How Do You Calculate Minimum Height for a Steel Boat to Float?

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To calculate the minimum height for a steel boat to float, the weight of the boat must equal the weight of the water it displaces. The boat's weight consists of the bottom's weight and the total volume of the sides multiplied by the density of steel and gravitational acceleration. The equation hmin = Mass / (Pf * A) is used, where Pf is the density of water and A is the area of the boat's base. The challenge lies in accurately determining the mass of the boat, which involves understanding the volume of the sides and the density of the materials. Properly balancing these equations is crucial for solving the problem effectively.
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Problem, again.. The bottom of a steel "boat" is a 7.00 m\times 9.00 m\times 5.00 cm piece of steel (Psteel=7900). The sides are made of 0.540 cm-thick steel.
What minimum height must the sides have for this boat to float in perfectly calm water?

Question- How the heck did the person in previous post get that big long equation?

My books says the hmin=Mass/Pf*A.

Im having trouble differing the Mass. I tried to find it from the equation Pavg=M/AH. 7900=x/5*10*.02...

Appreciate your help, this chapter is killing me.
 
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The boat displaces a weight of water equal to its own weight.

The left side of that equation is equal to the weight of the boat.

Weight of bottom + [total volume of the sides(2h(L+W))][density of the steel][g]

The right side is the weight of the water displaced by the boat, which is the volume of the boat times the density of water, times g.
 
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