stability of a rectangular pontoon

Experiment :       Stability of a rectangular pontoon.

Aim              :  1. To compare the theoretical  and experimental values of the metacentric height.

                         2. To verify that the position of the metacentre is independent of the position of

                              the centre of gravity.  

                          For a rectangular pontoon floating in water.

Apparatus    :      Rectangular pontoon with a horizontally adjustable weight ( jockey weight ) , 

                             vertically adjustable weight, plumb bob and an angular scale

                              Scale , Knife edge , Water tank

Theory          :       Consider a rectangular pontoon of length i, width b , weight W , with a jockey 

                               weight w1 and a vertically adjustable weight w2 floting in water.

                              The equilibrium position of the pontoon, with the jockey weight kept on the 

                              centreline is shown in figure. The centre of buoyancy B, centre of gravity G,

                               metacentre M and the submerged depth  d are also shown in figure 1 (a). 

                               

Procedure      :      The weight, length and the mass of the pontoon were measured   
                      
                     The pontoon was placed in still water.
                        
                     The vertically adjustable weight was kept at the centre.


                      The jockey weight was kept at the centre.




                                  The plumb bob was adjusted and the scale reading was set at 
                                    zero.
                                     
                                   The jockey  weight was shifted by a known distance ( 1.5 cm ) 
                                    and the   angle of θ was measured.
                                     
                                    Step was repeated for different positions of the jockey weight.




                                    The pontoon was balanced on a knife edge and the position of
                                     the centre of gravity was ditermined.                                      



                              
                                     The vertically adjustable weight was raised by 8 cm 
                                      ( y = 8cm position )  and steps 4 to 8 were repeated. 




       Calculation :   Find the metercentric height ( using theoratical value )