Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_136

⚡ Mecademy AIENG정역학 · ch5  Problem Statement A cable weighing 25 newtons per meter of length is suspended from point A and passes over the small pulley at B. Calculate the mass m of the attached cylinder which will produce the sag of 9 m. Also determine the horizontal distance from A to C. Because of the small sag-to-span ratio, use the approximation of a parabolic cable. Problem 5/136 (a) Mass of the attached cylinder 1. Formula: For a parabolic cable approximation, the vertical distance from the vertex to a support is related to the horizontal distance from the vertex by: The tension at any point is: At point , the tension is provided by the weight of the cylinder: . 2. Substitution: From the diagram: Total horizontal span . Vertical distance from the lower support to the lowest point (sag) is . Vertical distance from the higher support to support is , so the height of relative to is . Weight per unit length . Acceleration due to gravity . From the parabolic relations: m h x h= 2T 0 wx 2 x T= T +(wx) 0 2 2 BT = B mg L=x + A x = B 100 m ACh = A 9 m BA12 m BCh = B 9+12=21 m w=25 N/m g= 9.81 m/s 2 = x B x A = h B h A ≈ 21 9 0.65465 Substituting : Now calculate the horizontal tension : 3. Calculation: Tension at B: Mass 4. Result: ● Final Conclusion: The mass of the attached cylinder required to produce the specified configuration is approximately . (b) Horizontal distance from A to C 1. Formula: The horizontal distance from the left support to the lowest point is . From the s