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BACKGROUND
A body while floating in a liquid is provided with a small angular displacement, it starts oscillating about a fixed point, known as metacenter. This metacenter point is considered as fixed for the little angular heel, whereas it varies for sizeable angular heel. Metacentric height is a parameter to measure the static stability of a floating body, as it is defined as a distance between the center of gravity of a body and its metacenter. It has a direct relationship with the stability of the body. So, larger the metacentric height, more is the stability.1
The formula gives the metacentric height of a floating body:
GM = [ (w.d) / {(W+w)tanθ }]
Where, W = Weight of the floating body,
w = Weight of the added body,
θ = Angular displacement of the floating body,
d = Hanging distance from the body, and
GM = Metacentric height of body.
There are three equilibriums of a floating body:
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Unstable Equilibrium
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Neutral Equilibrium
In a stable equilibrium, a body returns to its original position via applied angular displacement. The condition for stability of a floating body is that the metacenter point should be above of its center of gravity. Similarly, in an unstable equilibrium condition, the body doesn’t return to its initial position. Also, its metacenter point is below the center of gravity of the floating body. While, in the neutral equilibrium condition, the metacenter coincides with the center of gravity.2 So, the body remains in an ideal state even after giving a small angular displacement.
The main purpose of this experiment is to determine the metacentric height of a floating body.
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REQUIREMENTS
Materials: Metacentric height Apparatus
Water Tank
Weights
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PROCEDURE
First of all, check the level of water without the floating body, and then again with the floating body. Now, by using the Archimedes’ Principle which states that the weight of the body is equal to the weight of the displaced fluid, calculate its mass. After this, adjust the pointer to zero on the protractor scale. Now, Put weights in gram on any side of the hanger and measure the distance from the center. Record the pointer’s tilt in the protractor. Repeat the same procedure about ten times by varying the distance to get the right metacentric height of floating body.
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CONCLUSION
The procedure of determination of metacentric height, as well as its application to the stability of floating bodies, has been discussed. For a stable equilibrium, the metacentric height must be above of its center of gravity.
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REFERENCES
- J. M. a. J. Kliava, “Metacenter and ship stability,” American Journal of Physics, vol. 78, no. 7, 2010.
- Y. M. J. C. S.H.Jeon, “Dynamic response of floating substructure of spar-type offshore wind turbine with catenary mooring cables,” Ocean engineering, vol. 72, no. 3, pp. 356-364, 2013.
