A rectangular block of wood is 40cm wide, 60cm long and 30cm deep. If its relative density is 0.7kg/m^3 and it floats with its 30cm side vertical, determine: a)the length of the block above the water surface and b)the minimum force required to completely submerge the block

Answer 1

W =0.4 m , L = 0.6 m , H = 0.3 m, ρ1 is the density of wood, ρ2 is the density of the liquid,
relative density is ρ1/ ρ 2 = 0.7 (dimensionless quantity!!!)
m•g = F (buoyant)
m•g = ρ1• V•g = ρ1•W•L•H•g,
F (buoyant) = ρ2• V1•g =
= ρ2•W•L•(H-x)•g.
ρ1•W•L•H•g = ρ2•W•L•(H-x)•g,
ρ1• H = ρ2• (H-x),
x = H•( (ρ1/ ρ2) – 1) =
= 0.3•( (1/0.7) – 1) = 0.129 m.

Answer 2

F + mg=F(buoyant)
F = F(buoyant) - mg = ρ2•W•L•H•g – ρ1•W•L•H•g = W•L•H•g•(ρ2– ρ1)