Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_84

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Determine the force required to (a) raise and (b) lower the 40-kg cylinder at a slow steady speed. The coefficient of friction between the cord and its supporting surface is 0.30. Problem 6/84 (a) Force required to raise the cylinder 1. Formula: The relationship between tensions in a belt/cord over a curved surface is given by the belt friction formula: where is the larger tension, is the smaller tension, is the coefficient of friction, and is the wrap angle in radians. To raise the cylinder, the force must overcome both the weight and the friction, so and . 2. Substitution: Mass Acceleration due to gravity Coefficient of friction Wrap angle from diagram: 3. Calculation: Calculate weight: Calculate exponent: Calculate friction factor: Final product: 4. Result: ● Final Conclusion: The force required to raise the 40-kg cylinder at a slow steady speed is . P P T = 2 T e 1 μβ T 2 T 1 μ βP T = 2 PT = 1 W=mg m=40 kg g= 9.81 m/s 2 μ=0.30 β=180= ∘ π rad P=(40×9.81)⋅e 0.30⋅π W=40×9.81=392.4 N μβ=0.30×π≈0.94248 e≈ 0.94248 2.5664 P=392.4×2.5664=1007.05 N P≈1007 N P 1007 N (b) Force required to lower the cylinder 1. Formula: When lowering the cylinder at a steady speed, the motion is impending in the direction of the weight. Therefore, the weight acts as the larger tension and the force acts as the smaller tension which controls the descent: 2. Substitution: Weight Coefficient of friction Wrap angle 3. Calculation: Use the previously calculat