Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_68

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the tension T in the cable to raise the 800-kg load if the coefficient of friction for the 30-mm bearing is 0.25. Also find the tension in the stationary section of the cable. The mass of the cable and pulley is small and may be neglected. Problem 6/68 (a) Tension T in the cable to raise the load 1. Formula: To raise the load at a steady speed, the pulley must rotate. The tension must overcome both the load and the friction torque at the bearing. The equations for a movable pulley with journal friction are: where is the pulley radius and is the friction circle radius with . Combining these gives: 2. Substitution: Substitute the given values: Mass , gravity Pulley radius Bearing radius Friction angle Friction circle radius 3. Calculation: T 0 T W=m⋅g T+T = 0 W (T−T )R= 0 M = f W⋅r f Rr = f rsinφφ= tanμ −1 T= 1+ 2 W ( R r f ) m=800 kgg= 9.81 m/s⟹ 2 W=800×9.81= 7848 N R= = 2 300 150 mm r= = 2 30 15 mm φ=tan(0.25)≈ −1 14.036 ∘ r = f 15sin(14.036) mm ∘ T= 1+ 2 7848 ( 150 15sin(tan0.25) −1 ) Calculate : Calculate the friction ratio: Calculate : 4. Result: ● Final Conclusion: The tension required to raise the load is . (b) Tension in the stationary section 1. Formula: Using the force equilibrium equation derived in the previous step: 2. Substitution: Substitute the previously calculated values: 3. Calculation: 4. Result: ● Final Conclusion: The tension in the stationary section of the cable is . ✨ Final Answer Summary (a) (b) M