What Minimum Height Must the Sides of a Steel Boat Have to Float?

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SUMMARY

The minimum height required for the sides of a steel boat to float in calm water is calculated to be 0.398 meters. This calculation is based on the principle of buoyancy, where the weight of the displaced water must equal the total weight of the boat, which includes the bottom and the sides. The bottom of the boat measures 7.00 m x 8.00 m x 0.05 m, and the sides are constructed from 0.540 cm thick steel. The equations used to derive this height involve the volume of the boat and the density of water and steel.

PREREQUISITES
  • Understanding of Archimedes' principle and buoyancy
  • Knowledge of basic physics equations involving weight and volume
  • Familiarity with density calculations (e.g., rho-steel = 7900 kg/m³)
  • Ability to manipulate algebraic equations to solve for unknowns
NEXT STEPS
  • Study the principles of buoyancy and Archimedes' principle in detail
  • Learn about the properties of materials, specifically steel and its density
  • Explore the calculations involved in determining the center of mass for floating objects
  • Investigate the effects of varying dimensions on buoyancy and stability in marine engineering
USEFUL FOR

This discussion is beneficial for physics students, marine engineers, and anyone involved in boat design or buoyancy calculations.

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Homework Statement



The bottom of a steel "boat" is a 7.00 m x 8.00 m x 5.00 cm piece of steel (rho-steel=7900 kg/m^3.) 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

The Attempt at a Solution



I figured the water displaced must equal the weight of the boat. Then the volume of that water displaced will equal the volume of the boat. But for whatever reason I am still not getting the correct answer. Any thoughts?
 
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Your line of thinking is correct. Please show your work out.
 
I'm having trouble with this one too.

I figure, the weight of the boat is equal to the weight of the bottom plus the weight of the sides. However, one thing that is unclear is if the sides are added to the very end of the bottom, or if they are placed on top. In the later case the height of the sides, h, would really be h+thickness of the bottom? Anywho, let's say that:

Weight of boat = Vbottom*rho*g + Vsides*rho*g = 7*8*.05*7900*9.8 + (2h*7*.0054+2h*8*.0054)*7900*9.8

Weight of displaced water = Vboat*rho*g = 7*8*(h+.05)*1000*9.8

where h is the height we are looking for. Setting these two equations equal to each other and solving for h, I get h = .398. Is this correct?

Thank for your help.
 

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