Determine (A) the tension in the cable (B) the reactions at A and B Please do not forget to include the free body diagram. ## Problem DescriptionA 240-kg uniform rectangular plate is supported in the position shown in the figure by hinges A and B and by a cable DCE that passes over a frictionless hook at C. Assume that the tension is the same in both parts of the cable and that hinge B does not exert any axial thrust.### Diagram ExplanationThe diagram illustrates a rectangular plate positioned horizontally. It is supported by two hinges, labeled A and B, which are attached to the underside of the plate. There is also a cable labeled DCE, creating tension support at three points: D, C, and E.### Dimensions and Positions- The plate is positioned within a 3D coordinate system with x, y, and z axes.- Length from hinge A to the edge of the plate in the z-direction is 90 mm.- Total length in the x-direction from C to the end of the plate is 690 mm.- The plate extends 90 mm from hinge B to its edge in the z-direction.- Cable DCE distances: - CD is 450 mm from point A. - CE is 675 mm in the x-direction from point A.- Cable positions: - D is directly above the plate, 960 mm from AC in the x-direction. - E is also above the plate, 675 mm from AB in the x-direction.### TaskDraw the free-body diagram required to determine the tension in the cable. Note that the cable DCE acts as a single cable.### Key Considerations- Center of mass located at the center of the plate, given it's a uniform rectangular plate.- Since points D, C, and E are connected by a cable, the tension throughout the cable is consistent.- Assume that hinge B exerts no axial thrust, simplifying calculation of forces. This problem requires understanding moments, forces, and equilibrium in three dimensions, as well as interpreting spatial diagrams for mechanical systems.

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Answered: A 240-kg uniform rectangular plate is…

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