For this question you may wish to use the fact the buoyancy force experienced by an...

  

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For this question you may wish to use the fact the buoyancy force experienced by an object is equal to the weight of the fluid that it displaces (Archimedes Law). Figure Al shows the triangular cross-section of the hull of a canoe that has length 3 m ('into the paper'). Assume that the canoe has a uniform hull cross-section as drawn in the figure and that it has two transverse beams (along its 3 m length) to give it rigidity. Also drawn in the figure is an outrigger that gives the canoe stability. Take gravitational acceleration to be 10 m/s² and the density of fresh-water to be 1000 kg/m². h BEAM 30¹ 30 CANGE HULL OUTRIGGER Figure A1 OUTRIGGER FLOAT (a) Ignoring the buoyancy contribution of the outrigger float, show that the draught at which the canoe floats is h 0.34 m when the canoe is used in fresh-water and it has total mass (canoe plus load) of 200 kg. (6 marks) (b) If the canoe enters salt-water (that has a density higher than that of fresh water), how does the value of the draught change? (2 marks) (c) Determine the compressive force in each of the two beams due to the hydrostatic pressure loading on the hull. (Hint: Consider the decomposition of the overall hydrostatic-pressure force into its horizontal and vertical components.) (7 marks) (d) Explain why is it correct to use the gauge pressure as opposed to the absolute pressure when determining the force in Part (c). (e) Explain (using sketches if helpful) how the outrigger stabilises the canoe to both clockwise and anti-clockwise rotations (roll) when the canoe is subjected to wave disturbances from the side. (6 marks) For this question you may wish to use the fact the buoyancy force experienced by an object is equal to the weight of the fluid that it displaces (Archimedes Law). Figure Al shows the triangular cross-section of the hull of a canoe that has length 3 m ('into the paper'). Assume that the canoe has a uniform hull cross-section as drawn in the figure and that it has two transverse beams (along its 3 m length) to give it rigidity. Also drawn in the figure is an outrigger that gives the canoe stability. Take gravitational acceleration to be 10 m/s² and the density of fresh-water to be 1000 kg/m². h BEAM 30¹ 30 CANGE HULL OUTRIGGER Figure A1 OUTRIGGER FLOAT (a) Ignoring the buoyancy contribution of the outrigger float, show that the draught at which the canoe floats is h 0.34 m when the canoe is used in fresh-water and it has total mass (canoe plus load) of 200 kg. (6 marks) (b) If the canoe enters salt-water (that has a density higher than that of fresh water), how does the value of the draught change? (2 marks) (c) Determine the compressive force in each of the two beams due to the hydrostatic pressure loading on the hull. (Hint: Consider the decomposition of the overall hydrostatic-pressure force into its horizontal and vertical components.) (7 marks) (d) Explain why is it correct to use the gauge pressure as opposed to the absolute pressure when determining the force in Part (c). (e) Explain (using sketches if helpful) how the outrigger stabilises the canoe to both clockwise and anti-clockwise rotations (roll) when the canoe is subjected to wave disturbances from the side. (6 marks)