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ENGR5002 / Week 2
ENGR217 2018 Q B2Past paperOld spec ENGR2172:125 marks30 min

ENGR217 Summer 2018 Q B2[VALID] official answers

Answer ALL parts (a) - (c).

Figure B2 (b): semi-submerged block, a 12.0 m cube floating with 6.0 m submerged; G is a distance y below the geometric centre.
Figure B2 (b): semi-submerged block, a 12.0 m cube floating with 6.0 m submerged; G is a distance y below the geometric centre.
Formulas you may need
  • Buoyancy: FB=ρgVdisplacedF_B = \rho g V_{displaced} (on the formula sheet)
  • Relative density: RD=ρ/ρwRD = \rho/\rho_w (on the formula sheet)
  • Rectangle second moment: I=bd312I = \dfrac{b d^3}{12} (on the formula sheet, shape table)
  • Metacentric radius: BM=IVBM = \dfrac{I}{V}; GM=BM−BGGM = BM - BG (learn this)
  • Heel (inclining) test: GM=wxWtan⁡θGM = \dfrac{w x}{W \tan\theta} (learn this)
  • Free-surface effect: ΔGM=ρliq∑iρswV\Delta GM = \dfrac{\rho_{liq} \sum i}{\rho_{sw} V} (learn this)
  1. (a)
    To find the metacentric height in roll of his 9.9 tonne vessel, a yachtsman uses a heavy container of mass 150 kg. When placed at one side of the deck, the container causes the yacht to heel by 4.2∘4.2^\circ. The container is then moved across the deck to the opposite side, and produces a heel of 4.2∘4.2^\circ the other way. The overall width of the deck is 9.5 m. What is the metacentric height in roll?
    [8]
  2. (b)
    A block in the form of a cube of side 12.0 m floats with half its height submerged as shown in Figure B2 (b). The mass of the block is not uniformly distributed: the centre of gravity G is below the geometrical centre by a distance y. (i) What is the height of the centre of buoyancy B above the bottom of the block? (2 marks) (ii) Find the value of the metacentric radius, BM, and so find the height of the metacentre M above the bottom of the block. (5 marks) (iii) If the block is to float stably as shown, what is the minimum distance y by which the centre of gravity G is below the geometric centre of the block? (2 marks)
    [9]
  3. (c)
    A ship of displacement 7000 tonne carries oil fuel in four tanks 10.0 m long and 5.0 m broad, the tanks arranged with their length in the fore-and-aft direction (lengthwise of the ship). The specific gravity of the oil is 0.84, and the density of sea-water in which the ship is floating is 1020 kg/m31020\ \mathrm{kg/m^3}. By how much is the metacentric height of the ship reduced by the oil contained in the tanks?
    [8]