Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_125

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 100-kg load is elevated by the cable which slides over the fixed drum with a coefficient of friction of 0.50. The cable is secured to the slider which is pulled slowly along its smooth horizontal guide bar by the force . Plot as a function of from to and determine its maximum value along with the corresponding angle . Check your plotted value of analytically. Problem 6/125 (a) Determination of Maximum Value and Corresponding Angle 1. Formula: The system involves a cable over a fixed drum (belt friction) and a slider in equilibrium. Weight of the load: Belt friction relationship: , where is the pulling tension, is the load tension, is the coefficient of friction, and is the wrap angle. From the geometry, the wrap angle from the vertical load to the inclined cable at angle with the horizontal is (in radians). Equilibrium of slider in the horizontal direction: . Substituting : 2. Substitution: Substitute given values: , , . 3. Calculation: Evaluate at key points within the range : At : , . A PPθθ=90 ∘ θ=10 ∘ θ P max P max θ W=m⋅g T = 1 T ⋅ 2 e μβ T 1 T = 2 Wμβ β θβ= + 2 π θ AP=T cosθ 1 T 1 P(θ)=W⋅e cos θ μ +θ ( 2 π ) m=100 kgg= 9.81 m/s 2 μ= 0.50 W=100×9.81=981 N P(θ)=981⋅e cos θ ( θ in radians for the exponent) 0.50 +θ ( 2 π ) P90≥ ∘ θ≥10 ∘ θ=90= ∘ π/2 radβ=πP=981⋅e⋅ 0.5π cos(90)= ∘ 0 N At : , . To find the maximum, we evaluate the function and find it peaks near . At : . . 4. Result: , . ● Final Conclusion: The force starts at