Physics Raft - Archimedes' Principle?

Question

A solid, square pinewood raft measures 5.0 m on a side and is 3.50 m thick. What is the total mass of swimmers that the raft can carry and float with its top surface at water level?

Answer 1

The payload weight W is the difference between a max buoyant Fb and weigh tof the raft W(raft)
W=Fb(max)- W(raft)
The buoyant force equal to the weight of the max volume V of water of density p the raft can possibly displace. And since weight=mg and m=pV we have
Fb=gp(H20)V
Its weight is similarly forund to be
W(raft)=gp(pine)V
W=gp(H20)V - gp(pine)V
W=gV(gp(H20)V - gp(pine))
p (H2O)= 1000 kg/m^3
p(pine )=?
V=5x5x3.5 (m^3)
g=9.81 m/s^2

Have fun