Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_157

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Determine the depth to which the solid oak cone will be submerged in the salt water. Problem 5/157 (a) Determine the submerged depth 1. Formula: According to Archimedes' Principle, a floating body displaces a volume of fluid whose weight is equal to the weight of the body. where is the weight of the solid oak cone and is the buoyancy force. In terms of densities and volumes: From this, the ratio of volumes is: For similar cones, the ratio of volumes is equal to the cube of the ratio of their heights (linear dimensions): 2. Substitution: From engineering reference tables (e.g., Table D/1 in common editions of the text), the typical density for oak is and for salt water is . 3. Calculation: Determine the density ratio: d d W = cone B W cone B ρ ⋅ oak g⋅V = total ρ ⋅ sw g⋅V submerged = V total V submerged ρ sw ρ oak = V total V submerged ( h d ) 3 ρ = oak 800 kg/m 3 ρ = sw 1030 kg/m 3 = ( h d ) 3 1030 800 = ρ sw ρ oak ≈ 1030 800 0.7767 Solve for the ratio of depths by taking the cube root: Calculate the numerical value: 4. Result: ● Final Conclusion: The solid oak cone will be submerged to a depth of , where is the total height of the cone. ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 5/157 = h d 3 0.7767 ≈ h d 0.9192 d=0.919h d=0.919h h d=0.919h