Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_95

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The device shown in section can support the load at various heights by resetting the pawl in another tooth at the desired height on the fixed vertical column . Determine the distance at which the load should be positioned in order for the two rollers and to support equal forces. The weight of the device is negligible compared with . Problem 3/95 (a) Analysis of Forces and Geometry 1. Formula: Establish a coordinate system and identify force locations. Let the centerline of the vertical column be the -axis and the horizontal line passing through roller be the -axis. Roller is at . Roller is at . The pawl pivot is at . From the detail, the pivot is located to the right of the column's right face. Assuming the column is symmetric, the right face is at . Thus, . The pawl contact point is on the right face of the column, below the pivot: . The load acts at . 2. Substitution: Forces from the column on the device: Normal forces at rollers and : (given condition). Both act to the left ( direction) because the device must push against the column to support the overhanging load. Reaction from the pawl at pivot : Since the pawl is a two-force member, the reaction force is directed along the line . Its horizontal and vertical components are (to the right) and (upwards). 3. Calculation: LC Db AB L y Bx B(−7,0) A(−7,20) P(x ,8) P 2 in. x=7 in.x = P 7+2=9 in. C3 in. (7,5) Lx=b ABF = A F = B F −x P R C CP R Cx R Cy Horizontal equilibrium: Vertica