Question

The bottom of a steel "boat" is a 8 m ? 18 m ? 2 cm piece of
steel (*?*_{steel} = 7900 kg/m^{3}). The
sides are made of 1.60 cm thick steel. What minimum height must the
sides have for this boat to float in perfectly calm water?

____ cm

Answer #1

2 cm = 2/100 = 0.02 m

thickness of steel = 1.60 cm = 1.60/100 = 0.016 m

Now, for the boat to float in calm water -

weight = Upthrust

=> weight of the bottom plate+weight of 2 short side plates+weight of 2 long side plates=Upthrust

=> (8x18x0.02x7900x9.8) + (8x0.02xhx2x9.8 x 7900) + (18x0.02xhx2x9.8 x 7900) = Vdg

=> 222969.6 + 24774.4 x h + 55742.4 xh = 8x18xhx1000x9.8

=> 222969.6 + 80516.8 x h = 1411200 x h

=> 222969.6 = 1330683.2 x h

=> h = 0.1676 m = 16.76 cm

So, the minimum height of the boat = 16.76 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)
THANKS

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