How to prove this density result?

A raft has a volume of 2.250 m^3 and a density of 380 kg/m^3. Prove it will float in sea (density 1240 kg/m^3)?

• I can't just say "raft is less dense then sea". How do I prove raft will float?

• Answer:

  show that the buoyant force on it will equal its weight the weight of the raft is 380kg/m^3 x 2.25m^3 x 9.8m/s/s = 8379 N now, for the raft to float, the seawater must provide sufficient buoyant force to support this weight; the buoyant force equals the weight of water displaced, and that equals: density of water x volume of water displaced x g now, let's see how much water has to be displaced to support 8379N of weight; if the volume displaced is greater than 2.25m^3, the volume of the raft, then the raft will sink; the volume that needs to be displaced is less than 2.25m^3, the raft will float therefore: buoyant force = 8370N = 1240kg/m^3 x 9.8m/s/s x V displaced solve for V: V = 0.689 m^3 this means the raft will float when it displaces 0.689m^3, meaning approx 2/3 of the raft is above water...note: the density you quote for sea water is high...density of sea water is approx 1030kg/m^3, the raft will still float, but that is a more realistic value for the density of sea water