Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_167

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The solid concrete cylinder 6 ft long and 4 ft in diameter is supported in a half-submerged position in fresh water by a cable which passes over a fixed pulley at A. Compute the tension in the cable. The cylinder is waterproofed by a plastic coating. (Consult Table D/1, Appendix D, as needed.) Problem 5/167 (a) Compute the tension in the cable ● Calculation Process 1. Present Final Formula: From the vertical equilibrium of the cylinder, the tension in the cable must balance the net downward force (weight minus buoyancy). Where: is the weight of the cylinder. is the buoyant force. is the total volume of the cylinder, and for a half-submerged cylinder. 2. Substitute Values: Identify geometric and material properties from the problem and Table D/1: Radius Length Specific weight of concrete (): (from Table D/1) Specific weight of fresh water (): (from Table D/1) Calculate volumes: T T F = ∑ y 0⟹T+F − B W=0⟹T=W−F B W=γ V c F = B γ V wsub VV = sub V 2 1 r= = 2 d = 2 4 ft 2 ft L=6 ft γ c 150 lb/ft 3 γ w 62.4 lb/ft 3 V=πrL= 2 π⋅(2 ft)⋅ 2 (6 ft)= 24 π ft 3 V = sub V = 2 1 12 π ft 3 3. Partial Operations: Calculate weight () and buoyant force (): 4. Final Calculation: Substitute back into the equilibrium equation: ● Final Conclusion: The tension in the cable required to support the cylinder in a half- submerged position is approximately (or ). ✨ Final Answer Summary (a) (or ) Mecademy AI Solution · ENGProblem 5/167 WF B W= (150 lb/ft)⋅ 3 (2