In order to check your vessel's stability, a weight of 40 tons is lifted with the jumbo boom, the boom head being 50 feet from the ship's centerline. The clinometer is then carefully read and shows a list of 5°. The vessel's displacement is 8,000 tons including the suspended weight. What will be the metacentric height of the vessel at this time?
• Inclining experiment formula for metacentric height (GM) using a known weight and observed angle of heel • How a suspended weight on a boom creates a heeling moment: weight × horizontal distance from centerline • Relationship between heeling moment, displacement (Δ), and tan(list angle)
• What is the standard formula that relates the inclining weight, its transverse distance from centerline, the vessel’s displacement, and tan of the heel angle to find GM? • How do you convert 5° to a trigonometric term in that formula, and why is tan(θ) used instead of sin(θ) or cos(θ)? • Once you compute GM from the formula, how can you quickly compare it to the multiple-choice options to see which is closest?
• Make sure you use the total displacement including the suspended weight (given as 8,000 tons) in your formula, not just the ship’s lightship or cargo weight. • Confirm you are using feet for distance and tons for weight consistently so the units in the GM result are in feet. • Double-check that you are using tan(5°) (not radians, and not sin or cos) when plugging the angle into your calculation.
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