Report that describe how manzana had to solve his production problem
TITLE:
THE STABILITY OF A FLOATING BODY
OBJECTIVES :
To determine determine the stability of a ontoon !ith its "enter of #ra$ity at $ario%s hei#hts& HYPOTHESIS:
The stability of a ontoon is different from its "enter of #ra$ity at $ario%s he i#hts& For floatin# body !ith bottom'hea$y is al!ays stable !hen the "enter of #ra$ity G is dire"tly belo! the "enter of b%oyan"y B and if the meta"enter ( is abo$e oint G& Ho!e$er) the body is %nstable if oint ( is belo! oint G&
INTRODUCTION:
The *%estion of the stability of a body bo dy li+e a shi floats in the s%rfa"e of the sea !ater is one of the ob$io%s si#nifi"ant& ,hether the e*%ilibri%m is stable) %nstable or ne%tral is determined by the hei#ht of its "enter of #ra$ity& In this e-eriment) the stability of a ontoon "an be determined !ith its "enter of #ra$ity # ra$ity at $ario%s hei#hts& A "omarison !ith "al"%lated stability also "an be made&
THEORY:
.onsider the re"tan#%lar ontoon sho!n floatin# in e*%ilibri%m on an e$en +eel) as sho!n in the "ross se"tion of Fi#%re /0a1& The !ei#ht of the floatin# body a"ts $erti"ally do!n!ards thro%#h its "entre of #ra$ity G and this is balan"ed by an e*%al and oosite b%oyan"y for"e a"tin# %!ards thro%#h the "entre of b%oyan"y B ) !hi"h lies at the "entre of #ra$ity of the li*%id disla"ed by the ontoon& To in$esti#ate the stability of the system) "onsider a small an#%lar disla"ement 23 from the e*%ilibri%m osition as sho!n on Fi#%re /0b1& The "en tre of #ra$ity of the li*%id disla"e by the ontoon shifts from B to / B & The $erti"al line of a"tion of the b%oyan"y for"e is sho!n on fi#%re and interse"ts the e- tension of line BG at M ) the meta"entre& The e*%al and oosite for"es thro%#h G and / B e-ert a "o%le on the ontoon) and ro$ided that M lies abo$e G 0as sho!n in Fi#%re /0b11 this "o%le a"ts in the sense of restorin# the ontoon to e$en +eel) i&e& the ontoon is stable& If) ho!e$er) the meta"entre M
lies belo! the "entre of #ra$ity G ) the sense of the "o%le is to in"rease the an#%lar
disla"ement and the ontoon is %nstable& The se"ial "ase of ne%tral stability o""%rs !hen
M
and G "oin"ides&
Fi#%re /0b1 sho!s "learly ho! the meta"entri" hei#ht GM may be established e-erimentally %sin# the ad4%stable !ei#ht 0of mass 5 1 to disla"e the "entre of #ra$ity side!ays from G & S%ose the ad4%stable !ei#ht is mo$ed a distan"e 2 x/ from its "entral osition& If the !ei#ht of the !hole floatin# assembly is W ) then the "orresondin# mo$ement of the "entre of #ra$ity of the !hole in a dire"tion arallel to the base of the ontoon is W
2 of restorin# the ontoon to e$en +eel) i&e& the ontoon is stable& If) ho!e$er) the meta"entre M
lies belo! the "entre of #ra$ityG ) the sense of the "o%le is to in"rease the an#%lar
disla"ement and the ontoon is %nstable& The se"ial "ase of ne%tral stability o""%rs !hen M
and G "oin"ides&
Fi#%re /0b1 sho!s "learly ho! the meta"entri" hei#ht GM may be established e-erimentally %sin# the ad4%stable !ei#ht 0of mass5 1 to disla"e the "entre of #ra$ity side!ays from G & S%ose the ad4%stable !ei#ht is mo$ed a distan"e 2 x/ from its "entral osition& If the !ei#ht of the !hole floatin# assembly is W ) then the "orresondin# mo$ement of the "entre of #ra$ity of the !hole in a dire"tion arallel to the base of the ontoon is / x W
2 5 & If this mo$ement rod%"es a ne! e*%ilibri%m osition at an an#le of a list
23 ) then in Fi#%re /0b1) /
G
is the ne! osition of the "entre of #ra$ity of the !hole) i&e&& If this
mo$ement rod%"es a ne! e*%ilibri%m osition at an an#le of a list 23 ) then in Fi#%re /0b1) /
G
is the ne! osition of the "entre of #ra$ity of the !hole) i&e&
