A rectangular prismatic box, which is floating on water has a length, L=1200 mm,

Question

A rectangular prismatic box, which is floating on water has a length, L=1200 mm, breadth, b=800 mm, height, h=500 mm, and a mass of 52.00 kg. When the box is loaded with the suspended hexagonal mass, the depth of its immersion is 300 mm, and when the mass is placed inside the box, the depth of immersion increases to 360 mm (Figure 3). The specific weight of water=9810 N/m3. The volume and weight of the string is negligible. What is (a) the volume, and (b) the specific weight of the hexagonal mass?

Explanation / Answer

F= ?gv

Fb=W (weight of floating body)

3. The attempt at a solution

Weight of Box:

W=52x9.81= 510.12 N

W=Fb=?gv

v=W?g

v= 510.129810= 0.052m3

v=dx1.2x0.8

d=0.0521.2x0.8=0.0541m = 54.166mm ? submergen due to the self weight of the box.

From First Case (LHS):

300-54.166= 245.83mm ? submerged due to weight pf hexagon

From Second Case (RHS):

Fb=?gv

v= 1.2x0.8x0.36=0.3456m3

Wtotal= Wbox + Whexagon

Wtotal=1000x9.81x0.3456=3390.3N

Whexagon= Wtotal - Wbox

Whexagon= 3390.3 - 510.12= 2880.2 N

a)

v=W?g

v=28809810 =0.29m3

b)

?=MassVolume

Mass=28809.81= 293kg

?=2930.29=1012.34

?= 1012.34x9.81=9931.03Nm 2

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