Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_159

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Engineering students are often asked to design a “concrete boat” as part of a design project to illustrate the buoyancy effects of water. As a proof of concept, determine the depth at which the concrete box will rest in the fresh water. The box has a uniform wall thickness of 3 in. on all sides and the bottom. Problem 5/159 (a) Determination of the submerged depth ● Calculation Process 1. Present Final Formula: Based on Archimedes' Principle, for a floating body, the weight of the body must be equal to the buoyancy force , which is the weight of the displaced fluid. Where: 2. Substitute Values: First, define the necessary constants and convert units: Specific weight of fresh water: Specific weight of reinforced concrete: (standard engineering value) Outer dimensions: Length , Width , Height Wall and bottom thickness: Calculate the volume of concrete : The inner dimensions of the open box are: Inner length: Inner width: Inner height: d d WF B W=F B W=γ ⋅ concrete V concrete F = B γ ⋅ water V = displaced γ ⋅ water (L⋅W⋅d) γ = water 62.4 lb/ft 3 γ = concrete 150 lb/ft 3 L=6 ftW=3 ftH=2 ft t=3 in.=0.25 ft V concrete L = i L−2t=6−2(0.25)=5.5 ft W = i W−2t=3−2(0.25)=2.5 ft H = i H−t=2−0.25=1.75 ft 3. Partial Operations: Total weight of the box: Buoyancy force in terms of : 4. Final Calculation: Equating weight and buoyancy: ● Final Conclusion: The concrete box will rest at a submerged depth of . ✨ Final Answer Summary (a) Mecademy AI So