A cubic block submerged in water is being held partially underwater by hand. When the hand releases it, the block starts floating up. The document provides the solution to calculating the velocity of the block when it is half submerged, using equations for buoyant force, total force, and simple harmonic motion. The calculated velocity is 1 m/s.

1. There isa cubicblockwhichissubmergedina lake (picture 1).The densityof the blockishalf of
the waterin the lake,sosomeone isusinghishandto keepthe blocksubmergedinthe water.
Suddenly,he hastoanswerhisphone andreleasesthe block,andthe blockstarts floatingup
(picture 2).
Question:whatis the velocityof the blockwhenhalf of the blockissubmergedinthe water?
(g=10m/s2
,the side lengthof the blockis20cm. Neglectthe waterresistance.)

2. Solution:
h isthe heightof the submergedfractionof the block.Histhe total height.FB isthe buoyant
force. A isthe area of the block.F isthe total force on the block.
FB=ρwgAh,F=ρwgAh-ρBgAH=ρwgA(h-0.5H)
So itis a simple harmonicmotion.
WhenF=0, h=0.5H.
Therefore the equilibriumpositionisatthe waterlevel
½ kx2
= ½ mv2
k=ρwgA,m= ½ ρwAH, x=0.5H
Therefore v=√0.5𝑔𝐻=1 m/s