Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_106

⚡ Mecademy AIENG정역학 · ch6  Problem Statement (a) Determine the tension which the shipworkers must develop in the cable to lower the 100- kg crate at a slow steady speed. The effective coefficient of friction at the railing is . (b) What would be the value of in order to raise the crate? Problem 6/106 (a) Tension required to lower the crate To lower the crate at a steady speed, the motion of the cable is directed toward the crate. Therefore, the friction force on the cable exerted by the railing acts toward the workers, helping them hold back the weight. In this case, the tension at the crate end () is the larger tension (), and the tension at the worker end () is the smaller tension (). 1. Formula: The belt friction (capstan) equation is: For lowering, , where the crate tension is equal to its weight, . Rearranging for the worker tension : 2. Substitution: Mass of crate, Acceleration due to gravity, Weight, Coefficient of friction, Angle of wrap : Based on the diagram, the cable turns from vertical to horizontal, so . 3. Calculation: Exponent: T μ=0.20 T T T crate T 2 TT 1 T = 2 T e 1 μβ T = crate Te μβ W= m⋅gT T=We −μβ m=100 kg g= 9.81 m/s 2 W=100×9.81=981 N μ=0.20 β β=90= ∘ radians 2 π T=981×e −0.20× 2 π μβ=0.20×1.5708=0.31416 Exponential term: Final product: 4. Result: ● Final Conclusion: The tension required to lower the crate at a slow steady speed is . (b) Tension required to raise the crate To raise the crate at a steady speed, the motion of the cable is directed towa