Question

The dimensions of a wooden raft (density $=150kg/m^3)$ are $3.0m\times 3.0m\times 1.0m$. What maximum load can it carry in seawater so that the plank just floats in water (density$=1020kg/m^3)$?

• A. $1350kg$
• B. $7830kg$
• C. $9200kg$
• D. $19,500kg$

Answer 1

Answer: (B)

$7830kg$

Buoyancy is the upward force that an object feels from the water and when compared to the weight of the object.

Buoyancy force can be calculated with the equation

$Fb=Vs\times D\times g$

where $F_b$ is the buoyancy force, $V_s$ is the submerged volume, $D$ is the density of the fluid the object is submerged in, and $g$ is the force of gravity.

It can also be given as the sum of the weight of the raft and the weight of the load. That is, $W_{raft}+W_{load}$ = $Fb=Vs\times D\times g$.

The weight of the raft

$W_{raft}=V_{raft}{D}_{raft}g$.

At maximum load, Volume of water displaced is equal to volume of the raft.

${max(W}_{load})=(D_{water}-D_{raft})V_{raft}g$.

=$(1020kg/m^3-150kg/m^3)(3m\times 3m\times 1m)g$

$=7830kg.$

Hence, the maximum load the raft can carry sea water so that the plank just floats in water is $7830kg.$