- #1
Metalsonic75
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[SOLVED] Buoyant force on a steel boat
The bottom of a steel "boat" is a 7.00 m \times 10.0 m \times 4.00 cm piece of steel ( \rho _{{\rm steel}}=7900\;{\rm kg}/{\rm m}^{3}). The sides are made of 0.550 cm-thick steel. What minimum height must the sides have for this boat to float in perfectly calm water?
I think I have to find the point where the weight of the boat is equal to the buoyant force of the water below. So, rho_b*V_b*g = rho_w*V_w*g. I'm confused on what to plug in for the volume of the boat, though. Wouldn't it be the volume of the base (7*10*0.04) plus the volume of two sides (2*7*0.0055*h) + (2*10*0.0055*h), where h is the height of the sides? But I don't know what to plug in for V_w, the volume of the water displaced. Is it equal to the volume of the boat? I'm really not sure if my equation or variables are correct, and I would really appreciate it if someone could help me out. Thanks.
The bottom of a steel "boat" is a 7.00 m \times 10.0 m \times 4.00 cm piece of steel ( \rho _{{\rm steel}}=7900\;{\rm kg}/{\rm m}^{3}). The sides are made of 0.550 cm-thick steel. What minimum height must the sides have for this boat to float in perfectly calm water?
I think I have to find the point where the weight of the boat is equal to the buoyant force of the water below. So, rho_b*V_b*g = rho_w*V_w*g. I'm confused on what to plug in for the volume of the boat, though. Wouldn't it be the volume of the base (7*10*0.04) plus the volume of two sides (2*7*0.0055*h) + (2*10*0.0055*h), where h is the height of the sides? But I don't know what to plug in for V_w, the volume of the water displaced. Is it equal to the volume of the boat? I'm really not sure if my equation or variables are correct, and I would really appreciate it if someone could help me out. Thanks.