The bottom of a steel “boat” is a 6.00 m by 9.00 m by 2.00 cm piece of steel(Rho steel=7900 kg/m^3.?
How do you solve this?
The bottom of a steel “boat” is a 6.00 m by 9.00 m by 2.00 cm piece of steel(Rho steel=7900 kg/m^3. The sides are made of 0.490 cm-thick steel.
What minimum height must the sides have for this boat to float in perfectly calm water?
You know that the weight of the water displaced by the boat must at least equal the total weight of the boat. Therefore, the weight of the bottom and sides of the boat must equal the weight of water equivalent to the entire volume of the boad.
Let h be the height of the boat needed to float. The volume of the boat is then 9*6*h = 54h m^3.
The density of water is 1g/cm^3, or 1000kg/m^3. So the weight of the equivalent amount of water will be 54*h*1000 = 54000h kg.
As for the steel, you know the weight of the bottom part will be 6*9*0.02*7900 = 8532 kg.
The weight of the sides will be relative to the height:
[6*0.0049*2 + (9 - 2*0.0049)*0.0049*2 ]*h*7900 = 1160.541h kg
The subtraction of the thickness is to account for the overlap at the corners of the boat, and each of them are multiplied by 2 because there are 2 sides with the same dimensions.
So now we just add up the weight oft he boat, and set it equal to the weight of the water:
8532 + 1160.541h = 54000h
Solving for h, we get the height is 0.161 meters, or 16.1 cm.
BoAT CM 09
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