Question

A raft of wood (density $600\mathrm{g}/{\mathrm{m}}^3$) of mass $120\mathrm{kg}$ floats in water. How much weight can be put on the raft to make it just sink?

Answer 1

Step 1: Given data

Density of wood, ${\rho }_{wood}=600\mathrm{g}/{\mathrm{m}}^3=0.6\mathrm{kg}/{\mathrm{m}}^3$

Mass of raft of wood, $m=120\mathrm{kg}$

Step 2: Formulas used

Density of an object, $\rho =\frac{m}{V}$, where $m$ is the mass and $V$ is the volume of the object.

Step 3: Calculate the mass needed to “just sink” the raft

The volume of the raft can be calculated as,

$V=\frac{m}{\rho }=\frac{120}{600}=0.2{\mathrm{m}}^3$

We know by Archimedes' principle that when an object of a certain volume is immersed in water, the same of volume water is displaced.

For a volume of $0.2{\mathrm{m}}^3$, the mass of water that will be displaced is,

$\begin{array}{rcl}{m}_{water}& =& V\times {\rho }_{water}\\ & =& 0.2\times {10}^3\left[\because {\rho }_{water}=1000\mathrm{kg}/{\mathrm{m}}^3\right]\\ \therefore m_{water}& =& 200\mathrm{kg}\end{array}$

So, the additional weight the raft can support $=m_{water}-m=200-120=80\mathrm{kg}$

Therefore, the additional weight that can be put on the raft to make it just sink is $80\mathrm{kg}$.