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

[CaityAnn]

Previous Thread
https://www.physicsforums.com/showthread.php?t=55809

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.

 

[Teegvin]

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.