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In my problem it states The bottom of a steel \"boat\" is a 7.0 m x 10 m x 3.0 c

ID: 1954022 • Letter: I

Question


In my problem it states

The bottom of a steel "boat" is a 7.0 m x 10 m x 3.0 cm piece of steel
ps=7900k/m^3. The sides are made of 0.52-cm-thick steel.

What minimum height must the sides have for this boat to float in perfectly calm
water?

I did the solution as,

I solved it as
Let h be the height of the boat needed to float.

The volume of the boat is then (10.00)(7.0)h = 70h m^3.

The density of water is 1000kg/m^3. So the weight of the equivalent
amount of water will be 70*h*1000 = 70000h kg.

As for the steel, the weight of the bottom part will be (7.00 m)(10.0m
)(0.03m )7900 = 16590kg.

The weight of the sides will be relative to the height:
[(10.0 m)(0.0053 m)2 + (7.0m)(0.0053 m)2]*h*7900 = 1396.7h Kg

i just added up the weight of the boat, and set it equal to the weight
of the water:
16590 kg.+ 1396.7hkg= 70000h kg
On Solving the above equation
h =
Solving for h, we get the height is .2418 which is 24.2 cm and i cant
figure out where i went wrong.

Explanation / Answer

Measurements of the boat is 7 m*10 m*3 cm density of the steel is s=7900 kg/m^3 thickness of sides is t =0.52 cm                                  =0.0052 m density of the water (standard value) is w=1000 kg/m^3 we know the formula density = mass/volume the mass of the bottom of the boat part is mb=density*volume                                                                =7900*7*10*0.03                                                                =16590 kg let the height of the boat to flot is =h volume of the boat is =7*10*h                                 =70h then the mass of the water is mw=density*volume                                                  =1000*70h                                                  =70000h kg The weight of the sides will be relative to the height:
[(10.0 m)(0.0052 m)*2 + (10-2*0.0052)0.0052*2]*h*7900 = 0.207891*h*7900                                                                                               =1642.345h kg weight of the boat =weight of the water 16590 kg.+ 1642.345h kg= 70000h kg h =0.2426 m    =24.26 cm

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