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.

Randomized Variables

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.

Question

Physics

Flopsy

18 March, 12:28

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.

Randomized Variables

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.

+2

Answers (1)

Know the Answer?

Franklin Stevenson · Answer 1

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