A wooden raft 3 m long x 2 m wide x 20 cm thick floats on a freshwater lake. A) Determine the buoyant force? B) If the raft itself has a mass of 600 kg, how many 65-kg people could it support?

Answer 1

A.Vr=300cm * 200cm * 20cm=1.2*10^6 cm^3 = Vol. of raft.

Dr = 6*10^5g / 1.2*10^6cm^3 = 0.5g/cm^3
= Density of raft with no load.
Vb = (Dr/Dw)*Vr.
Vb = (0.5/1)*1.2*10^6 = 6*10^5 cm^3 =
Vol. below surface = Vol of water displaced.

Ww = 6*10^5cm^3 * 1g/cm^3 = 6*10^5 g. =
600kg = Wt. of water displaced. = Buoyancy force

B. Drmax = Dw = 1g/cm^3 with full load.
Drmax = (6*10^5g+x)/1.2*10^6= 1.
6*10^5 + x = 1.2*10^6 .
X = 0.6*10^6 = 600kg = max load.

# People = 600kg / 65kg = 9, max.

Answer 2

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