Question

A wooden raft has a mass of 50 kg. when empty it floats in water (density 1000 kg/m3) with 69% of its volume submerged. what mass of sand can be put on the raft without it sinking?

Answer 1

First we find the volume of the boat.  

m*g*0.69V = 50*g 

 V = 50/(.69 * 1000) =0.072 m^-3 

 For the boat to be fully submerged the maximum buoyant force (p*g*V) must equal the total weight of boat & sand   

 p*g*V = (m + 50)*g   

 m = p*V - 50 = 1000*0.072 - 50 = 22 

 22 kg is the maximum amount of sand that can be put on before the boat sinks.