above equations

(400 + x)g = (0.666)(1000)g

400+ x= 666.67

x = 266.67 kg(maximum additional load raft can hold by just completely submerged in water ie without sinking.)

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