Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_82

⚡ Mecademy AIENG정역학 · ch3 To solve for the tension in the wire and the reaction at hinge , we will model the uniform rectangular panel in a three-dimensional coordinate system and apply the equations of static equilibrium.  Problem Statement The uniform rectangular panel has a mass of and is hinged at its corners and to the fixed vertical surface. A wire from to keeps edges and horizontal. Hinge can support thrust along the hinge axis , whereas hinge supports force normal to the hinge axis only. Find the tension in the wire and the magnitude of the force supported by hinge . Problem 3/82 (a) Tension in the wire 1. Formula: We establish a coordinate system where the -axis is vertical along the hinge line , the -axis is horizontal along the wall, and the -axis is horizontal and perpendicular to the wall. The weight of the panel acts at its center of mass . For equilibrium, the sum of moments about the -axis at point must be zero: where is the -coordinate of point , is the vertical component of the tension, is the -coordinate of the center of mass, and . 2. Substitution: Mass , . Dimensions: , . Panel opening angle: . coordinates: . coordinates: . From the diagram, the wire is attached to on the vertical hinge axis (or is at an angle such that it provides the vertical support). Assuming the most standard configuration for this problem where the wire makes an angle of with the B ABCD40 kgA BEDBCAD AABB TB B T z AByx WG xA M = ∑ Ax 0=y T − Dz y W G y D yDT z y G yW=mg m=40 kgW=40