Question

A cylindrical buoy is 2m in diameter and 2.5m long and weight 22kN . The specific weight of sea water is 10.25kN/m^3 . (I) Show that buoy does not float with its axis vertical. (II). What minimum pull should be applied to a chain attached to the center of the base to keep the buoy vertical?

Answer 1

`GM<0`

So the bouy does not float with its axis vertical

Step-by-step explanation:

From the question we are told that:

Diameter
`d=2m`

Length
`l=2.5m`

Weight
`W=22kN`

Specific weight of sea water
`\mu= 10.25kN/m^3`

Generally the equation for weight of cylinder is mathematically given by

Weight of cylinder = buoyancy Force

`W=(pwg)Vd`

Where

`V_d=\pi/4(d)^2y`

Therefore

`22*10^3=10.25*10^3 *\pi/4(2)^2y\\\\\22*10^3=32201.3247y\\\\\y=1.5m`

Therefore

Center of Bouyance B

`B=(y)/(2)=0.26m\\\\B=0.75`

Center of Gravity

`G=(I.B)/(2)=2.6m`

Generally the equation for\BM is mathematically given by

`BM=(I)/(vd)\\\\BM=(3.142/64*2^4)/(3.142/4*2^2*0.5215)\\\\BM=0.479m\\\\`

Therefore

`BG=2.6-0.476\\\\BG=0.64m`

Therefore

`GM=BM-BG\\\\GM=0.479m-0.64m\\\\GM=-0.161m\\\\`

Therefore

`GM<0`

So the bouy does not float with its axis vertical