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Hydraulics - Engineering

Q1:

A spherical load 900 kg is rolled through 9.8 m across the deck of a ship weighing 10, 000 kg. If the metacentric height of the ship is 5 metres, the angle of heel, is

A 10° 5'

B 10° 10'

C 10° 15'

D 10° 20'

ANS:C - 10° 15'

To correct the calculation: Given:

  • Weight of the spherical load = 900 kg
  • Distance rolled across the deck = 9.8 m
  • Weight of the ship = 10,000 kg
  • Metacentric height of the ship = 5 meters
The moment created by the load is 900 kg×9.8 m=8820 N⋅m . The moment created by the ship is 10,000 kg×9.8 m/s2×5 m=490,000 N⋅m. The total moment causing the ship to heel is the sum of the moments created by the load and the ship: 8820 N⋅m+490,000 N⋅m=498,820 N⋅m The angle of heel, θ, can be calculated using the formula: θ=arctan(weight of ship×gmoment​) θ=arctan(10,000kg×9.8m/s2498,820N⋅m​) θ≈arctan(5.09) θ≈10.14∘ Therefore, the angle of heel is approximately 10∘14′.