Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_61

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The uniform rectangular plate of mass is suspended by three cables. Determine the tension in each cable. Problem 3/61 (a) Tension in Cable AD ● Calculation Process 1. Present Final Formula: From the equilibrium of the plate, the vertical component of the tension at is determined by moment equilibrium about the edges in contact with the walls. Assuming the plate is horizontal and resting against the smooth vertical walls, we find the vertical components . The total tension is given by: 2. Substitute Values: The vertical components are found by solving the following system of equilibrium equations (derived from moments about the and axes and force balance in ): Solving this system yields: The geometry of cable from to gives: m A T ,T ,T AzBzCz T = A T ⋅ Az Δz AD L AD xy z M =∑ y-axis 0⇒0.8T + Az 0.8T = Bz 0.4mg M =∑ x-axis 0⇒0.8T + Bz 0.5T = Cz 0.4mg F =∑ z 0⇒T + Az T + Bz T = Cz mg T = Az 0.3125mg= m g 16 5 ADA(0.8,0,0)D(0.3,0,0.8) L = AD = (0.3−0.8)+(0−0)+(0.8−0) 222 = 0.5+0.8 22 0.8 Δz = AD 0.8 m Substituting into the tension formula: 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The tension in cable is . (b) Tension in Cable BE ● Calculation Process 1. Present Final Formula: 2. Substitute Values: From the previous system of equations: The geometry of cable from to gives: Substituting: T = A 0.3125mg⋅ 0.8 0.89 = 0.8 0.3125 0.390625= 64 25 T = A m g = 64 25 0.89 ⋅ 64 25 m g = 10 89 m g 128 5 89 T ≈ A 0.3125⋅1.17