Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_131

⚡ Mecademy AIENG정역학 · ch5  Problem Statement An advertising balloon is moored to a post with a cable which has a mass of 0.12 kg/m. In a wind the cable tensions at A and B are 110 N and 230 N, respectively. Determine the height h of the balloon. Problem 5/131 (a) Determination of the balloon height ● Calculation Process 1. Present Final Formula: For a catenary cable (where the weight is distributed along the length), the tension at any point is directly proportional to its vertical distance from the directrix: where is the weight per unit length. The height difference between two points and is therefore: 2. Substitute Values: First, calculate the weight per unit length using the given mass per unit length and the acceleration due to gravity : Now, substitute the known tensions and : 3. Partial Operations: Calculate the tension difference and then the final height: Tension difference: Division by weight per unit length: h Ty T=wy whA B h=y − B y = A w T −T BA w μ=0.12 kg/mg= 9.81 m/s 2 w=μ⋅g=0.12 kg/m× 9.81 m/s= 2 1.1772 N/m T = A 110 NT = B 230 N h= 1.1772 N/m 230 N−110 N ΔT=230−110=120 N h= 1.1772 120 4. Final Calculation: ● Final Conclusion: The height of the balloon is approximately . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 5/131 h=101.9368... m h101.9 m h=101.9 m