The average density of the duck is ρd = 740 kg/m3, while the density of water is ρ = 1.0 x 103 kg/m3. The volume of the duck is Vd = 0.00011 m3.
(a) Express the weight of the duck, W, in terms of ρd and Vd.
(b) Calculate the numerical value of W in Newtons.
(c) Express the magnitude of the buoyant force, F, in terms of ρ and the volume of water that the duck displaces, Vw.
(d) Express the volume of the duck in water, Vw, in terms of ρ, ρd and Vd.
(e) Calculate the numerical value of the volume of the duck in water, Vw in m3.
Im not quite sure where to go with this problem so any help would be greatly appreciated. Thank you in advance!
2 Answers

ρᵤ = 740 kg/m³
Vᵤ = volume of duck = 0.00011 m³
mass = volume x density = Vᵤ x ρᵤ = 0.00011 x 740 = 0.0814 kg
W = weight = mg = Vᵤρᵤg = 0.0814 x 9.81 ~= 0.799 N
iii) the buoyant force F upwards = weight of displaced liquid = Vᵥᵥρᵥᵥg
iv) since the duck floats(vertical equilibrium) this upward force F = duck’s weight = W = Vᵤρᵤg
=> Vᵤρᵤg = Vᵥᵥρᵥᵥg
=> Vᵥᵥ = Vᵤρᵤ / ρᵥᵥ
v) Vᵥᵥ = Vᵤρᵤ / ρᵥᵥ
= 0.0814 / 1000 = 8.14 x 10^(5) m³
hope this helps

Duck In Water