Question

The bottom of a steel "boat" is a 4 m ✕ 18 m ✕ 2 cm...

The bottom of a steel "boat" is a 4 m ✕ 18 m ✕ 2 cm piece of steel (ρsteel = 7900 kg/m3). The sides are made of 2.00 cm thick steel. What minimum height must the sides have for this boat to float in perfectly calm water? (Answer is not 22.6 cm)

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Answer #1

Volume due to the base: = 4x18x0.02 cu.m=1.44 cu. m
Volume due to the side walls: =2x((4xhx0.02)+(18xhx0.02))=2x(22xhx0.02) = 0.88h cu. m

Mass of the boat=(1.44+0.88h)x7900 Kg

Find the mass of the displaced water.
Volume of the displaced water =volume of the base of the boat+volume of the wall(considering closed)
=1.44+(hx4x18)=1.44+72h
Mass of the displaced water=(1.44+72h)x1000

These two must be equal
So, (1.44 + 0.88h)x7900=(1.44+72h)x1000

(1.44 + 0.88h)=(1.44+72h)0.126

1.44+0.88h=0.182+9.072h

1.258=8.192h
=>h=0.153 m=15.35cm

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