Question

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)

THANKS

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