Question

A raft of wood (ρ = 400kg/m3) of mass 120kg floats on water. How much weight can be put on the raft to make it 'just sink'

Answer 1

Given,

A wooden raft with density = $400kg/m^{3}$

Mass of raft = $120kg$

To find,

Weight that can be put on the raft to make it just sink.

Solution,

According to Archimedes' principle, a body resting in a fluid is acted upon by a force pushing upward called the buoyant force. This force is equal to the weight of the fluid that the body displaces.

For the system to be in equilibrium, the upward buoyant force should balance the weight of the wooden raft and additional weight put on it.

Calculating the buoyant force:

Volume of water displaced = mass of raft/ density of raft

                                             $= \frac{120kg}{400kg/m^{3} }\\= 0.3m^{3}$

Mass of water displaced =  volume of water*density of water.

                                             $=0.3m^{3}*1000kg/m^{3}\\= 300kg$

Buoyant force $= mg$

                        $= 300*10N\\= 3000N$

We have,

Buoyant force = Weight of raft + Extra weight

Extra weight = Buoyant force - Weight of raft

                      $= 3000N - 1200N\\= 1800N$

Therefore, $1800N$ extra weight can be put on the raft to make it just sink.