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?

Question

Physics

Stephany Mckay

7 November, 11:40

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?

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Popeye · 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.