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# STABILITY OF FLOATING BODY

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## zuhra abd rahman

on 23 April 2014

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#### Transcript of STABILITY OF FLOATING BODY

Potential energy has minimum value

Stability of a body such as a ship which is floats in the surface of a liquid should be concern

Stability of pontoon was determined in this experiment

When a body is submerged partly or fully in a fluid, it displaces a certain amount of fluid resulting in a vertically upward force, which is exerted by the fluid on the body (Archimedes principle)

A body will float in a liquid if the weight of the body is equal to the weight of the displaced fluid

The criterion of stability of a floating body is meta-centre

According to Garde (1997), if the centre of gravity is below M, the couple of forces due to the weight and the buoyant force are clockwise. The body therefore will be stable.

If the point M is below G , the moment created will further tilt the body and the body will be in unstable equilibrium.

When M and G coincide, there will be neutral equilibrium. GM is called the height of meta-center.

Floating body may be
in stable equilibrium against
rolling when B lies considerably
below G.
Experiment was conducted in order to determine the height of meta-center by using the tilting method.

Based on the result, center of gravity increasing with decreasing meta-centric height.

When the angle of tilt increase,the meta-centric height will decrease.
Question 1: Determine the GM, using the equation GM = wx/W tan θ(angle).
Plot GM versus angle. Determine the GM when angle=0.

Based on the equation, when θangle=0
GM 1= 54.489 mm
GM 2= 63.715 mm
GM 3= 85.286 mmθ

The all of three tests shows that the height of the meta-center increases as the center of gravity decrease.
CG : 130 mm>108mm>78mm
GM : 54.489 mm<63.715 mm< 85.286 mm

Theoretically, angles of tilt of the thread due to the movement of weight to both sides should be almost the same because the pontoon mass is symmetry. However, some errors might occur during the experiment that causes the data obtained is not accurate.

Question 2: Calculate the height of the meter-center (GM) for each case.

Based on the tests, the values of GM obtained from the graph are different from the GM values calculated using the following equation:
GM = BM-BG = (1/V) - [Y-(d/2)] = (1/V) - Y + (d/2)

Given:
Mass of the horizontal weight = 0.28078 kg
Total mass of pontoon with vertical weight = 1.16567 kg
Width of pontoon = 200 mm
Length of pontoon = 350 mm
Height of pontoon = 75 mm

For test 1:

GM = [(LB^3/12) x (p/W)] – Y + (d/2)

= [(350)(200³)(1 x 10⁻⁶)/(12 x 1.16567)] - 130 + (20/2)
= 80.171mm
For test 2: GM= 103.171mm
For test 3: GM= 133.671mm
Question 3: Does the location of the meter-center depend on the location of
the center of gravity?
The meter-center position is depend on the position of the center of gravity of the body.

Question 4: Does the location of the meter-center vary with the angles of tilt?

The position of meta-centre will change and according to the angle
from the equation:
Meter-center position, GM = wx/W tan⁡θ(angle)

The position of meta-center of the body is linear with 1/tan (angle)
smaller the angle, GM become greater and vice versa

ERRORS
The pontoon pole is not connected tightly to the pontoon.

Accuracy of distance from pontoon stabilizer to the depth of pontoon base is not high.

Measurement tool is not sensitive to take the data during the experiment.

Movement of water surface is always wavy.
PRECAUTIONS
Make sure the fan and window are closed.

Make sure the eyes of the observer must parallel to the measuring apparatus.

Avoid zero error of the ruler.

Ensure the angle of tilt at zero before the horizontal weight is shift to left or right.
Thank You Dr. Sani

See u again ^^

: To determine the height of meta-center using the tilting method
Stability may be varied depends on the height of the center of gravity.
Result obtained can be compared with calculation methods result.
Related to head of meta-center (GM).
Meta-center can be defined when a floating body is given small displacement.

: To prepare different center gravity by take out the horizontal
weight and fix the height of the vertical weight on the mass of
pontoon.
: Observe the angle of tilt of the thread
: Count the height of the meta-center

: Gain more knowledge on the stability of pontoon
: Understand the stability of floating body
: Determine the condition of the floating body
: Relate the application of the concept with future career

Pontoon
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