Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_14

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 50-kg wheel rolls on its hub up the circular incline under the action of the 12-kg cylinder attached to a cord around the rim. Determine the angle at which the wheel comes to rest, assuming that friction is sufficient to prevent slippage. What is the minimum coefficient of static friction which will permit this position to be reached with no slipping? Problem 6/14 (a) Determination of the angle ● Calculation Process 1. Present Final Formula: To find the equilibrium position, we sum the moments about the contact point between the wheel's hub and the circular track. This eliminates the unknown normal force and friction force. 2. Substitute Values: Let be the track radius, be the hub radius, and be the rim radius. The distance from the center of curvature to the wheel center is . Taking as the origin, the coordinates of are and the contact point is at . The horizontal distance from to the center of mass is: The cord is on the right side of the rim (radius ), so its horizontal position is . The horizontal distance from to the cord is: Summing moments about with gravity : θ θ B M = ∑ B 0 R=600 mm=0.6 mr = h 75 mm=0.075 mr = r 200 mm=0.2 m OGL= R−r= h 525 mm=0.525 mOG (Lsinθ,−Lcosθ)B(Rsinθ,−Rcosθ) BG d = w x − B x = G (R−L)sinθ=r sinθ h r r x = cord x + G r r B d = c x − cord x = B (Lsinθ+r )− r Rsinθ=r − r (R−L)sinθ=r − r Bg m g(d )− ww m g(d )= cc 0 50(75sinθ)−12(200−75sinθ)=0 3. Partial Operations: Expand the moment equation: Com