Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_28

⚡ Mecademy AIENG정역학 · ch3  Problem Statement Cable passes over the small ideal pulley without a change in its tension. What length of cable is required for static equilibrium in the position shown? What is the tension in cable ? Problem 3/28 (a) Tension in cable 1. Formula: For the small ideal pulley to be in static equilibrium, the sum of the forces acting on it must be zero. The tension in cable is constant and equal to the weight it supports, . Let be the angle of cable with the horizontal. 2. Substitution: Substitute : 3. Calculation: Calculate the components of tension : 4. Result: ● Final Conclusion: The tension in cable required for equilibrium is . (b) Length of cable ABC CDT CD TCD C AB T = AB 50 lbθCD F = ∑ x Tcosθ−T cos45= AB ∘ 0 F = ∑ y Tsinθ+T sin45− AB ∘ T = AB 0 T = AB 50 lb Tcosθ=50cos45 ∘ Tsinθ=50−50sin45 ∘ T T = x 50cos45= ∘ 50×0.7071=35.355 lb T = y 50(1−sin45)= ∘ 50(1−0.7071)=14.645 lb T= = T +T x 2 y 2 = 35.355+14.645 22 =1250+214.47 ≈ 1464.4738.27 lb T=38.3 lb TCD38.3 lb CD 1. Formula: From the geometric relationship of the cable segment , the vertical distance from the ceiling to pulley is related to the length and the angle by: 2. Substitution: First, find the angle from the components calculated in part (a): Given vertical distance : 3. Calculation: 4. Result: ● Final Conclusion: The length of cable required for static equilibrium is . ✨ Final Answer Summary (a) (b) Mecademy AI Solution · ENGProblem 3/28 CD hCL CD θ L = CD sinθ h θ tanθ= = T x T y =