Question

Three solid objects (A, B, and C) are placed in water. The objects each have constant densities of 160, 260, and 745 kg/m3, respectively. a.) How do you immediately know all three objects will float? b.) Find the fraction of the volume submerged for each object. A: B: C: c.) If object C has the dimensions (length=8 m, width=7 m, height=3 m), how far does this object stick out of the water when floating (in this orientation)? m

Answer 1

(a)

The density of water is 1000 kg/m³. All the three objects density is less than water density.

Hence, they will float.

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( b )

The bouyant force must be equal to weiht of object

m.g = .V .ρ.g
A)
ρ_a =160 kg/m³

For same mass, the volume of fluid displaced is invesely proportinal to density

V1_imm / V ₁ = ρ_a/ρ_w = 160 / 1000 = 0.16 (16% submerged)

B)

ρ_a =260 kg/m³

Ratio of immersed volume to volume of object

V_{2imm /} V ₂ = ρ_b/ρ_w = 260 kg/m³ / 1000 = 0.26 (26% submerged)
C)

Similarly
V3imm/V3 = ρc/ρw = 745 kg/m³ / 1000 = 0.745 (74.5 % submerged)

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c)
Volume V₃ = ( 8 ) ( 7 ) ( 3 ) = 168 m³ and V_3imm = V₃ ( 0.745 ) = 125.16 m³.

The volume above the water is

V_3ab = V₃ - V_3imm = 42.8 m³

stick out of the water for h = V_3ab / ( 8 ) ( 7 ) = 0.765 m