Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_180

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The accurate determination of the vertical position of the center of mass of a ship is difficult to achieve by calculation. It is more easily obtained by a simple inclining experiment on the loaded ship. With reference to the figure, a known external mass is placed a distance from the centerline, and the angle of list is measured by means of the deflection of a plumb bob. The displacement of the ship and the location of the metacenter are known. Calculate the metacentric height for a 12 000-t ship inclined by a 27-t mass placed 7.8 m from the centerline if a 6-m plumb line is deflected a distance m. The mass is at a distance m above . [Note that the metric ton (t) equals 1000 kg and is the same as the megagram (Mg).] Problem 5/180 (a) Calculation of the metacentric height ● Calculation Process 1. Present Final Formula: The metacentric height is determined from the equilibrium of the heeling moment caused by shifting the mass and the restoring moment of the ship's buoyancy. The standard formula for an inclining experiment is: where: is the inclining mass. is the distance the mass is moved from the centerline. is the total displacement (total mass) of the ship. is the angle of list (heel). 2. Substitute Values: Identify the given parameters from the problem: Total displacement, Inclining mass, Horizontal distance, G m 0 d θ M GM a=0.2m 0 b=1.8M GM GM m 0 GM= W⋅tanθ m ⋅d 0 m 0 d W θ W=12000 t m = 0 27 t d=7.8 m Plumb line length, Plu