Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_85

⚡ Mecademy AIENG정역학 · ch6  Problem Statement A dockworker adjusts a spring line (rope) which keeps a ship from drifting alongside a wharf. If he exerts a pull of 200 N on the rope, which has turns around the mooring bit, what force can he support? The coefficient of friction between the rope and the cast-steel mooring bit is 0.30. Problem 6/85 (a) Calculation of the supported force 1. Formula: The relationship between the tensions at the ends of a rope wrapped around a fixed curved surface is given by the belt friction equation: where: is the larger tension (the force being supported). is the smaller tension (the pull exerted by the worker). is the coefficient of static friction. is the total angle of wrap in radians. 2. Substitution: From the problem statement, we have: Worker's pull, Coefficient of friction, Number of turns, turns Angle of wrap, Substituting these into the formula: 3. Calculation: Calculate the exponent: Calculate the exponential factor: 1 4 1 T T T = 2 T e 1 μβ T 2 T T 1 μ β T = 1 200 N μ=0.30 n=1 = 4 1 1.25 β=n×2π=1.25×2π=2.5π rad T=200⋅e (0.30⋅2.5π) 0.30×2.5π=0.75π≈2.35619 rad e≈ 2.35619 10.5507 Final multiplication: 4. Result: ● Final Conclusion: The dockworker can support a maximum force of (or ) from the ship with a pull of . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 6/85 T=200×10.5507=2110.14 N T≈2110 N 2110 N 2.11 kN200 N T=2110 N