A barge floating in fresh water (rho = 1000 kg/m^3) is shaped like a hollow rectangular prism with base area A = 550 m^2 and height H = 2.0 m. When empty the bottom of the barge is located H0 = 0.55 m below the surface of the water. When fully loaded with coal the bottom of the barge is located H1 = 1.35 m below the surface.
A = 750 m²
H₀ = 0.55 m
Hᵢ = -1.1 m
(A) Write an equation for the buoyant force on the empty barge in terms of the known data.
(B) Determine the mass of the barge in kilograms.
A ) When empty , H₀ length of barge is inside water .
volume of barge inside water = A x H₀
Weight of displaced water = AH₀ x ρ x g
Buoyant force = weight of displaced water = AH₀ ρg
B) It should balance the weight of barge
Weight = buoyant force
Weight = AH₀ ρg
mass of barge = weight / g
weight / g = AH₀ ρ
= 550 x .55 x 1000
= 302500 kg