Meriam, Kraige & Bolton — Statics of Particles: Problem 2_120

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/120 The structure shown is constructed of circular rod which has a mass of 7 kg per meter of length. Determine the moment about caused by the weight of the structure. Find the magnitude of . Given: Mass per unit length: Acceleration due to gravity: Dimensions: Vertical segment: Horizontal segment parallel to -axis: Horizontal segment parallel to -axis: Final horizontal segment parallel to -axis: Problem 2/120 1. Weight per unit length calculation The weight of the rod per unit length () is calculated by multiplying the mass per unit length () by the acceleration due to gravity (): 2. Coordinate and Weight analysis of rod segments Based on the provided diagram, the origin is at the base of the vertical rod. The structure consists of four straight segments. We define their positions by the coordinates of their centers of gravity () and their weights (). By inspecting the axes, the horizontal segments extend in the negative and negative directions relative to the origin . Segment 1 (Vertical): M O O M O μ=7 kg/m g= 9.81 m/s 2 2 m x1.1 m y0.8 m x1.2 m w μg w=μ⋅g=7 kg/m⋅ 9.81 m/s= 2 68.67 N/m O CGW = i w⋅L i xy O Length: Weight: : Segment 2 (Parallel to ): Length: Weight: : Segment 3 (Parallel to ): Length: Weight: : Segment 4 (Parallel to ): Length: Weight: : 3. Calculation of Moment The moment of a weight force acting at position about the origin is given by: Summing the moments for all segments: : : (since all weight forces are pa