Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_147

⚡ Mecademy AIENG정역학 · ch5 To solve the problem of determining the height of the blimp, we will treat the mooring cable as a catenary under its own weight.  Problem Statement The blimp is moored to the ground winch in a gentle wind with 100 m of 12-mm cable which has a mass of 0.51 kg/m. A torque of 400 N·m on the drum is required to start winding in the cable. At this condition, the cable makes an angle of 30° with the vertical as it approaches the winch. Calculate the height H of the blimp. The diameter of the drum is 0.5 m. Problem 5/147 (a) Calculation of the height H of the blimp ● Calculation Process 1. Determine cable properties and tension at the winch: First, we calculate the weight per unit length of the cable, assuming standard gravity : The tension in the cable at the winch is derived from the torque and the drum radius : 2. Determine catenary parameters: The cable makes an angle of with the vertical, which corresponds to an angle with the horizontal at the winch: The horizontal component of the tension is constant for a catenary: The characteristic catenary parameter is then: H w g= 9.81 m/s 2 w=μg=0.51 kg/m× 9.81 m/s= 2 5.0031 N/m T 1 M r r= = 2 d = 2 0.5 m 0.25 m T = 1 = r M = 0.25 m 400 N⋅m 1600 N 30 ∘ φ 1 φ = 1 90− ∘ 30= ∘ 60 ∘ T 0 T = 0 T cosφ = 11 1600cos60= ∘ 1600×0.5=800 N c 3. Calculate intrinsic coordinates at the winch (point 1): We find the arc length from the lowest point of the imaginary catenary curve to the winch: The vertical distance from the ca