Answer to Question #202703 in Mechanical Engineering for Lihle

Question

A barge with an elliptical waterline has vertical sides. The barge has a length and width of 225m and 19,5 m respectively. It has a draught of 12,5 m in a fresh water canal. The centre of gravity is 10,5 below the deck and the side have a height of 18m. It then sails out to sea.,with a water density of 1028 kg/m^3. A sudden storm causes two 27-ton containers to move 14m across the deck of the barge. Determine the angle of tilt caused by this.

Answer 1

center of gravity on horizontal top surface = 112.5m length and 9.75m width

centre of gravity = 11.5m length, 9.75m width, 10.5m height.

Volume of barge = 225m × 19.5m × 18m = 78975m³

Volume of water displaced = 225m × 19.5m × 12.5m = 54843.75m³

Volume of barge below cog = 225m × 19.5 × (18-10.5)m = 32906.25m³ (below water)

Volume of both half sides of the barge below cog = 32906.25/2 = 16453.125m³

mass of both half sides

16453.125m³ × 1028kg/m³ = 16913812.5

mass of half side with container = 16913812.5 + 54000 = 16967812.5

$\theta = tan^{-1}\dfrac{16967812.5}{16913812.5} =0.79°$